Brenda Laca

Introduction

This paper is mainly concerned with the uses of the subjunctive in Modern Spanish (section 3). 1 Section 2 gives a brief sketch of those aspects of the temporal-aspectual system of Spanish that constitute a necessary background for the interpretation of subjunctive forms. Section 4 briefly describes the conditional, which exhibits very close links to some subjunctive forms. The imperative mood is discussed in the subsection devoted to the subjunctive in root contexts (3.3.4).

The temporal-aspectual system of Spanish

The neo-Reichenbachian system proposed by Demirdache & Uribe-Etxeberria (2007) proves particularly useful for representing the tense-aspect system of Spanish. In this system, tense is modelled as a relation between the time of evaluation (Ast-T, a direct descendant of the Reichenbachian R understood as an interval) and a highest anchor, which is normally the time of speech (Utt-T) in matrix contexts. Possible relations are anteriority (anchor after anchored), inclusion or coincidence, and posteriority (anchor before anchored). These relations are replicated for aspect, which expresses a relation between the time of the event (Ev-T) and Ast-T. The analysis I propose for Spanish is summarized in Table 1. Tenses are illustrated with the 1 st Pers. Sing. of the verb cantar 'sing', aspects with aspectualized infinitival forms. Table 1 : Tense and grammatical aspect in Spanish I assume that aspect is not expressed by simple tenses in Spanish, with the notable exception of the preterite, which is a perfective tense requiring that Ast-T includes Ev-T [START_REF] Laca | Périphrases aspectuelles et temps grammatical dans les langues romanes[END_REF]. All other simple forms leave the relation between Ast-T and Ev-T unspecified and are in this sense "aspectually neutral" [START_REF] Smith | The parameter of aspect[END_REF][START_REF] Reyle | Ups and downs in the theory of temporal reference[END_REF], Schaden 2007: Chap.3). "Aspectually neutral" forms are not totally unconstrained, but whatever preferences they exhibit result (a) from polarisation effects due to the existence of an aspectually marked competing form -thus, an imperfect will strongly prefer imperfective interpretations in the contexts in which it contrasts with the preterite, a simple future will prefer perfective interpretations by contrast with a progressive future [START_REF] Laca | Périphrases aspectuelles et temps grammatical dans les langues romanes[END_REF]; (b) from the temporal structure of the eventuality description, according to a very general pattern which essentially excludes imperfective interpretations of bona-fide telic descriptions (Demirdache & Uribe-Etxeberria 2007).

Deictic and anaphoric (or zero) tenses are distinguished by supposing that the latter do not have Utt-T, but an interval not identical with Utt-T, dubbed here Tx, as anchor. The notion of anaphoric tense used here is very restrictive, in that this anchor can only be provided by an embedding predicate of propositional attitude: in the sense used here, an anaphoric tense can only appear in reported speech or reported thought contexts. The introduction of Tx in the system 2 is designed to provide a unified interpretation of forms exhibiting imperfect morphology (the imperfect itself, as well as the pluperfect and the conditional) and to solve the well known problem posed by perfect conditional forms (habría cantado 'would have sung') without assuming a third layer of temporal relations next to Tense and Aspect. It can also prove useful in accounting for the fact that such forms consistently develop counterfactual uses. The splitting of the imperfect into two uses, a bona fide past tense and an anaphoric "present of the past", is justified by the behavior of the imperfect with modal verbs -a point that cannot be developed here.

Aspect is explicitly expressed in Spanish by a set of periphrastic combinations exhibiting a characteristic behavior [START_REF] Laca | Périphrases aspectuelles et temps grammatical dans les langues romanes[END_REF]. Periphrastic combinations formed with haber + PP are uniformly treated as compound or perfect tenses (perfect, pluperfect, future and conditional perfect) in the Spanish grammatical tradition, and carry the main bulk of the expression of secondary anteriority relations. The Spanish progressive shows a very similar distribution to that of the English progressive, and the prospective closely parallels the English be-going-to-construction.

The subjunctive

Subjunctive morphology

In Modern Spanish, the subjunctive exhibits two simple forms, the present and the imperfect, as well as two compound forms, the perfect and the pluperfect. The present is built on the present stem of the verb by a change of the thematic vowel, a > e for verbs of the first conjugation class and e/i > a for verbs of the second and third classes. To the exception of a handful of irregular cases, the stem normally appears in the form it takes in the 1 st pers. sing. present indicative. The imperfect is built on the preterite/perfect stem (the one of preterite indicative), and exhibits the peculiarity of having two distinct markers, -ra-and -se-, which are traditionally held to be in allomorphic variation. Person marking corresponds to the general pattern of the language, with -∅ for 1 st and 3 rd pers. sing., -s for 2 nd pers. sing., -mos for 1 st pers. pl., -is for 2 nd pers. pl., and -n for 3 rd pers. pl [START_REF] Boyé | The structure of allomorphy in Spanish verbal inflection[END_REF]. Compound forms are built with the past participle and the auxiliary haber, which appears in the present subjunctive in the formation of the perfect (haya cantado), and in the imperfect subjunctive in the pluperfect (hubiera/ hubiese cantado).

The set of forms of the subjunctive is radically reduced in comparison to that of the indicative on account of the lack of a perfective/imperfective (neutral) contrast in the past forms, on the one hand, and of the lack of a present/future contrast on the other. Medieval and Classical Spanish had a form for the future subjunctive. Built on the preterite/perfect stem with the marker -re-(cantare/ quisiere/ saliere), this simple form was flanked by a corresponding compound form with haber in the future subjunctive (hubiere cantado). Although surviving in some set expressions (sea como fuere 'be as it may'), in juridical language, and possibly in some reduced dialectal areas, future subjunctive forms seem to have disappeared from general usage as far back as the 18 th century [START_REF] Ridruejo | ¿Cambios iterados en el subjuntivo español?[END_REF][START_REF] Camus Bergareche | El futuro de subjuntivo en español[END_REF][START_REF] Eberenz | Sea como fuere. En torno a la historia del futuro de subjuntivo español[END_REF]/1990).

A comparison with the original Latin subjunctive paradigm shows that the main differences are directly or indirectly related to the loss of a conjugation system based on the contrast between infectum and perfectum and to the concomitant generalization of compound forms for perfects. The main reinterpretation processes are the following: (i) the Latin pluperfect subjunctive is reinterpreted as a general past (imperfect) subjunctive (canta(vi)sse > cantase).

(ii) the Latin perfect subjunctive conflates with the Latin future perfect indicative to give the form of the future subjunctive (canta(ve)rim/ canta(ve)ro > cantare). The resulting form is indistinguishable from the Latin imperfect subjunctive for all verbs lacking a perfect stem form distinct from the present stem (cantare(m)), so that the latter can be held either to have been entirely given up or to have concurred in the formation of the future subjunctive [START_REF] Ridruejo | ¿Cambios iterados en el subjuntivo español?[END_REF]). (iii) the Latin pluperfect indicative is reinterpreted as a subjunctive form (canta(ve)ram > cantara), and ends up being largely equivalent to the imperfect subjunctive arisen from the Latin perfect subjunctive. This process sets on in Medieval Spanish and stretches well into the contemporary language. The details of this semantic development are extremely complex, though clearly linked to a cross-linguistically widespread phenomenon which consists in exploiting past morphology for the expression of counterfactuality [START_REF] Ridruejo | ¿Cambios iterados en el subjuntivo español?[END_REF][START_REF] Iatridou | The grammatical ingredients of counterfactuality[END_REF]. In contemporary language, the -ra-form preserves some of its etymological uses in contexts from which the -se-form is excluded, most notably as a pluperfect or preterite indicative in subordinate clauses, and with the modals deber 'must', poder 'can', and querer 'wish' in independent clauses. It tends to fully replace the -se-form for the expression of the imperfect subjunctive in a large number of regional, specially American varieties.

Although lacking any direct impact on the stock of subjunctive forms, the emergence of a conditional in Romance -together with changes in the uses of the imperfect indicativehas profoundly affected the distribution and interpretation of the subjunctive.

Temporal and aspectual relations

The comparatively poor stock of subjunctive forms and the fact that the subjunctive is a dependent mood appearing mainly in sequence-of-tense contexts have given rise to a debate as to the temporal interpretation of subjunctive forms. This debate concentrates on the contrast between the present and the imperfect subjunctive and is formulated in the generative tradition as a question concerning the existence of an independent Tense feature in subjunctive clauses. The issue carries over to the contrast between the compound forms of the subjunctive: although both convey a secondary anteriority relation, they contrast as to the possible highest anchors for this relation. On the basis of the distribution in (1a-b), [START_REF] Picallo | El nudo FLEX y el parámetro de sujeto nulo[END_REF][START_REF] Picallo | El nudo FLEX y el parámetro de sujeto nulo[END_REF]) has argued that subjunctive clauses lack independent Tense, and that subjunctive forms are selected via a necessary anaphoric link with the temporal features of the matrix sentence, in such a way that a PAST in the matrix determines an imperfect/pluperfect subjunctive, whereas a NON-PAST in the matrix determines a present/perfect subjunctive: This claim has been challenged on a number of grounds. Strict temporal selection holds only in a restricted type of contexts, particularly those involving subjunctive selection by a forward-shifting predicate 3 or in causative constructions, and subjunctive licensing in subject clauses of copular sentences. Even in these contexts, it often takes the form of a constraint banning certain crossed combinations, but not others. Thus, forward-shifting predicates exclude an imperfect subjunctive under a matrix NON-PAST (2c), but allow a present subjunctive under a matrix PAST (2b), whereas copular sentences allow an imperfect subjunctive under a matrix NON-PAST (3b), but exclude a present subjunctive under a matrix PAST (3c) (for further details, see [START_REF] Suñer | Concordancia temporal y subjuntivo[END_REF]/1990[START_REF] Kempchinsky | Más sobre el efecto de referencia disjunta del subjuntivo[END_REF][START_REF] Quer | Mood at the interface[END_REF] The conclusion seems thus inescapable that subjunctive forms make a temporal contribution of their own: what appears as strict temporal selection is a result of the interaction between the semantic properties of the context and this temporal contribution.

1 a.
The interpretation of the PAST / NON-PAST combinations in (2b) and (3b) offers an immediate clue as to what this contribution is. ( 2b) is an instance of a double access configuration, in which the time of the subordinate clause is calculated with Utt-Time as anchor [START_REF] Kempchinsky | Más sobre el efecto de referencia disjunta del subjuntivo[END_REF]): the requested arrival must follow Utt-Time. On the other hand, (3b) contrasts with (3c): the arrival must precede the time of epistemic evaluation in (3b), which reports present epistemic uncertainty about an already settled matter, whereas it follows the time of evaluation in (3c), which reports past metaphysical uncertainty about a matter not yet settled at that time. I would like to suggest that the contrast between the present and the imperfect subjunctive parallels that between the corresponding indicative tenses. The present is a deictic tense, always anchored with regard to Utt-Time. The imperfect can be an anaphoric tense, taking Tx as anchor ("present of the past"), but it can also have a deictic interpretation, in which case it signals anteriority with regard to Utt-Time. This latter interpretation becomes prominent whenever the matrix context does not provide a past temporal anchor, i.e. a suitable Tx.

The temporal contrast between the present and the imperfect subjunctive is somewhat obscured by the fact that the latter gives rise to interpretations in which the event time is simultaneous or forward-shifted with regard to Utt-T. The imperfect subjunctive cannot be understood either as a deictic past or as an anaphoric "present of the past" in main clauses expressing wishes (with ojalá as a licensing adverb), nor in the antecedent of conditionals. It does not contrast in temporal location with the present subjunctive or with the present indicative, respectively: 5 a. Ojalá estuvieran/ estén en casa. hopefully be.IMPF.SBJ.3PL /be.PRS.SBJ.3PL in house 'I wish they were/ I hope they are at home' b. Si estuvieran/ están en casa... if be.IMPF.SBJ.3PL /be.PRS.IND.3PL in house 'If they were/ are at home... Such cases can be assimilated to the numerous instances of past tenses being used for signaling counterfactuality or non-realistic modal bases (see [START_REF] Iatridou | The grammatical ingredients of counterfactuality[END_REF]. 4 By contrast with the present subjunctive resp. indicative versions, which only indicate epistemic uncertainty, in the imperfect subjunctive versions the world of evaluation w0 is assumed not to be a world in which they are at home in (5a-b). In fact, counterfactual uses of the imperfect subjunctive rather reinforce the analogy with the imperfect indicative, which in some so-called modal uses locates event-time simultaneouly or subsequently to Utt-T, but does not locate it in the world of evaluation: 6

Yo que tú no se lo contaba. I that you not him/her it tell IMPF.IND.1SG 'If I were you, I wouldn't tell him/her'

The simple forms of the subjunctive are aspectually neutral. The compound forms convey an anteriority relationship whose highest anchor can be Utt-T in the case of the perfect subjunctive, and is normally a Tx preceding Utt-T in the case of the pluperfect: The subjunctive is compatible with the periphrastic expression of prospective aspect, but prospective subjunctives are excluded in forward-shifting matrix contexts such as volitionals and directives. To sum up, the temporal-aspectual organization of the subjunctive does not differ radically from that of the indicative. It has a deictic form indicating coincidence with Utt-T, the present, and a form that can function anaphorically, indicating coincidence with Tx, or deictically, indicating precedence with regard to Utt-T, the imperfect. This latter form is exploited for counterfactual uses, signaling coincidence with Utt-T in a "world history" different from w0. Forms indicating coincidence regularly give rise to forward-shifted readings, sometimes as a function of the forward-shifting properties of the matrix context, but often simply as a result of the type of eventuality described in the clause. Compound forms indicate a secondary anteriority relation. When the highest anchor for this secondary anteriority relationship is Utt-T, the perfect subjunctive is very close to a deictically functioning imperfect subjunctive.

The meaning and uses of the subjunctive

General semantic characterizations of mood are notoriously difficult. The subjunctive is clearly an expression of modality, in as far as all its uses involve consideration of sets of alternative possible worlds, i.e. non totally realistic modal bases. However, this characterization captures a necessary, but not a sufficient condition for subjunctive use. Whereas the indicative corresponds to the default mood, appearing in main assertions, but also in questions and in a number of dependent clauses, the subjunctive is a dependent mood, which is subject to specific licensing conditions. This does not mean that the subjunctive is restricted to subordinate clauses, although the widest array of its uses does involve syntactic subordination. We will first discuss the subjunctive in dependent clauses and then the subjunctive in root contexts.

Argument clauses

Two distinctions have proven particularly useful when describing uses of the subjunctive. The first opposes intensional contexts to polarity contexts [START_REF] Quer | Mood at the interface[END_REF]) as subjunctive licensors. In intensional contexts, the subjunctive is triggered by the lexical properties of a predicate, which can be a verb, but also an adjective or a noun: 9

Quiere que hablen de él. want.PRS.IND.3SG that talk.PRS.SBJ.3PL of him 'He wants people to talk about him'

In polarity contexts, it is essentially a negation in the matrix context that licenses a subjunctive which would be otherwise excluded.

10

Nunca dijo que estuviera enfermo. never say PRT.IND.3SG that be IMPF.SBJ.3SG ill 'S/he never said that he was ill'

The second, more traditional distinction, opposes contexts of rigid subjunctive selection to contexts in which mood alternation is possible. Thus, the subjunctive is the only possible option in ( 9) whereas (10) also admits the indicative. However, the two distinctions do not overlap: (11a-c) show cases of mood alternation for "intensional" subjunctives. 'S/he consented not to be paid/ admitted that s/he was not being paid'

The clear meaning differences between the subjunctive and the indicative versions in (11a-c) give precious clues as to the semantic contribution of the subjunctive. In (11a), the subjunctive version reports a directive speech act, whereas the indicative version reports a statement of fact. This sort of contrast extends to a large class of verbs of communication. In (11b), the indicative version asserts that the subject of the main verb checked a fact. The subjunctive version signals that the subject has a vested interest in this fact, and has possibly contributed to its coming about, for instance by closing the door herself. Finally, in (11c), the indicative version conveys acknowledgement of the truth of the propositional content of the object clause, whereas the subjunctive version indicates acquiescense or agreement with a suggestion. What is common to all the subjunctive versions is (a) an "element of will" on the side of the subject of the propositional attitude verb as to the coming about of the state of affairs described in the subordinate clause, and (b) the fact that the subject is involved as a causal factor that can possibly favor or prevent this coming about. Bouletic modality and causation are involved in most cases of rigid subjunctive selection, 5 namely with volitionals, as in (9), and with directives, implicatives, and causatives (12). Note that the latter two cases assert the truth of the propositional content of the subjunctive clause, thus infirming the widely held view that the subjunctive signals lack of assertion: However, some emotive-factive predicates exhibit uses as verbs of communication. They report speech acts which convey at the same time the assertion of a fact and an evaluation of this fact by the subject of the propositional attitude. In such uses, they lose their factive status, in as far as they do not presuppose the truth of their complement, and they occasionally give rise to mood alternation:

15

Se lamenta -injustificadamente-de que nadie REFL complain PRS.IND.3SG unjustifiedly of that nobody lo comprende/ comprenda. him understand.PRS.IND.3SG/ understand.PRS.SBJ.3SG 'He unjustifiedly complains about not being understood by anybody' Mood alternation is sensitive, in such contexts, to the foregrounding of the propositional content of the subjunctive clause (indicative) or of the emotive-factive predicate (subjunctive), as shown by the fact that the focus of pseudo-cleft structures allows the indicative even in the absence of reported-speech readings [START_REF] Quer | Mood at the interface[END_REF][START_REF] Grae | /to appear. Nueva gramática de la lengua española[END_REF] As argued by [START_REF] Quer | Mood at the interface[END_REF], the causation component in the semantics of emotivefactive predicates is a decisive factor in mood selection. At the same time, these predicates convey the (positive or negative) evaluation of a fact on the side of the Experiencer. Evaluative predicates constitute another major class of subjunctive selectors. They include a couple of verbs such as bastar'suffice', convenir'be advisable', urgir'be urgent', and a large class of adjectives and nouns, as well as the adverbs bien 'well, right, proper' and mal 'bad, unfair, inappropriate' [START_REF] Grae | /to appear. Nueva gramática de la lengua española[END_REF] The subjunctive is triggered whenever the propositional content of the argument clause is not merely asserted, but located in a space of possibilities. This is the case with modal predicates expressing epistemic or metaphysical possibility or necessity, but also with predicates expressing frequency and with those expressing falsity:

18

Es probable/ usual/ erróneo. be.PRS.IND.3SG likely/ usual/ mistaken que surjan conflictos. that arise.PRS.SBJ.3PL conflicts 'It is likely/ usual/ false that conflicts (should) ensue' Among predicates of propositions, only those that are equivalent to the assertion of the proposition, as for example es verdad/ cierto/ exacto/ seguro 'it is true/ correct/ exact/ sure', consistently select the indicative mood. Note that with modal predicates, the truth of the subjunctive proposition may be entailed in some cases. Together with the implicative subjunctive triggers mentioned above (12), this fact casts some doubt on the role of nonveridicality [START_REF] Giannakidou | The Landscape of Polarity Items[END_REF] in the distribution of the subjunctive.

To sum up, subjunctive triggering in intensional contexts is intimately related to the notions of causation and evaluation. Mood selection is usually rigid in such contexts, which is probably an indication of the fact that argument clauses in such configurations cannot escape the scope of the selecting predicate. Note that the more complex scope configurations involved in pseudo-clefts, possibly disrupting subordination, permit the indicative, as in ( 16) above, and that when causal relations do not involve the embedding of an argument clause, no subjunctive is licensed ( 19a-b Possible subjunctive licensors include first and foremost sentential negation, but also nonupward entailing environments, such as contexts containing downward-entailing elements, questions and conditional antecedents [START_REF] Ridruejo | Modo y modalidad. El modo en las subordinadas sustantivas[END_REF][START_REF] Grae | /to appear. Nueva gramática de la lengua española[END_REF] This can be taken to mean that indicative clauses in polarity contexts convey the speaker's endorsement of the truth of the complement. The indicative version of ( 21), in which subject of belief and speaker coincide, seems to report contradictory beliefs. By contrast, the subjunctive in polarity contexts does not convey any attitude of the speaker as to the truth of the complement clause: it indicates that the complement clause is under the scope of the propositional attitude verb and the operator affecting it.

This scopal dependency of the subjunctive -contrasting with the outscoping effects of the indicative-is further confirmed by the fact that polarity contexts license negative polarity items in subjunctive, but not in indicative complement clauses [START_REF] Bosque | Las bases gramaticales de la alternancia modal[END_REF]

Relative clauses

As stated above, in polarity contexts the subjunctive indicates that the clause containing it is in the scope of the licensing context. Mood alternation in relative clauses follows an analogous interpretive pattern. The descriptive content of an indicative relative is evaluated in w0 (the world in which non-modalized assertions are evaluated). By contrast, the descriptive content of a subjunctive relative is evaluated in a non-totally realistic modal base contributed by an intensional environment. This explains the well known fact that noun phrases containing subjunctive relatives are typically interpreted non-specifically (23a) or attributively (23b): a. Pidieron un libro que fuera fácil de leer. ask. PRT.IND.3PL a book that be.IMPF.SBJ.3SG easy of read.INF 'They asked for a book that was easy to read' b. Le dieron un libro a cada cliente que him give.PRT.IND.3PL a book to every customer that hubiera gastado más de 10 euros. have. IMPF.SBJ.3SG spend.PP more of 10 euros 'They gave a book to any customer having spent over 10 euros' Non-specific relatives do not entail the existence in w0 of an object verifying the description. Attributive relatives are characterized by the fact that the link between the content of the nominal description and the property denoted by the rest of the sentence is a law-like one, grounded in generalizations that extend to counterfactual cases and usually involve causality.

Mood alternation is excluded in appositive relatives. Since these constitute independent subsidiary assertions, they only take the indicative [START_REF] Ridruejo | Modo y modalidad. El modo en las subordinadas sustantivas[END_REF]). 6 The licensing environments for subjunctive relatives share, to a certain extent, the properties of the environments licensing subjunctive argument clauses. As a matter of fact, restrictive relatives contained in subjunctive argument clauses admit themselves the subjunctive [START_REF] Grae | /to appear. Nueva gramática de la lengua española[END_REF] As for subjunctive relatives not contained in subjunctive clausal environments, they are excluded in contexts involving totally realistic modal bases (25a), and they are licensed in modal environments such as those involving bouletic modality (25b), but also in those containing modal verbs (25c), future tense or prospective aspect, or exhibiting a habitual/generic interpretation [START_REF] Quer | Mood at the interface[END_REF][START_REF] Grae | /to appear. Nueva gramática de la lengua española[END_REF] The problem is that, in relative clauses, the subjunctive itself can be the only overt element triggering a non-totally realistic interpretation of the environment. Usually, unexpected subjunctives are linked to the possibility of establishing an intentional link between the will of an agent and the descriptive content of the noun phrase, and are thus assimilable to bouletic modality. This is particularly clear in the case of so-called "purpose relatives" exemplified in (26) [START_REF] Ridruejo | Modo y modalidad. El modo en las subordinadas sustantivas[END_REF]), but also extends to subtler cases:

26

Hicieron un cobertizo build PRT.IND.3PL a shed que los protegiera de la lluvia. that them protect IMPF.SBJ.3SG of the rain 'They built a shed as a protection against the rain' Note that such cases are analogous to subjunctive-triggering with implicative verbs, in as far as entailments of existence are not suspended by the subjunctive, which only adds a forwardshifting element of will.

Although we have exemplified subjunctive relatives mainly in indefinite nounphrases, all determiners, to the notable exception of demonstratives, are compatible with subjunctive relatives [START_REF] Quer | Mood at the interface[END_REF]. Occasional difficulties with the definite article should probably be attributed to a mismatch between the presuppositions of the article and the descriptive content of the noun phrase. Semantic definites -those in which the unicity presupposition is guaranteed by the descriptive content of the noun phrase, such as superlatives or descriptions containing ordinals-pose no problem for the subjunctive [START_REF] Ridruejo | Modo y modalidad. El modo en las subordinadas sustantivas[END_REF]):

27

Iban a comprar el libro go.IMPF.IND.3PL to buy.INF the book que contuviera #(más) ilustraciones. that contain IMPF.SBJ.3SG more illustrations ' They were going to buy the book with the greatest number of illustrations' Bare plurals (28), but also count singular algún 'some', free choice items, and negative indefinites strongly favor subjunctive relatives [START_REF] Quer | Mood at the interface[END_REF]). In the first case, this is a consequence of the scopal dependency of bare plurals; in the other cases, scopal dependency is reinforced by the fact that the items in question require licensors roughly corresponding to those required by the subjunctive:

28

Buscan libros que search.PRS.IND.3PL books that ??contienen/ contengan ilustraciones. contain.PRS.IND.3PL /contain PRS.SBJ.3PL illustrations 'They are looking for books containing illustrations' Free relatives also clearly favor the subjunctive, possibly as a consequence of the tendency to interpret them attributively and of their proximity to free-choice items [START_REF] Giannakidou | The Landscape of Polarity Items[END_REF][START_REF] Quer | Mood at the interface[END_REF] To sum up, relatives clauses exhibit mood alternation. The subjunctive requires that the descriptive content of the clause be evaluated in a non-totally realistic modal base, which is more often than not guaranteed by its dependence from an intensional context and gives rise to non-specific or attributive readings for the NP containing it.

Adverbial and/or adjunct clauses

Due to space limitations, only information concerning some prominent types of subjunctive adverbial/adjunct clauses and some limited types of mood alternation will be given in this section. Subjunctive use in these contexts is sensitive to roughly the same type of semantic factors we have been discussing. Thus, for instance, purpose clauses (30a), which involve bouletic modality, and clauses negating concomitance (30b), in which the proposition expressed is necessarily under the scope of the negative sin 'without', take the subjunctive. Both types of interclausal relations are expressed by a preposition governing a complement clause (GRAE 2008): 7 30 a. Lo hice para que se enterara. it do.PRT.IND.1SG for that REFL inform.IMPF.SBJ.3SG 'I did it so that he would notice it' b. Lo hice sin que se enterara.

it do.PRT.IND.1SG without that REFL inform.IMPF.SBJ.3SG 'I did it without his noticing it' Modern Spanish exhibits the peculiarity that all forward shifted temporal clauseswhose time of evaluation is ordered after the highest anchor Utt-T or Tx -take the subjunctive. This holds of temporal clauses introduced by any syntactic type of subordinating expression, and expressing simultaneity, posteriority or anteriority:

31

Cuando llegue, se lo decimos. when arrive. PRS.SBJ.3SG him/her it tell.PRS.IND.1PL 'When s/he arrives, we'll tell him/her' Some authors classify these uses of the subjunctive as "suppletive" future tenses, but the assumption of a "different" subjunctive seems unwarranted. Furthermore, before-temporal clauses always take the subjunctive (i.e., not only when they are forwardshifted), whereas after-temporal clauses only take it in European Spanish [START_REF] Grae | /to appear. Nueva gramática de la lengua española[END_REF].

Conditional antecedents and subjunctive concessive clauses figure prominently among the contexts in which the temporal contrast between present and imperfect subjunctive forms is reinterpreted, with imperfect subjunctive forms being used for the expression of nonrealistic modal bases. Thus, both (32a-b) and (33a-b) locate the time of the subordinate after resp. before Utt-T. But (32b) The factors linked to the presence of the subjunctive in main clauses parallel those we find in dependent clauses, in as far as they involve evaluation with regard to non-totally realistic modal bases.

The conditional

The verbal form built on the infinitive/future stem by adding to it the desinences of the imperfect (cantar-ía/ habr-ía cantado) is predominantly classified as a temporal form of the indicative mood. It is not surprising that it should have modal uses: the future and imperfect indicative are known to exhibit a number of modal uses, which clearly predominate over temporal uses in the case of the former, so that it is only to be expected that a form combining the morphology of both tenses will have a still more pronounced modal profile. I would like to suggest, however, that there are good reasons for assuming a split in uses of this form, with some of them corresponding to a tense ("future of the past" and, more interestingly, "past of the future"), and others constituting the mood of choice when non-realistic modal bases are involved, i.e. when w0 is excluded from the domain of quantification in a modal environment.

In "future of the past" uses, the conditional behaves as a strictly anaphoric tense: it requires a past anchor contributed by a verb of thinking or speaking (41a), which may be implicit in free indirect speech contexts and in so called quotative or evidential uses of the conditional [START_REF] Squartini | The internal structure of evidentiality in Romance[END_REF] What I'd like to label "past of the future" readings are practically equivalent to future perfects in contexts expressing a conjecture [START_REF] Squartini | The internal structure of evidentiality in Romance[END_REF]. Spanish makes abundant use of future morphology for indicating that the propositional content is advanced as a possibility, and not as an unqualified assertion. If the propositional content concerns a time preceding Utt-T, anteriority can be expressed by the future perfect, but also by the conditional:

42

No vino a la fiesta. What the semantics of conditionals, want-verbs, and modals have in common is the fact that they require consideration of non-totally realistic modal bases. It is thus natural to assume that "conditional mood" requires sets of alternative worlds to operate on. To judge from its effects in conditional sentences, what it does in such contexts is to exclude the world of evaluation from the domain of quantification, signaling that w0 does not belong to the modal base. The non-totally realistic modal base contributed by the modal element on which the conditional is grafted becomes a non-realistic modal base. When talking about the past -by means of perfect morphology on the conditional or on an embedded infinitive-non-realistic modal bases result in clearly counterfactual interpretations involving non-realized possibilities or unfulfilled wishes: "Conditional mood" -by contrast with the temporal conditional-is a counterfactual form. As such, it interferes in a number of contexts with imperfect and pluperfect subjunctives, which have been shown to exhibit counterfactual interpretations. As stated above, pluperfect subjunctives compete with perfect conditionals in the consequent of past counterfactuals. The same competition exists with modals and with verbs of wish. This connection is reinforced by the use of the imperfect subjunctive in root clauses containing the modals poder, querer and deber.

Notes

1 I am greatly indebted to Ignacio Bosque (GRAE, Madrid). The materials and analyses proposed in GRAE (2008/ to appear) have profoundly influenced my views on the Spanish subjunctive. I gratefully acknowledge the support by the Fédération Typologie et Universaux CNRS for the programm Temporalité: typologie et acquisition.

2 A temporal anchor different from Utt-T, labelled Tx, is introduced, albeit with different characterizations, by [START_REF] Giorgi | Tense and aspect. From semantics to morphosyntax[END_REF] and by [START_REF] Iatridou | The grammatical ingredients of counterfactuality[END_REF]. Adoption of Tx could lead to a more precise formulation of the intuition regarding "inactual" tenses on which [START_REF] Coseriu | Das romanische Verbalsystem[END_REF] based his analysis of the Romance verbal system.

3 Forward-shifting predicates are characterized by the fact that the clauses they introduce are evaluated at a time that cannot precede the matrix time. Volitionals, directives, and verbs of planning belong to his class. For a discussion, see [START_REF] Abusch | On the temporal composition of infinitives[END_REF], for an analysis of modal verbs as forward-shifting, see [START_REF] Condoravdi | Temporal interpretations of modals. Modals for the present and for the past[END_REF].

4 Non-realistic modal bases are domains excluding the world of evaluation (w0). They are contrasted in the text to non-totally realistic modal bases, which contain w0 but are nonsingleton sets of worlds, and to totally realistic modal bases, which are singleton sets whose only member is w0. The latter form the background for factual, non-modalized statements. For a discussion, see [START_REF] Kaufmann | Formal approaches to modality[END_REF], as well as Giorgi & Pianesi (1997: 205-217).

5 Assertions as to rigid subjunctive selection or exclusion should be taken with a pinch of salt whenever the verb involved is a modal [START_REF] Grae | /to appear. Nueva gramática de la lengua española[END_REF], since modals can appear in the indicative in subjunctive-selecting contexts, and in the subjunctive in indicative-selecting contexts. 6 This means that the -ra-forms appearing in appositive relatives in certain registers should be analysed as indicative forms. As for their role in restrictive relatives, it is subject to debate (see [START_REF] Rivero | Especificidad y existencia[END_REF][START_REF] Rivero | Especificidad y existencia[END_REF]). 7 Mood alternation distinguishes purpose (subjunctive) from result clauses (indicative) with prepositional expressions such as de manera/modo/forma tal (que) 'so as/ so that'. 8 A possible exception is that of counterfactual suggestions or wishes, for instance: (i) Me lo hubieras dicho antes. me it have IMPF.SBJ.2SG say.PP before 'You should have told me before' 9 3 rd person imperatives are not usually acknowledged as such in the Spanish descriptive tradition, which assimilates the sentences containing them to desideratives [START_REF] Grae | /to appear. Nueva gramática de la lengua española[END_REF]. However, some of their uses cannot be semantically assimilated to desideratives: (i) Que hagan el menor error, y los denuncio. that make.PRS.SBJ.3SG the least mistake and them report..PRS.IND.1SG 'Let them commit the slightest mistake, and I'll report them'

  11

  Habrías podido/ tenido que prestar atención. have COND..2SG can.PP/ have PP that lend.INF attention 'You could/ should paid attention' b. Preferiría haberme enterado inmediatamente. prefer. COND.1SG have.INF-me inform immediately 'I'd have rather learnt about it right away'

Table 2 : The morphology of the simple forms of the subjunctive

 2

  IMPF.IND.3SG likely that arrive.PRS.SBJ.3PL / arrive.IMPF.SBJ.3PL to time 'It was likely that they would arrive on time'

		):
	2	a. Les pidió	que llegaran	a tiempo.
		them ask.PRT.IND.3SG that arrive.IMPF.SBJ.3PL to time
		'S/he asked them to arrive on time'
		b. Les pidió	que lleguen	a tiempo.
		them ask.PRT.IND.3SG that arrive.PRS.SBJ.3PL to time
		'S/he asked them to arrive on time'
		c. Les pide	que lleguen/	*llegaran a tiempo.
		them ask.PRS.IND.3SG that arrive.PRS.SBJ.3PL /arrive.IMPF.SBJ.3PL to time
		'S/he asks them to arrive on time'
	3	a. Es	probable que lleguen	a tiempo.
		be. PRS.IND.3SG likely that arrive PRS.SBJ.3PL to time
		'It's likely that they will arrive on time'
		b. Es	probable que llegaran	a tiempo.
		be. PRS.IND.3SG likely that arrive.IMPF.SBJ.3PL to time
		'It is likely that they arrived on time'
		c. Era	probable que *lleguen/	llegaran	a tiempo.
		be.

  me surprise PRS.IND.1SG that it have PRS.SBJ.3PL/ have IMPF.SBJ.3PL seePP 'I'm surprised that they (should) have seen it' b. Me sorprendió que lo hayan/ hubieran visto. me surprise PRT.IND.1SG that it have PRS.SBJ.3PL/ have IMPF.SBJ.3PL seePP 'I was surprised that they had/ should have seen it'However, just like the imperfect subjunctive can locate event-time simultaneously with Utt-T in counterfactually interpreted contexts, the pluperfect subjunctive can express a single anteriority relation, locating the eventuality before Utt-T in such contexts. Pluperfect and perfect do not contrast in temporal location in (8a-b), but the pluperfect versions indicate that w0 is not assumed to be a world in which they arrived on time, whereas the perfect versions merely express epistemic uncertainty as to w0 being or not such a world IMPF.SBJ.3PL / have.PRS.SBJ.3PL arrive.PP to time 'I wish they had / I hope they have arrived on time' b. Si hubieran / han llegado a tiempo... if have.IMPF.SBJ.3PL / have.PRS.IND.3PL arrive.PP to time 'If they had / have arrived on time...

		a. Me sorprende	que lo hayan/	*hubieran	visto.
	8	a. Ojalá	hubieran /	hayan	llegado a tiempo.
		hopefully have.

  insist PRS.IND.3SG in that arrive.PRS.SBJ.3PL/ arrive.PRS.IND.3PL at three 'S/he insists on their arriving/ that they arrive at 3 o'clock' b. Se aseguró de que la puerta estuviera/ REFL make-sure. PRT.IND.3SG of that the door be.IMPF.SBJ.3SG/

	estaba	cerrada.
	be. IMPF.IND.3SG closed
	'S/he saw to it/ checked that the door was closed'
	c. Admitió	que no le	pagaran/	pagaban.
	admit. PRT.IND.3SG that not him/her pay IMPF.SBJ.3PL/ pay IMPF.IND.3PL

a. Insiste en que lleguen/ llegan a las tres.

  PRT.IND.3SG/ obtain. PRT.IND.3SG/ make PRT.IND.3SG que le pagaran. that him/her pay IMPF.SBJ.3PL 'S/he demanded/ managed to be paid'/ 'S/he made them pay him/her' In some cases, causation alone triggers rigid subjunctive selection. This is the case when a causal relation between two eventualities is established by means of a verbal predicate (13a-b), but also in the complement clauses of nouns and adjectives denoting causal relations: That REFL refuse IMPF.SBJ.3PL to pay--him/her gave place to a quarrel Their refusal to pay him/her caused a quarrel' Emotive-factive predicates express a relationship between an Experiencer and a Stimulus, such that the Stimulus causes a psychological reaction in the Experiencer. They consistently select the subjunctive in their argument clauses: Him/her surprise PRS.IND.3SG that have-PRS.SBJ.3SG arrive.PP late 'S/he is surprised that s/he should have arrived late'

		Exigió/		Consiguió/	Hizo.
	demand. 13 a. El mal tiempo explica que llegara	tarde.
		The bad weather explains that arrive.IMPF.SBJ.3SG late
		'The bad weather explains his/her late arrival'
		b. Que se	negaran	a pagarle	dio lugar a una disputa.
	14	Le	sorprende	que haya	llegado tarde.

  PRS.SBJ.3SG arrive.PP/ arrive.PRT.IND.3SG late 'What surpriseshim/her is that s/he (should have) arrived late'

						):
	16	Lo	que le	sorprende	es	que
		That.N.SG that him/her surprise PRS.IND.3SG be.PRS.IND.3SG that
		haya llegado/	llegó	tarde.
		have-

  Subjunctive selection in argument clauses is much less rigid in polarity contexts.

			):
	19	a. ¿Le	molesta	si fumo?
		you/him/her bother.PRS.IND.3SG if smoke PRS.IND.1SG
		'Do you/ Does s/he mind if I smoke?'
		b. Se aburrió	porque siempre lo criticaban.
		REFL annoy.PRT.IND.3SG because always him criticize.IMPF.IND.3PL
		'S/he got fed up because he was always being criticized'

  . Thus, the indicative is the only possible choice in (20a), but the subjunctive is allowed in (20b):Mood alternation in polarity contexts produces extremely subtle effects which involve the attitude of the speaker towards the propositional content of the argument clause. Note that first person present negated belief reports select the subjunctive[START_REF] Quer | Mood at the interface[END_REF]):

	20	a. Creían/	Afirmaban	que Juan
		believe. IMPF.IND.3PL/ claim. IMPF.IND.3PL that Juan
		*estuviera/	estaba enfermo.
			be. IMPF.SBJ.3SG/ be.IMPF.IND.3SG ill
		'They believed/ claimed that Juan was ill'
		b. No creían/	afirmaban	que Juan
		not believe. IMPF.IND.3PL/ claim. IMPF.IND.3PL that Juan
		estuviera	/estaba	enfermo.
		be. IMPF.SBJ.3SG/ be.IMPF.IND.3SG ill
		They didn't believe/ claim that Juan was ill'
	21	No creo	que
		not believe. PRS.IND.1SG that
		estuviera/	*estaba enfermo.
		be. IMPF.SBJ.3SG/ be.IMPF.IND.3SG ill
		'I don't believe s/he was ill'

  and (33b) signal that the speaker views Pedro's confession as improbable resp. as contrary to fact: Conditionals and subjunctive concessives show parallel patterns in tense-mood distribution[START_REF] Quer | Mood at the interface[END_REF], with one important exception: conditionals introduced by the conjunction si 'if' never accept present/perfect subjunctive forms (34a). This restriction does not hold of other expressions, as shown by (34b): They hold my hand// We hold his/her hand' Thus, clitic position is held to discriminate between subjunctive and imperative in cases such as le tenga/ téngale, etc.[START_REF] Grae | /to appear. Nueva gramática de la lengua española[END_REF].Apart from certain set expressions and set patterns expressing wishes (39), desiderative sentences require a licensing element preceding the subjunctive. The most usual are the complementizer que and the particle ojalá 'hopefully' illustrated above.Adverbs expressing uncertainty license the subjunctive in main clauses when they precede the verb, but never when they follow it, as shown by the following contrast:

		a. Aunque Pedro confiese,
		even-that Pedro confess. PRS.SBJ.3SG a. tenme / tenedme / téngame
		yo seguiré hold-IMP.2SG-me/ hold-IMP.2PL-me/ hold-IMP.3SG-me negando.
		I follow.FUT.IND.1SG deny.GER ténganme/ tengámosle	la mano
		'Even if Pedro confesses, I'll go on denying it. hold-IMP.3PL-me/ hold-IMP.1PL-him/her the hand
		b. Aunque Pedro confesara, 'Hold my hand / Let's hold his/her hand'
		even-that Pedro confess.IMPF.SBJ.3SG b. me tienes/ me tenéis /	me tenga
		yo seguiría.COND.1SG negando. me hold-IND.2SG-me/ me hold-IND.2PL-me/ me hold-SBJ.1/3SG
		I follow deny.GER me tengan/ le	tengamos la mano
		'Even if Pedro confessed, I would go on denying it' me hold-SBJ.3PL/ him/her hold.SBJ.1PL the hand
	33 'You/ I/ S/he/ 39 a. Aunque Pedro haya even-that Pedro have.PRS.SBJ.3SG confess.PP confesado, yo seguiré FUT.IND.1SG negando. I follow deny.GER 'Even if Pedro has confessed, I'll go on denying it' b. Aunque Pedro hubiera confesado, even-that Pedro have.IMPF.SBJ.3SG confess.PP yo seguiría negando. a. Dios te ayude.
		I follow COND.1SG deny.GER God you help PRS.SBJ.3SG
		'Even if Pedro had confessed, I would go on denying it' '(May) God help you'
	40	a. Quizás/ Probablemente esté/	está	enfermo.
		perhaps/ probably	be.PRS.SBJ.3SG be.PRS.IND.3SG ill
	34	a. Si Pedro confiesa/ 'Maybe/ Probably s/he is ill'	/*confiese,
		if Pedro confess.PRS.IND.3SG / confess.PRS.SBJ.3SG b. *Esté/ Está enfermo, quizás/ probablemente.
		yo también confesaré. be.PRS.SBJ.3SG be.PRS.IND.3SG ill	maybe/ probably
		I also 'S/he is ill, maybe/probably' confess. FUT.IND.1SG
		'If Pedro confesses, I will confess too'
		b. En caso de que Pedro *confiesa/	confiese,
		in case of that Pedro confess.PRS.IND.3SG / confess.PRS.SBJ.3SG
		yo también	confesaré.
		I also confess. FUT.IND.1SG
		'If Pedro confesses, I will confess too'
	Counterfactual conditionals and subjunctive concessives with an imperfect or a pluperfect
	subjunctive normally have conditional forms in the main clause. However, there is a marked
	tendency to replicate a pluperfect subjunctive in the main clause:
	35	Si/Aunque hubiera	confesado,
		if even-that have IMPF.SBJ.3SG confess.PP
		lo habrían/	%hubieran	condenado.
		him have.COND.3PL/ have.IMPF.SBJ.3PL condemn.PP
		'If / Even if he had confessed, he would have gotten a sentence'
	Causal subordinates do not of themselves license the subjunctive (36a). However,
	under negation, as well as under emotive-factive or evaluative predicates, the subjunctive is

  . It thus contrasts with prospective aspect, whose past anchor can be contributed by an adverbial (41b) or by the tense of an independent previous sentence not go-out PRT.IND.1PL because rain COND.3SG / go IMPF.IND.3SG to rain 'We didn't go out because it would rain/ was going to rain'

	(41c):
	41	a. Pensó/	Afirmó	que llovería /	iba	a llover.
		think.PRT.IND.3SG/claim PRT..3SG that rain.COND.3SG/ go.IMPF.IND.3SG to rain
		'S/he thought/claimed that it would rain/ it was going to rain'
		b. Ayer	*llovería /	iba	a llover.
		yesterday rain. COND.3SG / go IMPF.IND.3SG to rain
		'Yesterday it would rain/ was going to rain'
		c. No salimos	porque *llovería /	iba	a llover.

  not come PRT.IND.3SG to the party

		Estaría/	Habrá		estado enfermo.
		be.COND.3SG/ have.FUT.IND.3SG be.PP ill
		'He didn't come to the party. He might have been ill'
	Modal uses of the conditional, on the other hand, are only licensed in a particular
	subset of modal environments, comprising (a) modal verbs; (b) verbs expressing wishes or
	preferences; (c) the consequent of counterfactual or hypothetical conditional sentences (Laca
	2006).
	43	a. Podrías/	Tendrías	que prestar atención.
		can.COND.2SG/ have. COND.2SG that lend.INF attention
		'You could/ should pay attention'
		b. Querría/	Preferiría/	Me gustaría
		want. COND.1SG/ prefer.COND.1SG/ me like.COND.3SG
		que prestaras	atención.
		that lend.IMPF.SBJ.2SG attention
		'I wish/ I'd prefer you would pay attention/ I'd like it for you to pay attention'
		c. Si te	importara,		prestarías	atención.
		if you.DAT mind. IMPF.SBJ.3SG lend.COND..2SG attention
		'If you minded, you would pay attention'

Root contexts

In main clauses, the subjunctive invariably signals that the propositional content is not being asserted. This is the case in directive (37a) and desiderative sentences (37b), but also in sentences expressing some forms of epistemic modality (37c Note that in all cases, the subjunctive requires a licensor that precedes it: negation in (37a), the complementizer que or the particle ojalá (37b), and an adverb in ((37c). 8 The subjunctive alternates with the imperative in directives. Negative directives cannot be expressed in the imperative, and 3 rd pers. imperatives are indistinguishable from subjunctive forms. 9 Since the politeness form of address is a 3 rd pers. form, and the only form for plural addressees in American Spanish is the politeness form, this leads to considerable overlap between imperative and subjunctive. Table 3 shows that there are only two distinct forms for the imperative in European Spanish, and only one in American Spanish : Although the wisdom of maintaining a separate mood for two, resp. one distinct inflection may be questioned, imperative sentences not introduced by negation or by a complementizer share with infinitives and gerunds the peculiarity of not allowing proclitics:


Banglei Guan
email: banglei.guan@hotmail.com

Pascal Vasseur
email: pascal.vasseur@univ-rouen.fr

Cédric Demonceaux
email: cedric.demonceaux@u-bourgogne.fr

Friedrich Fraundorfer
email: fraundorfer@icg.tugraz.at

Visual odometry using a homography formulation with decoupled rotation and translation estimation using minimal solutions

In this paper we present minimal solutions for two-view relative motion estimation based on a homography formulation. By assuming a known vertical direction (e.g. from an IMU) and assuming a dominant ground plane we demonstrate that rotation and translation estimation can be decoupled. This result allows us to reduce the number of point matches needed to compute a motion hypothesis. We then derive different algorithms based on this decoupling that allow an efficient estimation. We also demonstrate how these algorithms can be used efficiently to compute an optimal inlier set using exhaustive search or histogram voting instead of a traditional RANSAC step. Our methods are evaluated on synthetic data and on the KITTI data set, demonstrating that our methods are well suited for visual odometry in road driving scenarios.

I. INTRODUCTION

Visual odometry and visual SLAM [START_REF] Scaramuzza | Visual odometry [tutorial] part1: The first 30 years and fundamentals[END_REF] play an immensely important role for mobile robotics. Many different approaches for visual odometry have been proposed already, and for a wide variety of applications visual odometry has been used successfully. However, reliability, long-term stability and accuracy of visual odometry algorithms are still a topic of research as can be seen by the many contributions to the KITTI visual odometry benchmark [START_REF] Geiger | Are we ready for autonomous driving? the kitti vision benchmark suite[END_REF]. Most approaches for visual odometry follow the scheme where first feature correspondences between subsequent views are established, then they are screened for outliers and then egomotion estimation is done on inliers only [START_REF] Scaramuzza | Visual odometry [tutorial] part1: The first 30 years and fundamentals[END_REF]. The reliability and robustness of such a scheme is heavily dependent on the outlier screening step. In addition the outlier screening process has to be fast and efficient. The use of RANSAC [START_REF] Fischler | RANSAC random sampling concensus: A paradigm for model fitting with applications to image analysis and automated cartography[END_REF] is widely accepted for this step.

However, the complexity of the RANSAC process being exponentially related to the minimal number of points necessary for the solution estimation, reducing this number is very interesting. For instance, a standard solution for twoviews egomotion estimation is to use the essential matrix with 5 matching points [START_REF] Nistér | An efficient solution to the five-point relative pose problem[END_REF] in a RANSAC process to increase the robustness. Nevertheless, the number of points needed for estimating the parameters is really crucial for the RANSAC algorithm. Indeed, the runtime of the RANSAC increases exponentially according to the number of points we need. Thus, before estimating the parameters, we have to be sure that we use the minimal number of points for that. One such idea is to take motion constraints into account, e.g. a planar motion (2pt algorithm) or the Ackermann steering motion for self-driving cars (1pt algorithm [START_REF] Scaramuzza | Real-time monocular visual odometry for on-road vehicles with 1point ransac[END_REF]). Another idea is to utilize an additional sensor like an inertial measurement unit to improve this step. Traditional sensor fusion methods [START_REF] Weiss | Real-time metric state estimation for modular vision-inertial systems[END_REF] perform a late fusion of the individual vision and IMU measurements. However, it is possible to utilize the IMU measurements much earlier to aid the visual odometry algorithm for outlier screening. This idea has already been utilized in [START_REF] Fraundorfer | A minimal case solution to the calibrated relative pose problem for the case of two known orientation angles[END_REF], [START_REF] Gim | Relative pose estimation for a multi-camera system with known vertical direction[END_REF], [START_REF] Naroditsky | Two efficient solutions for visual odometry using directional correspondence[END_REF], [START_REF] Saurer | Homography based egomotion estimation with a common direction[END_REF] in which partial IMU measurements have been used to design more efficient motion estimation algorithms for outlier screening.

In this paper we follow this idea by proposing a low complexity algorithm for unconstrained two-view motion estimation that can be used for efficient outlier screening and initial motion estimation. Our method assumes a known gravity vector (measured by an IMU) and is based on a homography relation between two views. In [START_REF] Saurer | Homography based egomotion estimation with a common direction[END_REF] a 2pt algorithm has been proposed exactly for this case. In this work we will improve on [START_REF] Saurer | Homography based egomotion estimation with a common direction[END_REF] and show that actually an algorithm can be found that needs fewer than 2 data points for a motion hypothesis. To achieve this, the first step is to separate the rotation and translation estimation. This is possible if the scene contains features that are far away. Such features are only influenced by rotation and only the x-coordinate of a single feature point is sufficient to find the remaining rotational degree of freedom (DOF), so we call this the 0.5pt method. After this the remaining 3 DOFs for the translation t x , t y , t z are computed. We present a linear solution that needs 1.5pt correspondences. However, more important is our proposal of using a discrete sampling for determining one of the remaining parameters and then use a 1pt algorithm for the remaining 2 parameters. This makes it possible to completely determine a motion hypothesis from a single point correspondence. Thus, we obtain an extremely fast algorithm even within a RANSAC loop. The actual motion hypotheses can be computed exhaustively for each point correspondence and the best solution can be found by a voting scheme.

The proposed methods are evaluated experimentally on synthetic and real data sets. We test the algorithms under different image noise and IMU measurement noise. We demonstrate the proposed algorithms on KITTI [START_REF] Geiger | Are we ready for autonomous driving? the kitti vision benchmark suite[END_REF] data set and evaluate the accuracy compared to the ground truth.

These experiments also demonstrate that the assumptions taken hold very well in practice and the results on the KITTI data set show that the proposed methods are useful within the self-driving car context.

II. RELATED WORK

With known intrinsic parameters, a minimum of 5 point correspondences is sufficient to estimate the essential matrix [START_REF] Nistér | An efficient solution to the five-point relative pose problem[END_REF], and a minimum of 4 point correspondences is required to estimate the homography if all the 3D points lie on a plane [START_REF] Hartley | Multiple View Geometry in Computer Vision[END_REF]. Then the essential matrix or the homography can be decomposed into the motion of the camera between two views, i.e. a relative rotation and translation direction.

A reduction of the number of needed point correspondences between views is important in terms of computational efficiency and of robustness and reliability. Such a reduction is possible if some additional information is available or assumptions about the scene and camera motion are taken. If for instance the motion is constrained to be on a plane, which is typical for ground based robots or self-driving cars, 2 point correspondences are only needed for computing the 3-DOFs motion [START_REF] Ortin | Indoor robot motion based on monocular images[END_REF]. If further the motion is constrained by Ackermann steering typical for cars only 1 point correspondence is necessary [START_REF] Scaramuzza | Real-time monocular visual odometry for on-road vehicles with 1point ransac[END_REF]. In contrast if additional information e.g. from an IMU is available and the complete rotation between the two views is provided by the IMU, the remaining translation can be recovered up to scale using only 2 points [START_REF] Kneip | Robust real-time visual odometry with a single camera and an imu[END_REF].

Using this concept a variety of algorithms have recently been proposed for egomotion estimation when knowing a common direction [START_REF] Fraundorfer | A minimal case solution to the calibrated relative pose problem for the case of two known orientation angles[END_REF], [START_REF] Kalantari | A new solution to the relative orientation problem using only 3 points and the vertical direction[END_REF], [START_REF] Naroditsky | Two efficient solutions for visual odometry using directional correspondence[END_REF]. The common direction between the two views can be given by an IMU (measuring the gravity direction) or by vanishing points extraction in the images. All these works propose different algorithms for solving the essential matrix with 3 point correspondences. For this they start with a simplified essential matrix (due to the known common direction) and then derive a polynomial equation system for the solution.

To further reduce the number of point correspondences, the homography relation between two views can be used instead of the epipolar constraint expressed by the essential matrix. Under the assumption that the scene contains a large enough plane that is normal or parallel to the gravity vector measured by an IMU (a typical case for indoor or road driving scenarios) the egomotion can be computed from 2 point correspondences [START_REF] Saurer | Homography based egomotion estimation with a common direction[END_REF]. This idea however can be extended even further which is what we propose in this work.

We start with the formulation of [START_REF] Saurer | Homography based egomotion estimation with a common direction[END_REF] where the cameras are aligned to the gravity vector and the remaining DOFs are one rotation parameter and three translation parameters. We solve for rotation and translation separately. This uses the fact that for far scene points, the parallax-shift (induced by translation) between two views is hardly noticeable. The motion of these far points is close enough to a pure rotation case such that the rotation between two views can be estimated firstly (and independent from translation) using these far points. Every single point correspondence can produce a hypothesis for the remaining rotation parameter which can be used in a 1pt RANSAC algorithm for rotation estimation or for histogram voting by computing the hypothesis from all the point matches. This step also allows to separate the correspondences into two sets, a far set and a near set. The further processing for the translation estimation can then be continued on the smaller near set only, as the effect of translation is not noticeable in the far set. Such a configuration is typical for road driving imagery. For estimating the remaining translation parameters we propose a linear 1.5pt algorithm. However, practically this solution does not give a direct computational advantage over the 2pt algorithm of Saurer et al. [START_REF] Saurer | Homography based egomotion estimation with a common direction[END_REF]. Instead we propose to use a combination of discrete sampling and parameter estimation. The idea is that 1 parameter of the remaining 3 is sampled in discrete steps. For each sampled value it is possible to estimate the remaining parameters from a single point correspondence. This can be then done efficiently using a 1pt RANSAC step or an exhaustive search to find the globally optimal value. The great benefit about this approach is that instead of performing 2pt RANSAC a sequence of 1pt RANSAC steps with a constant overhead for bounded discrete sampling is used. This exhaustive search gives us an efficient way to find the globally optimal solution.

III. BASICS AND NOTATIONS

With known intrinsic camera parameters, a general homography relation between two different views is represented as follows [START_REF] Hartley | Multiple View Geometry in Computer Vision[END_REF]:

λx j = Hx i , (1)
where x i = [x i , y i , 1] T and x j = [x j , y j , 1] T are the normalized homogeneous image coordinates of the points in views i and j, λ is a scale factor. The homography matrix H is given by:

H = R - 1 d tN T , (2)
where R = R y R x R z and t = [t x , t y , t z ] are respectively the rotation and the translation from views i to j. R y , R x and R z are the rotation matrices along y-, x-and z-axis, respectively. With the knowledge of the vertical direction the rotation matrix R can be simplified such that R = R y by pre-rotating the feature points with R x R z , which can be measured from the IMU (or alternatively from vanishing points [START_REF] Bazin | Motion estimation by decoupling rotation and translation in catadioptric vision[END_REF]). After this rotation, the cameras are in a configuration such that the camera plane is vertical to the ground plane. d is the distance between the view i frame and the 3D plane. N = [n 1 , n 2 , n 3 ] T is the unit normal vector of the 3D plane with respect to the view i frame.

For this gravity aligned camera configuration the plane normal N of the ground plane is [0, 1, 0] T . Consequently, Equation 2 that only considers points on the ground plane can be written as:

H =   cos (θ) 0 sin (θ) 0 1 0 -sin (θ) 0 cos (θ)   - t d   0 1 0   T (3)
The homography relation is defined up to scale, so there are 4 DOFs remaining being the rotation around the y-axis and the translation parameters t x , t y , t z .

IV. 0.5PT ROTATION ESTIMATION METHOD

The rotation angle can be computed from a single point correspondence. In fact, it can be computed from only the x-coordinate of a single feature point. Rotation estimation can be done independently from the translation estimation if the scene contains far points. These points, that can be considered at infinity, are not affected any more by a translation. Consequently, the translation component is zero for these points and the Equation 3 simplifies to a rotation matrix:

H =   cos (θ) 0 sin (θ) 0 1 0 -sin (θ) 0 cos (θ)   (4)
In order to further eliminate the unknown scale factor λ, multiplying both sides of Equation 1 by the skew-symmetric matrix [x j ] × , yields the equation:

[x j ] × Hx i = 0. (5)
Substituting Equation 4into the above equation and expand it:

  0 -1 y j 1 0 -x j -y j x j 0     cos (θ) 0 sin (θ) 0 1 0 -sin (θ) 0 cos (θ)     x i y i 1   = 0 (6)
By rewriting the equation, we obtain:

-x i y j sin(θ) + y j cos(θ) -y i = 0 (7)

(x i x j + 1)sin(θ) + (x i -x j )cos(θ) = 0 (8) -y j sin(θ) -x i y j cos(θ) + x j y i = 0 (9)
These equations are now derived for the case of points that lie on a plane normal to the y-axis of the cameras and which are infinitely far away. In this case, all the points have to lie on the horizon, which means that the y-coordinate of such a point in normalized coordinates is 0 (normalized coordinates are image coordinates in pixel after multiplication with the inverse calibration matrix). This equates Equation 7and Equation 9 to zero. Only Equation 8remains to be used. Considering the trigonometric constraint sin 2 (θ) + cos 2 (θ) = 1, the rotation parameter sin(θ) can be obtained:

sin(θ) = ± x i -x j x i 2 x j 2 + x i 2 + x j 2 + 1 (10)
Due to the sign ambiguity of sin(θ), we obtain two possible solutions for the rotation angle. For every point correspondence a rotation hypothesis can be calculated. A 1pt RANSAC loop can be utilized to find a consistent hypothesis with only a few samples. Alternatively the globally optimal solution can be computed by performing an exhaustive search or histogram voting. The exhaustive search is linear in the number of point correspondences and a hypothesis can be computed for every point correspondence. The hypothesis with the maximum number of inliers is the globally optimal solution. To avoid computing the inliers and outliers for every hypothesis a histogram voting method can be used. For this all the hypothesis are collected in a histogram with discrete bins (e.g. a bin size of 0.1 degree) and the bin with the maximum count is selected as the best solution. Alternatively the mean of a window around the peak can be computed for a more accurate result.

The inliers of the pure rotation formulation belong to scene points that are very far away and don't influence the translation. For further translation estimation these point correspondences can be removed to reduce the number of data points to process. Translation estimation only needs to consider the outlier set of the rotation estimation.

V. TRANSLATION ESTIMATION METHOD

After estimation of the rotation parameter as described in the previous section, the feature points in views j can be rotated by the rotation matrix around the yaw axis:

xj = R T y x j , (11)
This aligns both views such that they only differ in translation t = [ tx , ty , tz ] for x i ↔ xj . Equation 3 therefore is written as:

H =   1 0 0 0 1 0 0 0 1   - 1 d   tx ty tz     0 1 0   T (12)
In the following subsections we describe 4 different methods of how to estimate the translation parameters.

A. 1.5pt linear solution

This subsection describes a linear method to compute the remaining translation parameters. Three equations from two point correspondences are used to set up a linear equation system to solve for the translation.

The camera-plane distance d is unknown but the translation can be known only up to scale. Therefore d can be absorbed by t. We then obtain:

H =   1 -tx 0 0 1 -ty 0 0 -tz 1   (13)
Substituting Equation 13into the Equation 5, the homography constraints between x i and xj can be expressed:

  0 -1 ỹj 1 0 -x j -ỹ j xj 0     1 -tx 0 0 1 -ty 0 0 -tz 1     x i y i 1   = 0 (14)
By rewriting the equation, we obtain:

     y i ty -y i ỹj tz = y i -ỹj -y i tx + xj y i tz = xj -x i y i ỹj tx -xj y i ty = x i ỹj -xj y i (15)
Even though Equation 15has three rows, it only imposes two independent constraints on t, because the skewsymmetric matrix [x j ] × has only rank 2. To solve for the 3 unknowns of t = [ tx , ty , tz ], one more equation is required which has to be taken from a second point correspondence. In principle, an arbitrary equation can be chosen from Equation 15, for example, the second and third rows of the first point x i ↔ xj , and the second row of the second point x i ↔ x j are stacked into 3 equations in 3 unknowns:

     -y i tx + xj y i tz = xj -x i y i ỹj tx -xj y i ty = x i ỹj -xj y i -y i tx + x j y i tz = x j -x i (16)
The linear solution for t = [ tx , ty , tz ] can be obtained by:

                   tx = x i x j y i + xj y i x j -xj x j y i -xj y i x i y i x j y i -xj y i y i ty = y i x j y i + y i ỹj x j + x i ỹj y i -y i ỹj x i -xj y i y i -ỹj x j y i y i x j y i -xj y i y i tz = x i y i + y i x j -xj y i -y i x i y i x j y i -xj y i y i (17)
The translation t from views i to j can be obtained:

t = R T y t. (18)
For finding the best fitting translation t a RANSAC step should be used. Here it is however possible to evaluate the full point set. From the estimated rotation and translation parameters an essential matrix can be constructed (E = [t] × R y ) and the inliers can be tested against the epipolar geometry. This test is not limited to points on the ground plane and the final inlier set contains all scene points. For a most accurate result a non-linear optimization of the Sampson distance on all the inliers is advised. The techniques of constructing the epipolar geometry and performing the nonlinear optimization are also applicable to other translation estimation methods.

B. 1pt method by discrete sampling of the relative height change

Translation estimation as explained in the previous section needs 1.5pt correspondences. However, if one of the remaining parameters is known only a single point correspondence is needed for computing the remaining two parameters. This leads to 1pt algorithm for the translation. It is possible to perform a discrete sampling of a suitable parameter within a suitable bounded range. This allows to perform an exhaustive search to find the global optimal solution which produces the highest number of inliers. The time complexity of this exhaustive search is linear in the number of point correspondences if the number of discrete samples is significantly smaller than the number of point correspondences.

In order to use the sampling method, Equation 12 can be written as:

H =   1 0 0 0 1 0 0 0 1   - ty d   tx / ty 1 tz / ty     0 1 0   T (19)
In this variant the relative height change over ground a = ty /d is sampled in discrete steps which leads to an equation system with only 2 unknowns, b = tx / ty , c = tz / ty . Only 1pt is needed to compute a solution b and c for a given a. In the same way, we can choose the second and third row from Equation 15to compute b and c:

       b = ax j y i + x i ỹj -xj y i ay i ỹj c = aby i + xj -x i ax j y i (20)
Based on the value of b and c, we can recover t = [b, 1, c] T up to scale. Then the estimated translation t between views i and j is also recovered up to scale by Equation 18.

C. 1pt method by discrete sampling for x-z translation direction

The sampling method in the previous section worked by discretizing the relative height change between two views. As this can be up to scale there is no obvious value for the step sizes and bounds. However, if one is to sample the direction vector of the translation in the x-z plane this represents the discretization of an angle between 0...360 degrees. In this case a meaningful step size can easily be defined.

For this variant Equation 12 can be written as:

H =   1 0 0 0 1 0 0 0 1   - t2 x + t2 z d   cos(δ) ty / t2 x + t2 z sin(δ)     0 1 0   T (21)
The translation direction can be represented as an angle δ and e.g. can be sampled in steps of 1 degree from 0 • to 360 • , which leads to an equation system with only 2 unknowns, a = t2

x + t2 z /d, b = ty / t2

x + t2 z . Only 1pt is needed to compute a solution a and b for a given angle δ.

In the same way, we can choose the second and third row from Equation 15to compute a and b:

       a = xj -x i xj y i sin(δ) -y i cos(δ) b = ay i ỹi cos(δ) + xj y i -x i ỹj ax j y i (22)
Based on the vector [cos(δ), b, sin(δ)] T , we can recover t up to scale. Then we obtain t by Equation 18.

D. 1pt method by discrete sampling of the in-plane scale change

The method described in this section is another variant of choosing a meaningful parameter for discrete sampling. For easy explanation of this idea one should imagine a camera setup with downward looking cameras with a camera plane parallel to the ground plane. The previously aligned camera setup with the camera plane normal to the ground plane can easily be transformed into such a setup by rotating the feature points about 90 • around the x-axis of camera by multiplication with a rotation matrix R d .

Moving a camera looking downwards at a plane (e.g. the street) up and down results in an in-plane scale change of the image, i.e. the points will move inwards to or outwards from the center. The scale change directly corresponds to the effects of a translation in z-direction. This makes the scale change a good parameter for discrete sampling, as the in-plane scale change can be expressed in pixel distances.

In this approach discrete values for the scale change are sampled and the remaining translation direction in the x-y plane can be computed for every point correspondence from a single point. Points lying on the same plane, have exactly the same translation shift for all the feature matches. Now, we derive the formula in detail.

We assume that (x i , y i , 1) ↔ (x j , y j , 1) are the normalized homogeneous image coordinates of the points in downward looking views i and j. The heights of the downward looking views i and j are h i and h j , respectively. The ground points can be represented in the camera coordinate system of views i and j:

X i = h i * [x i , y i , 1] T , X j = h j * [x j , y j , 1] T .
The translation between views i and j can be computed directly:

td = h j   x j y j 1   -h i   x i y i 1   =   (x j h j -x i h i ) (y j h j -y i h i ) h j -h i   (23)
We set the in-plane scale κ = f * (h i /h j ), f is the focal length. We substitute κ into the above equation. We can obtain the translation vector directly as the difference of the image coordinates:

td =   f x j -κx i f y j -κy i f -κ   (24)
By sampling the in-plane scale κ, we can compute the translation vector td using one point, and choose the solution which has the maximum number of inliers. This sampling interval is defined in pixels and allows setting a meaningful step size (e.g. 1 pixel).

The final translation t between two views can be obtained:

t = R T y R T d td (25)

VI. EXPERIMENTS

We validate the performance of the proposed methods using both synthetic and real scene data. The experiments with synthetic scenes will demonstrate the behavior of our derivations in the presence of image noise and IMU noise. The experiments using the KITTI data set [START_REF] Geiger | Are we ready for autonomous driving? the kitti vision benchmark suite[END_REF] will demonstrate the suitability of the methods for use in road driving scenarios. This experiments will also demonstrate that the assumptions taken will hold for real scenarios.

A. Experiments with synthetic data

To evaluate the algorithms on synthetic data we choose the following setup. The distance of the ground to the first camera center is set to 1. The baseline between two cameras is set to be 0.2 and the direction is either along the x-axis of the first camera (sideways) or along the z-axis of the first camera (forward). Additionally, the second camera is rotated around every axis, three rotation angles varies from -90 • to 90 • . The Roll angle (around z-axis) and Pitch angle (around x-axis) are known. The generated scene points can be set to lie on the ground plane or be distributed freely in space.

We evaluate the accuracy of the presented algorithms on synthetic data under different image noise and IMU noise. The focal length is set to 1000 pixels. The solutions for relative rotation and translation are obtained by RANSAC or histogram voting. We assess the rotation and translation error by the root mean square error of the errors. We report the results on the data points within the first two intervals of a 5quantile partitioning 1 (Quintile) of 1000 trials. The proposed methods are also compared against the 2pt method [START_REF] Saurer | Homography based egomotion estimation with a common direction[END_REF].

In all of the experiments, we compare the relative rotation and translation between views i and j separately. The error measure compares the angle difference between the true rotation and estimated rotation. Since the estimated translation between views i and j is only known up to scale, we compare the angle difference between the true translation and estimated translation. The errors are computed as follows:

• Rotation error: ξ R = arccos((T r(R gt R T ) -1)/2) • Translation error: ξ t = arccos((t T gt t)/( t gt t )) R gt , t gt denote the ground-truth transformation and R, t are the corresponding estimated transformations.

1) Pure planar scene setting ("PLANAR"): In this setting the generated scene points are constrained to lie on the ground plane. The scene points consist of two parts: near points (0 to 5 meters) and far points (5 to 500 meters). Both parts have 200 randomly generated points.

Figure 1(a) and (b) show the results of the 0.5pt method and histogram voting for rotation estimation for gradually increased image noise levels with perfect IMU data. It is interesting to see that our method performs better for forward motion than for sideways motion. The histogram voting has an higher error, because of the binning which has more effect than the image noise. Figure 1 (b) does not show a clear trend with increased image noise levels. It seems that the influence of the sideways motion is stronger than the influence of the image noise. Figure 1(c)-(f) show the influence of increasing noise on the IMU data while assuming image noise with 0.5 pixel standard deviation.

Figure 2 shows the results of the 1.5pt linear solution method, 1pt method by sampling for x-z translation direction and 2pt method, for gradually increased image noise levels with perfect IMU data or increasing noise on the IMU data while assuming image noise with 0.5 pixel standard deviation. Note that we use the histogram voting method to compute the rotation first, in order to compare the accuracy of different translation estimation methods. The 1.5pt linear solution method and the 1pt method by sampling for x-z translation direction are robust to the increased image noise and IMU data noise.

2) Mixed scene setting ("MIXED"): In this experiment not all the scene points were constrained to lie on the ground plane. Far points (from 5 to 500 meters distance) do not lie on the ground only. They are generated a heights that vary from 0 to 10 meters. The near points however (from 0 to 5 meters distance) are constrained to lie on the ground plane. Both sets, near points and far points consist of 200 randomly generated points. Figure 3 shows the results of the 0.5pt method and histogram voting for rotation estimation for gradually increased image noise levels with perfect IMU data, or increasing noise on the IMU data while assuming image noise with 0.5 pixel standard deviation.

Figure 4 shows the results of the 1.5pt linear solution method, 1pt method by sampling for x-z translation direction and 2pt method, for gradually increased image noise levels with perfect IMU data or increasing noise on the IMU data while assuming image noise with 0.5 pixel standard deviation. In Figure 4 (f) a sensitivity of the 1.5pt linear solution method to noise in Pitch angle can be seen in sideways motion.

The experiments on synthetic data validate the derivation of the minimal solution solvers and quantify the stability of the solvers with respect to image noise and IMU noise. The synthetic data did not contain outliers. The use of the methods within a RANSAC loop for outlier detection is part of the experiments using real data.

B. Experiments on real data

Experiments on real data were performed on the KITTI data set [START_REF] Geiger | Are we ready for autonomous driving? the kitti vision benchmark suite[END_REF]. For the evaluation we utilized all the available 11 sequences which have ground truth data (labeled from 0 to 10 on the KITTI webpage) and together consist of around 23000 images. The KITTI data set provides a challenging environment for our experiments, however, such a road driving scenario does fit our method very well. In all the images a large scene plane is visible (the road) and features at far distances are present as well. For our experiments we performed SIFT feature matching [START_REF] Lowe | Distinctive image features from scale-invariant keypoints[END_REF] between consecutive frames. The ground truth data of the sequences is used to pre-rotate the feature-points by R x R z , basically simulating IMU measurements. Then the remaining relative rotation and translation are estimated with our methods. We perform 3 sets of experiments with the KITTI data set. In a first experiment we test the effectiveness of our proposed quick test for rotation inliers. In the second experiment we compute rotation and translation using all our proposed methods and compare it to the ground truth. We also compare the results to the 5pt method [START_REF] Nistér | An efficient solution to the five-point relative pose problem[END_REF] and 2pt method [START_REF] Saurer | Homography based egomotion estimation with a common direction[END_REF]. In a third experiment we test the quality of the inlier detection by using the different methods. 1) Rotation estimation inlier selection using y-coordinate test: The 0.5pt method for rotation estimation is working under the assumption that a scene point is far away. Using RANSAC or histogram voting the inliers of this assumption can be found. However, even before computing rotation hypothesis with the 0.5pt method the point correspondences can already be checked if they stem from far points, to remove all the near points. For a far point in this setting the y coordinate of a point feature does not change. So any point correspondence where the y coordinate changes is a near feature that can be discarded for the rotation estimation. This allows to significantly remove a big part of feature points for the rotation estimation to make it more efficient. Table I can be removed already based on this simple criteria. For this test a feature was classified as a far feature if the y coordinate does not change more than 1 pixel. N umSIF T is the average number of point correspondences within a sequence, N umRemove is the average number of outliers removed, and Ratio = N umRemove/N umSIF T is the average of the percentage of the removed outliers. It can be seen that at least more than 52% feature matches can be removed due to this criteria.

2) Comparison of rotation and translation estimation to ground truth: In this experiment we compare the rotation and translation estimates of our methods to ground truth and also to the results of the 5pt method [START_REF] Nistér | An efficient solution to the five-point relative pose problem[END_REF] and the 2pt method [START_REF] Saurer | Homography based egomotion estimation with a common direction[END_REF]. The rotation value at the peak in the histogram is then selected. Both 0.5pt method and histogram voting method provide better results than the 5pt method and 2pt method. The histogram voting method is slightly more accurate than the 0.5pt method. In subsequent experiments, we use the histogram voting method to estimate the rotation first, then estimate the translation using the different methods.

The translation error for all sequences is shown in Table III. All the four methods for translation estimation, the 1.5pt linear solution method (1.5pt lin), the 1pt method by discrete sampling of the relative height change (1pt h), the 1pt method by discrete sampling for x-z translation direction (1pt d) and the 1pt method by discrete sampling of the inplane scale change (1pt s) are compared to ground truth. The 1.5pt method is used within a RANSAC loop with a fix number of 100 iteration and an inliers threshold of 2 pixel. For the 1pt methods an exhaustive search is performed and the solution with the highest number of inliers is used.

The table shows that all of our methods provide better results than the 2pt method. The 1pt methods for translation estimation and the 5pt method are more accurate than the linear solution using 1.5pt. The 1pt d method offers the best overall performance among all the translation estimation methods. 3) Inlier recovery rate: The main usage for our proposed algorithms should be to efficiently find a correct inlier set which can then be used for accurate motion estimation using e.g. non-linear optimization (maybe also using our motion estimates as initial value). We therefore perform an experiment that tests how many of the real inliers (calculated from the ground truth) can be found by our methods. This inlier recovery rate is shown in Table IV as an average over all sequences (an inlier threshold of 2 pixels). All of our four methods can be used to find a correct inlier set, and provide a more complete inlier set than the 2pt method. The inlier recovery rate of 1pt d method is slightly better than the 5pt method. Inlier detection using the 1pt d method is shown in Figure 5. VII. CONCLUSION The presented algorithms allow to compute motion estimation and inlier sets by exhaustive search or by histogram voting. This is an interesting alternative to the traditional RANSAC method. RANSAC finds an inlier set with high probability but there is no guarantee that it is really a good one. Also, our experiments demonstrate that the assumptions taken in these algorithms are commonly met in road driving scenes (e.g. the KITTI data set), which could be a very interesting application area for it.

Fig. 1 .

 1 Fig. 1. Rotation error with "PLANAR" setting: Evaluation of the 0.5pt method, histogram voting and 2pt method. Left: forward motion, right: sideways motion. (a) and (b) are with varying image noise. (c), (d), (e) and (f) are under different IMU noise and constant image noise 0.5 pixel standard deviation. (c) and (d) are with Roll angle noise. (e) and (f) are with Pitch angle noise.

Fig. 2 .

 2 Fig. 2. Translation error with "PLANAR" setting: Evaluation of the 1.5pt linear solution method, 1pt method by sampling for x-z translation direction and 2pt method. Left: forward motion, right: sideways motion. (a) and (b) are with varying image noise. (c), (d), (e) and (f) are under different IMU noise and constant image noise 0.5 pixel standard deviation. (c) and (d) are with Roll angle noise. (e) and (f) are with Pitch angle noise.

Fig. 3 .

 3 Fig. 3. Rotation error with "MIXED" setting: Evaluation of the 0.5pt method, histogram voting and 2pt method. Left: forward motion, right: sideways motion. (a) and (b) are with varying image noise. (c), (d), (e) and (f) are under different IMU noise and constant image noise 0.5 pixel standard deviation. (c) and (d) are with Roll angle noise. (e) and (f) are with Pitch angle noise.

Fig. 4 .

 4 Fig. 4. Translation error with "MIXED" setting: Evaluation of the 1.5pt linear solution method, 1pt method by sampling for x-z translation direction and 2pt method. Left: forward motion, right: sideways motion. (a) and (b) are with varying image noise. (c), (d), (e) and (f) are under different IMU noise and constant image noise 0.5 pixel standard deviation. (c) and (d) are with Roll angle noise. (e) and (f) are with Pitch angle noise.

Fig. 5 .

 5 Fig. 5. Inlier detection example, left: previous frame; right: current frame. (a). Ground truth inliers: 885 matches; (b). Inliers detected by the 1pt d method: 884 matches.

  )

		0.2					Forward motion						0.2					Sideways motion
		0.18			2pt method	1.5pt method		1pt sampling method		0.18			2pt method	1.5pt method		1pt sampling method
		0.16												0.16
	Translation error (degree)	0.06 0.08 0.1 0.12 0.14											Translation error (degree)	0.06 0.08 0.1 0.12 0.14
		0.04												0.04
		0.02												0.02
			0													0
				0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1			0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1
							Noise standard deviation (pixel)									Noise standard deviation (pixel)
			14					Forward motion						35					Sideways motion
						2pt method	1.5pt method		1pt sampling method						2pt method	1.5pt method		1pt sampling method
			12													30
	Translation error (degree)	4 6 8 10											Translation error (degree)	10 15 20 25
			2													5
			0													0
				0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1			0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1
							Rotation Noise in Degree (Roll)									Rotation Noise in Degree (Roll)
			30					Forward motion						45					Sideways motion
						2pt method	1.5pt method		1pt sampling method			40			2pt method	1.5pt method		1pt sampling method
			25
																35
	Translation error (degree)	10 15 20											Translation error (degree)	15 20 25 30
																10
			5
																5
			0	0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1		0	0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1
							Rotation Noise in Degree (Pitch)									Rotation Noise in Degree (Pitch)

  shows how many of the feature points

			0.016					Forward motion						0.045						Sideways motion
			0.014			2pt method		0.5pt method	Histogram voting				0.04				2pt method	0.5pt method	Histogram voting
			0.012													0.035
	(a)	Rotation error (degree)	0.006 0.008 0.01											(b)	Rotation error (degree)	0.015 0.02 0.025 0.03
			0.004														0.01
			0.002													0.005
				0	0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1				0	0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1
								Noise standard deviation (pixel)												Noise standard deviation (pixel)
				0.12					Forward motion								0.4					Sideways motion
							2pt method		0.5pt method	Histogram voting									2pt method	0.5pt method	Histogram voting
																		0.35
				0.1
																			0.3
	(c)	Rotation error (degree)	0.04 0.06 0.08											(d)	Rotation error (degree)	0.15 0.2 0.25
																			0.1
				0.02														0.05
				0	0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1				0	0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1
								Rotation Noise in Degree (Roll)												Rotation Noise in Degree (Roll)
				0.25					Forward motion								0.6						Sideways motion
							2pt method		0.5pt method	Histogram voting									2pt method	0.5pt method	Histogram voting
				0.2															0.5
	(e)	Rotation error (degree)	0.1 0.15											(f)	Rotation error (degree)	0.2 0.3 0.4
				0.05
																			0.1
				0	0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1				0	0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1
								Rotation Noise in Degree (Pitch)												Rotation Noise in Degree (Pitch)

TABLE I EFFECT

 I OF THE Y-COORDINATE TEST FOR OUTLIER REMOVAL.

	Sequences	N umSIF T	N umRemove	Ratio
	00 (4541 images)	634	463	74.15%
	01 (1101 images)	398	213	52.26%
	02 (4661 images)	648	508	78.74%
	03 (801 images)	886	572	65.50%
	04 (271 images)	561	421	74.83%
	05 (2761 images)	672	450	69.82%
	06 (1101 images)	539	383	71.32%
	07 (1101 images)	750	446	63.97%
	08 (4071 images)	658	460	71.65%
	09 (1591 images)	581	434	75.27%
	10 (1201 images)	652	454	73.35%

  Table II lists the results of the rotation estimation and Table III lists the results for the translation estimation. In this experiment the relative rotations and translations between two consecutive images are compared to the ground truth relative poses. The tables show the median error for each

			0.2					Forward motion						0.2					Sideways motion
			0.18			2pt method	1.5pt method		1pt sampling method			0.18			2pt method	1.5pt method	1pt sampling method
			0.16													0.16
	(a)	Translation error (degree)	0.06 0.08 0.1 0.12 0.14											(b)	Translation error (degree)	0.06 0.08 0.1 0.12 0.14
			0.04													0.04
			0.02													0.02
				0														0
					0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1				0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1
								Noise standard deviation (pixel)										Noise standard deviation (pixel)
				16					Forward motion							12					Sideways motion
							2pt method	1.5pt method		1pt sampling method							2pt method	1.5pt method	1pt sampling method
				14
																		10
	(c)	Translation error (degree)	4 6 8 10 12											(d)	Translation error (degree)	4 6 8
				2														2
				0	0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1			0	0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1
								Rotation Noise in Degree (Roll)										Rotation Noise in Degree (Roll)
				35					Forward motion							40					Sideways motion
							2pt method	1.5pt method		1pt sampling method							2pt method	1.5pt method	1pt sampling method
				30														35
	(e)	Translation error (degree)	10 15 20 25											(f)	Translation error (degree)	10 15 20 25 30
				5														5
				0	0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1			0	0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1
								Rotation Noise in Degree (Pitch)										Rotation Noise in Degree (Pitch)

TABLE II ROTATION

 II ERROR FOR KITTI SEQUENCES [DEGREES].

	Seq.	0.5pt method Histogram voting	5pt	2pt
	00	0.060	0.051	0.13 0.24
	01	0.073	0.063	0.12 0.23
	02	0.068	0.057	0.12 0.26
	03	0.068	0.057	0.11 0.21
	04	0.074	0.030	0.11 0.17
	05	0.049	0.032	0.11 0.21
	06	0.073	0.050	0.11 0.21
	07	0.052	0.034	0.11 0.19
	08	0.051	0.037	0.12 0.19
	09	0.079	0.094	0.12 0.24
	10	0.059	0.048	0.12 0.22
	individual sequence. For rotation estimation the RANSAC
	variant and the histogram voting scheme was tested. For the
	RANSAC variant a fixed number of 100 iterations with an
	inlier threshold of 2 pixels has been used. For the histogram
	voting a rotation hypothesis is computed for every point
	correspondence exhaustively and entered into a histogram.

TABLE III TRANSLATION

 III ERROR FOR KITTI SEQUENCES [DEGREES].

	Seq.	1.5pt lin 1pt h	1pt d 1pt s	5pt	2pt
	00	4.23	1.90	1.64	1.58	1.93	8.03
	01	7.34	2.01	1.18	1.20	1.41	10.74
	02	3.68	1.83	1.53	1.54	1.53	6.47
	03	4.69	2.13	1.88	2.58	2.12	8.61
	04	2.64	0.95	0.88	0.92	1.19	5.45
	05	3.92	1.57	1.37	1.34	1.67	7.90
	06	4.02	1.27	1.20	1.12	1.37	5.57
	07	4.89	2.20	1.82	1.89	2.37	10.09
	08	4.23	2.17	1.86	1.84	2.06	7.41
	09	4.20	2.04	1.53	1.53	1.54	7.20
	10	3.90	1.78	1.61	1.58	1.73	7.39

TABLE IV INLIER

 IV RECOVERY RATE FOR ALL KITTI SEQUENCES.

	Seq.	1.5pt lin	1pt h	1pt d	1pt s	5pt	2pt
	all	88.47%	96.97%	98.29%	96.51%	98.27%	84.37%

ACKNOWLEDGMENT

This work has been partially funded by CopTer Project of Grands Réseaux de Recherche Haut-Normands.


Fabrice Dupuis

Aurélie Lelièvre

Sandra Pelletier

Tatiana Thouroude

Julie Bourbeillon

Sylvain Gaillard

PREMS / ELVIS : A local plant biological resource management system ELVIS PREMS

PREMS / ELVIS : A local plant biological resource management system

Fabrice 1 , Aurélie LELIÈVRE , Sandra PELLETIER 1 , Tatiana THOUROUDE 1 , Julie BOURBEILLON 1 and Sylvain GAILLARD 1

The management of biological resources collection is a major key for quality of research results. It is also mandatory to keep trace from data to studied organism through every experimental steps including sampling, culture conditions and description of the subject of the study. To achieve this goal in the context of plant science, there are some notable software such as Doriane Labkey and GreenGlobal. After evaluating these solutions with other laboratories we ended with the conclusion that, for different reasons, neither fulfill our needs especially when dealing with perennial plants such as fruit trees (apple or pear trees) or ornamental bush (rose). We then decided to provide our own solution based on the needs and feedbacks from the different teams of the IRHS in the fields of biological resources management, breeding, genetics, molecular biology, physiology and phenotyping.

We introduce here two pieces of software:

-ELVIS: an information system that takes care of data management and provides an extensible set of python libraries to interact with. These libraries are used here to provide a JSON-RPC API exposed as web services. This is the foundation of the LIMS of our laboratory.

-PREMS: a dynamic web interface for biological resources management. This is one of the interfaces developed to interact with ELVIS.

Plant management:

-

ELVIS

Qooxdoo libraries

PREMS

PREMS

The plant resource management system

Multi-criteria Variety search gives a list of Varieties. A selection in that list displays a detailed view of the Lots and Accessions for that Variety. This view provides quick access to denomination and passport data.

On Lots, the view gives access to phenotyping notations and location of the plants or the seeds bag. The user can also enter new notations.

ELVIS and PREMS are made available to the community through the SourceSup forge under CeCILL license. ELVIS can provide access to the data by implementing compatible API to interact with other tools. For instance, we are deploying a PHIS installation with the integration of IRHS team in the PHENOM project and are working on ways to make the two applications interact.

https://sourcesup.renater.fr/projects/elvis/ https://sourcesup.renater.fr/projects/prems/

ELVIS PREMS

1

  IRHS, INRA, AGROCAMPUS-Ouest, Université d'Angers, SFR 4207 QUASAV, 42 rue Georges Morel, 49071 Beaucouzé Cedex,