Basilio Calderone
email: basilio.calderone@univ-tlse2.fr

Nabil Hathout
email: nabil.hathout@univ-tlse2.fr

Franck Sajous
email: franck.sajous@univ-tlse2.fr

From GLÀFF to PsychoGLÀFF: a large psycholinguistics-oriented French lexical resource

Keywords: French lexicon, lexical resource for psycholinguistic studies, Wiktionary

In this paper, we present two French lexical resources, GLÀFF and PsychoGLÀFF. The former, automatically extracted from the collaborative online dictionary Wiktionary, is a large-scale versatile lexicon exploitable in Natural Language Processing applications and linguistic studies. The latter, based on GLÀFF, is a lexicon specifically designed for psycholinguistic research. GLÀFF, counting more than 1.4 million entries, features an unprecedented size. It reports lemmas, main syntactic categories, inflectional features and phonemic transcriptions. PsychoGLÀFF contains additional information related to formal aspects of the lexicon and its distribution. It contains about 340,000 entries (120,000 lemmas) that are corpora-attested. We explain how the resources have been created and compare them to other known resources in terms of coverage and quality. Regarding PsychoGLÀFF, the comparison shows that it has an exceptionally large repertoire while having a comparable quality.

Introduction

Lexical resources play an important role in psycholinguistics by providing researchers with a set of experimentally relevant corpus information concerning words and, to a lesser extent, their sub-lexical components. In particular, psycholinguists working on lexical access need to manipulate a set of formal properties of words, such as syllabification, phonemic transcription, lemmas, inflected forms or orthographic/phonological neighborhood (i.e., the number of words differing from the target word by only one character/phoneme). Word frequency is possibly the most crucial information to be accounted for in psycholinguistic studies, and it is generally provided for either wordforms, lemmas, or both. The most well-known resource for English, German and Dutch is probably CELEX (Baayen et al. 1995). Many other languages, including French, lack a similar resource. Some freely available French morphological lexicons, such as Lefff [START_REF] Clément | Morphology based automatic acquisition of large-coverage lexica[END_REF]) and Morphalou [START_REF] Romary | Standards going concrete: from LMF to Morphalou[END_REF]), contain inflected forms, lemmas and morphosyntactic tags. These resources, designed in the first place for natural language processing (NLP) or lexicography do not include, however, phonemic transcriptions that are necessary to set up psycholinguistics experiments, for extensive morphology and in the design of tools such as phonetizers. One noticeable exception is Lexique [START_REF] New | Lexique 3: Une nouvelle base de données lexicales[END_REF]), a free lexicon quite popular in psycholinguistics. This lexicon includes phonemic transcriptions, word frequencies and various features relevant to this field. However it has a limited coverage, especially in terms of inflected forms. All other resources that have both exploitable coverage and phonemic transcriptions, such as BDLex [START_REF] Pérennou | BDLEX lexical data and knowledge base of spoken and written French[END_REF], ILPho (Boula De Mareuil et al. 2000) or GlobalPhone [START_REF] Schultz | GlobalPhone: A multilingual text & speech database in 20 languages[END_REF] are not free. Besides their cost, derivative works cannot be redistributed, which constitutes an impediment for collaborative research. As of today, no French lexicon meets all following requirements: free license, wide coverage, phonemic transcriptions and word frequencies. In this article, we present a psycholinguistics-oriented resource based on Wiktionnaire,1 the French edition of Wiktionary. In a previous work (Sajous et al. 2013a), we automatically extracted GLÀFF, "a Large Versatile French Lexicon". This large-scale resource contains, for each entry, inflectional and phonemic information. PsychoGLÀFF is a new step leveraging Wiktionnaire's content.2 Grounded on GLÀFF, PsychoGLÀFF is a lexicon that contains additional features specifically designed for meeting psycholinguistic needs. The paper is organized as follows: Section 2 gives an overview of Wiktionnaire and its features relevant to lexical resources building. GLÀFF is then described in Section 3. Finally, we present in Section 4 PsychoGLÀFF, a lexicon designed for psycholinguistics use and compare it to Lexique in terms of coverage and word frequency. Conclusions and future directions of work are discussed in Section 5.

Wiktionnaire as a source of lexical knowledge

Wiktionary is a free multilingual dictionary available online. As its mother project Wikipedia, Wiktionary is based on the wiki paradigm: every internet user may contribute by adding content or modifying existing one. Launched in 2003, the Wiktionary project boasts, ten years later, more than two million entries for its French language edition, the Wiktionnaire. The impressive size of its headword list has to be tempered: inflected forms, discussion pages and, more surprisingly, "pages describing in French words from other languages" are counted as regular entries. However, once these latter entries excluded, Wiktionnaire still accounts for 1.4 million entries (186,000 lemmas). While Wikipedia has been extensively used in various disciplines, its lexicographic counterpart seems to have received less attention from the scientific community. Wiktionary was first used in NLP by [START_REF] Zesch | Extracting Lexical Semantic Knowledge from Wikipedia and Wiktionary[END_REF] to compute semantic relatedness. Its potential as an electronic lexicon was studied for the first time by [START_REF] Navarro | Wiktionary and NLP: Improving synonymy networks[END_REF] for French and English synonymy mining. Along the same line of research, Anton Perez et al. (2011) realized the integration of the Portuguese edition of Wiktionary in the ontology Onto.PT (Gonçalo Oliveira and Gomes 2010). Serasset (2012) designed Dbnary, an open-source resource containing "easily extractable entries". The French subpart of this resource contains 260,467 entries. Works led by [START_REF] Meyer | OntoWiktionary -Constructing an Ontology from the Collaborative Online Dictionary Wiktionary[END_REF] and [START_REF] Gurevych | UBY -A Large-Scale Unified Lexical-Semantic Resource Based on LMF[END_REF] resulted in German and English ontologies based on Wiktionary. [START_REF] Sajous | Semi-automatic Endogenous Enrichment of Collaboratively Constructed Lexical Resources: Piggybacking onto Wiktionary[END_REF] has made available a structured XML version of this lexicon for French and English, called WiktionaryX. 3Although Wiktionnaire presents interesting features (unprecedented coverage, definitions, phonemic transcriptions, semantic relations, translations, free license),4 the information it contains is difficult to extract. This probably explains the relatively small number of works using it. Wiktionnaire, as other Wiktionary's language editions, is released as an "XML dump", where XML only marks the macrostructure. The microstructure is encoded in a format called wikicode, inherent in the content management system MediaWiki. This format has no formally defined syntax, evolves over time, and is not stable from one language edition to another. This underspecified syntax makes therefore the automatic information extraction from the collaborative dictionary uneasy: multiple deviations from a "prototypical article" should be expected, as well as missing information, redundancy and inconsistency. Figure 1 shows the entry affluent (adjective and noun 'affluent', and two inflection forms of the verb affluer 'to flow into/to pour in') as it is visible in Wiktionnaire. The corresponding wikicode of this article is shown in Figure 2. Inflected forms may appear in the article related to their lemma (as it is the case in Figure 1). They may also have a dedicated page (cf. Figures 3 and4).

The table of the adjective inflected forms (top-right in Figure 1) is not explicitly present in the wikicode, but is generated by the template {{fr-accord-cons|a.fly.ɑ|t}} (cf. Figure 2). There are hundreds of similar patterns in the wikicode. An example of the non-systematic wikicode's format and resulting article's layout can be seen in Figure 3: unlike the template {{f}} that defines the feminine gender of the form, there is no template specifying the grammatical number. The number can only be extracted by parsing the definition "Féminin singulier". The heterogeneity of the wikicode also concerns the phonemic transcriptions: they occur sometimes in the Ligne de forme (the line following the part of speech heading), as in Figure 3 for 'affluente', and sometimes, on the contrary, they are specified in a separate "Prononciation" section as in Figure 4 for 'affluentes'.

To build GLÀFF and PsychoGLÀFF, we automatically extracted the inflected forms and lemmas in their dedicated pages, and detected the inflection templates. We also identified the phonemic transcriptions wherever they occur. We finally parsed the conjugation tables (cf. Figure 5). We thus collected as much (possibly redundant) information as possible and applied some heuristics to automatically detect major inconsistencies.

GLÀFF

In this section, we summarize some relevant characteristics of GLÀFF, first introduced in (Sajous et al. 2013a), from which PsychoGLÀFF is derived. The latest version of GLÀFF includes nouns, verbs, adjectives, adverbs, and function words. As can be seen in Figure 6, GLÀFF specifies for each entry:

• the wordform; • the lemma; • the part of speech and morphosyntactic features in GRACE format [START_REF] Rajman | Format de description lexicale pour le francçais. Partie 2 : Description morpho-syntaxique[END_REF]); • the phonological transcription(s) (when specified in Wiktionnaire) in IPA and in SAMPA with syllable boundaries.

Figure 6: Extract of GLÀFF

Coverage

GLÀFF differs from the lexicons currently used in NLP and psycholinguistics by its exceptional size. Table 1 shows the number of inflected forms and lemmas for simple words (only letters) and non-simple words (containing spaces, dashes or digits) in five different French lexicons. GLÀFF contains from 3 to 4 times more tokens and from 3 to 9 times more inflected forms than the other lexicons. Table 2 reports the intersection of GLÀFF with the other lexicons. We observe that the magnitude of the intersection depends on the size of the lexicons: the bigger a lexicon, the larger its intersection with the other ones. Three groupings emerge: Lexique has the smallest coverage, only containing 9% of GLÀFF and 22% to 26% of the entries of the other lexicons. BDLex, Lefff and Morphalou cover 76% to 80% of Lexique and about 30% of GLÀFF. Finally GLÀFF is clearly on top with coverage of 85% to 93%. In total, its coverage is 5% to 65% higher than the other lexicons. The vocabulary is restricted to the forms that occur at least once, 2, 5, 10, 100 and 1000 times. The ranking of the corpora by coverage is the same for the five lexicons. Although their size affects the order, their nature is also crucial. For example, FrWaC being a collection of web pages, it contains a large number of "noisy" forms (foreign words, missing or extra spaces, missing diacritics, random spelling, etc.). Again, we see the division of lexicons into three groups. BDLex, Lefff and Morphalou have a quite close coverage. Except for Frantext 20 e , Lexique has the smallest coverage. GLÀFF has the largest coverage for all corpora, except for LM10 at the 1000 threshold where it is surpassed by Lefff by 0.2%. The best coverage of Lexique for the Frantext 20 e corpus, above the 10 threshold, while it has the weakest coverage in all other cases, is explained by the design of its vocabulary, extracted from this corpus. For the other corpora and up to the 100 threshold, the size of GLÀFF explains its larger coverage with respect to the other lexicons (at the threshold 1, 14% to 53% larger for LM10 and 30% to 120% larger for FrWaC; at the threshold 10, 4% to 16% for LM10 and 15% to 47% for FrWaC). NLP tools that integrate GLÀFF should therefore offer an improved performance in the treatment of these corpora. In a qualitative study described in [START_REF] Sajous | Ne jetons pas le Wiktionnaire avec l'oripeau du Web ! Etudes et réalisations fondées sur le dictionnaire collaboratif[END_REF], we observed that GLÀFF specific entries contains not only rare neologisms, but also very common words such as attractivité 'attractivity', brevetabilité 'patentability', diabolisation 'demonization', employabilité 'employability', homophobie 'homophobia', hébergeur 'host', fatwa, institutionnellement 'institutionally', anticorruption 'anti-corruption', etc. missing from the other lexicons.

Phonemic transcriptions

GLÀFF provides a phonemic transcription for about 90% of the entries. We evaluated the consistency of these transcriptions with respect to those of BDLex and Lexique (after conversion into IPA encoding). Tables 4a to 4c report the top ten variations between pairs from the three lexicons. We only considered one phoneme differences, ignoring syllabification. The differences in transcriptions between GLÀFF and the other two lexicons are comparable to the differences observed between BDLex and Lexique. In particular, these differences are mostly due to the distinctions between the mid vowels, i.e. the front-mid vowels: -mid). This alternation is a well-known aspect of French phonology resulting from diatopic variations (North vs. South), as described in [START_REF] Detey | Les variétés du français parlé dans l'espace francophone[END_REF]. Such expected oppositions account for about 91% of the divergences between BDLex and Lexique. Table 5 reports the percentage of identical phonological transcriptions shared by the lexicons and the percentage of the 'comparable' phonological transcriptions, i.e. disregarding the distinction between close-mid and open-mid vowels. GLÀFF and Lexique give identical transcriptions for 79.5% of entries whereas the percentage between GLÀFF and BDLex is lower, at 61.7%. Table 5 also reports the results of the comparison of syllabification in the three lexicons (performed on the basis of identical transcriptions only). This comparison shows that the three lexicons are quite similar with respect to syllabification (98%).

Comparing GLÀFF with the major resources that contain the same type of information clearly shows that the overall quality of the lexicon is quite satisfactory and is in all respect comparable to those of these resources.

Oper

Overview

Our goal in creating PsychoGLÀFF is to provide psycholinguists with a set of features related to the formal aspects of the lexicon entries. For this purpose, we selected from GLÀFF only forms having non-zero frequency in at least one of the corpora mentioned in section 3.1. This means that PsychoGLÀFF only contains lexical entries attested in the corpora, amounting to about 340,000 forms for 120,000 lemmas.

In addition to GLÀFF's features, PsychoGLÀFF includes the following information for each entry:

• the absolute and relative frequencies of the wordform and of the lemma in the aforementioned French corpora (Frantext 20 e , LM10 and FrWac); • the length of the wordform (number of characters); • the length of the phonological transcription(s) (number of phonemes); • the syllabification and the CV structure of the wordform; • the number of syllables; • the geometric mean of the conditional character probabilities of bigrams, which calculates the probability of the bigram occurring given the preceding bigram; • the geometric mean of the conditional character probabilities of trigrams, which calculates the probability of the trigram occurring given the preceding trigram; • the geometric mean of the conditional character probabilities of 4-grams, which calculates the probability of the 4-gram occurring given the preceding 4-gram; • the geometric mean of the conditional phoneme probabilities respectively calculated for bigrams, trigrams and 4-grams.

•

the size of the orthographic neighbourhood, i.e. the number of words in the lexicon differing by one character (via deletion, insertion, or substitution); • the size of the phonological neighborhood, i.e. the number of words differing from the phonological transcription by one phoneme (via deletion, insertion, or substitution); • the size of the ratio between the number of consonants and syllables composing the phonological form. This score is meant to provide an estimate of the 'syllabic complexity' of the form.

The n-gram conditional probability represents a measure of phonotactic occurrence, defining the likelihood of occurrence of n-grams in French. This kind of measure is expected to be particularly helpful for the design of experimental stimuli in lexical access experiments [START_REF] Storkel | The influence of part-word phonotactic probability/neighborhood density on word learning by preschool children varying in expressive vocabulary[END_REF].

Comparison with Lexique

We compare hereafter, in terms of coverage and word frequencies, PsychoGLÀFF and Lexique, the most frequently used French lexicon in psycholinguistics.

Being directly extracted from GLÀFF, PsychoGLAFF stands out with respect to the lexicons currently used in psycholinguistics mostly for its size, as it counts 337,572 entries. Table 6 shows the number of inflected forms and lemmas of Lexique and PsychoGLAFF. The relative coverage of these lexicons is reported in We observe that PsychoGLÀFF is more than twice larger than Lexique (for both inflected forms and lemmas) and has a total coverage of about 79% with respect to Lexique (which covers only 36.1% of the inflected forms of PsychoGLÀFF). PsychoGLÀFF reports the absolute and relative frequencies for its wordforms and lemmas. Frequencies are calculated on the basis of three stylistically different corpora of written French: the abovementioned Frantext20 e , LM10 and FrWaC (literature, newspaper and web corpora). Lexique reports word frequency estimates too. It exploits two smaller corpora: a) a written corpus made up of 218 books from Frantext 20 e ; b) a corpus of French subtitles for 9,474 movies and television series, assumed to be more representative of spoken French. While GLÀFF and PsychoGLÀFF frequencies are exclusively based on written French, Lexique mixes together spoken-like and written resources for the calculation of wordform and lemma frequencies. Although the corpora used by the two lexicons have very different sizes, we attempted a comparison of the PsychoGLÀFF's frequencies with respect to the frequencies reported in Lexique, looking only at the intersection of the two lexicons. Table 8 reports the correlation between the normalized frequencies of wordforms in PsychoGLÀFF (separately for Frantext, LM10 and FrWac) and Lexique (separately for books and movie subtitles). The data were normalized by one million words. It is not surprising that the correlation between Frantext's frequencies and Lexique's book frequencies is quite high (Pearson's coefficient ρ = .81), the latter being a sub-corpus of Frantext 20 e . Although PsychoGLÀFF frequencies are based exclusively on written corpora, we found a statistically significant correlation ρ = .68 between Lexique's subtitle frequencies and the Frantext frequencies (the value slightly decreases for the subtitles/FrWac correlation). This seems indicate that the lexical coverage of PsychoGLÀFF, though based on written sources, is comparable to a relevant extent to the coverage of corpora specifically devoted to spoken French. An additional property of PsychoGLÀFF worth noting to is the presence of infrequent lexical items. This feature clearly derives from the nature of Wiktionnaire: being an online dictionary, it has not to conform to the same size constraints as printed ones. Bootstrapped by importation of articles from public domain dictionaries, it contains dated entries. Finally, being crowdsourced, it is regularly updated and contains general-domain neologisms, as well as subculture vocabulary and technical terms [START_REF] Sajous | Ne jetons pas le Wiktionnaire avec l'oripeau du Web ! Etudes et réalisations fondées sur le dictionnaire collaboratif[END_REF]). As a consequence, PsychoGLÀFF contains a large number of specific entries. The bigger the corpus, the more low-frequency lexical items are likely to be included (while the size of the corpus is not likely to have a strong impact on the number of those words that are frequent or very frequent in a language, representing to a certain extent the 'essential lexicon' of that language). The Figure 7 illustrates this point by showing the distribution of different frequency intervals for both Lexique's and PsychoGLÀFF's sub-corpora. A normalized frequency range of 10.01 or more corresponds to very high words frequency and is situated at the right edge of the graph. A frequency range of 0.01-0.1 corresponds to very low words frequency and is situated at the left edge of the figure.

Lexique

Six intermediate ranges capture the frequency differences of the entire lexicon. The figure shows that the distribution of the frequency intervals is approximately the same for Lexique and PsychoGLÀFF, with the significant exception of the least frequent word class (< 0.2), for which the number of lexical items in PsychoGLÀFF is almost twice as large as that of Lexique. At the same time, PsychoGLÀFF contains many words of ordinary usage that are absent from Lexique, such as acceptabilité 'acceptability', centralité 'centrality', Saturne 'Saturn', etc. In this sense PsychoGLÀFF offers a much larger lexical repertoire not only in terms of tokens, but also in terms of types, which represents a particularly interesting feature for psycholinguistic studies and corpus investigations.

Conclusions and future directions

This paper presents a first version of PsychoGLÀFF, a large lexicon designed for psycholinguistic experimentation.

PsychoGLÀFF was built on top of the and phonemic lexicon GLÀFF, itself acquired from Wiktionnaire, the French edition of the collaborative dictionary Wiktionary. In particular, PsychoGLÀFF contains the subset of GLÀFF's corpora-attested entries. This resource complements the inflectional and phonological information present in GLÀFF with features needed for experimental material calibration including frequency, lexical neighborhood, syllabic complexity and phonotactic likelihood. Like GLÀFF, PsychoGLÀFF is characterized by an exceptional coverage, much higher than those of comparable resources as Lexique on one hand and Morphalou and Lefff on the other. We also show that the "primary" information (parts of speech, phonemic transcriptions, frequency) of PsychoGLÀFF and GLÀFF has a satisfactory quality. PsychoGLÀFF is a free resource distributed under a copylefted license and is available to all psycholinguistic researchers working on French. We hope that it will soon be adopted by this community whose feedback will allow us to improve the resource and appropriately respond to its needs.

In the near future, we plan to improve PsychoGLÀFF on several aspects. One of them will concern the description completeness and consistency of the lexicon. An online interface, comparable to GLÀFFOLI (the GLÀFF OnLine Interface) will also be developed, that will enable users to query the lexicon and develop experimental material interactively.

Figure 1 :Figure 4 :

 14 Figure 1: Article of the word 'affluent' in Wiktionnaire

  [e] (close-mid) vs. [ɛ] (open-mid) and the back-mid vowels: [o] (close-mid) vs. [ɔ] (open

Figure 7 :

 7 Figure 7: Distribution of forms with respect to their corpus frequency.

Table 1 :

 1 Size of five French lexicons (counting only nouns, verbs, adjectives and adverbs).

		Categorized inflected forms	Categorized lemmas
		Simple	Non simple	Total	Simple Non simple	Total
	Lexique	147,912	4,696	152,608	46,649	3,770	50,419
	BDLex	431,992	4,360	436,352	47,314	1,792	49,106
	Lefff	466,668	3,829	470,497	54,214	2,303	56,517
	Morphalou	524,179	49	524,228	65,170	7	65,177
	GLÀFF	1,401,578	24,270 1,425,848 172,616	13,466 186,082

  up of the archives of the newspaper Le Monde from 1991 to 2000. The third corpus, containing 260 million words, consists of the articles from the French Wikipedia. Finally, FrWaC(Baroni et al. 2009) is a 1.6 billion words corpus of French web pages. Table3shows the coverage of the five lexicons with respect to the four corpora.

	Threshold: frequency ≥	1	2	5	10	100	1000
		#forms	145,437	95,189	61,813	43,919 10,767	1,376
		Lexique	66.76	84.35	94.00	96. 91	99.15	99.27
	Frantext	BDLex Lefff	70.86 71.89	84.69 85.63	92.47 93.21	95.74 96.21	99.12 99.08	99.20 98.90
		Morphalou	73.93	86.66	93.29	96.00	98.48	97.09
		GLÀFF	76.92	88.57	94.54	96.72	98.77	98.76
		#forms	300,606 172,036 106,470	77,936 29,388	83.21
		Lexique	29.59	47.28	65.23	76.31	93.81	98.58
	LM10	BDLex Lefff	37.77 39.64	55.79 58.22	71.76 74.33	80.93 83.20	95.53 95.99	98.69 98.90
		Morphalou	39.06	56.82	71.92	80.32	93.27	97.48
		GLÀFF	45.24	63.83	78.63	86.23	96.46	98.68
		#forms	953,920 435,031 216,210 136,531 35,621	7,956
		Lexique	9.13	18.27	31.52	43.03	78.58	95.72
	Wikipedia	BDLex Lefff	12.29 12.88	22.89 23.94	36.80 38.26	48.04 49.65	79.39 80.57	95.33 95.71
		Morphalou	13.05	23.96	37.87	48.87	78.74	94.16
		GLÀFF	16.42	29.00	44.13	55.45	83.21	96.10
		#forms	1,624,620 846,019 410,382 255,718 74,745 22,100
		Lexique	5.83	10.85	20.84	30.81	66.00	89.47
	FrWaC	BDLex Lefff	9.36 9.85	15.85 16.67	27.28 28.57	37.48 39.16	69.61 71.61	90.03 91.16
		Morphalou	10.09	16.89	28.53	38.68	69.36	88.51
		GLÀFF	13.13	21.13	34.29	45.35	76.39	92.76
			Lexique BDLex Lefff Morphalou GLÀFF
		Lexique	-	26.03 25.20	22.46	8.95
		BDLex	76.02	-79.87	70.40	28.75
		Lefff	79.50	86.28	-	72.32	30.04
		Morphalou	79.58	85.43 81.24	-	32.03
		GLÀFF	84.83	93.26 90.23	85.66	-

Table 2: Intersection of five French lexicons (% of the categorized inflected forms).

Size is a crucial aspect of the lexicons used for research in derivational and inflectional morphology or, more generally, in the development of NLP tools such as morphosyntactic taggers and parsers. In order to asses that GLÀFF's largest size is actually useful, we compared the five lexicons with the vocabulary of four corpora of various types. Frantext 20 e is constituted by 515 novels of 20th century French literature containing 30 million words. LM10 is a 200 million word corpus made Table 3: Lexicon/corpus coverage (% of non-categorized inflected forms).

Table 4 :

 4 The 10 most frequent differences in phonemic transcriptions (Operations: r = replacement, i = insertion, d = deletion)

			Phonemic transcriptions Syllabification
	Lexicons	Intersection Identical Comparable	Identical
	BDLex Lexique	112,439	58.31	96.88	98.92
	GLÀFF Lexique	123,630	79.50	97.81	98.48
	GLÀFF BDLex	396,114	61.72	96.88	98.30

Table 5: Inter-lexicon agreement: phonemic transcriptions and syllabification 4 From GLÀFF to PsychoGLÀFF

Table 7 .

 7

		Categorized inflected forms Categorized lemmas	Lexique PsychoGLÀFF
	Lexique	153,934	50,419	Lexique	36.1 %
	PsychoGLÀFF	337,572	121,021	PsychoGLÀFF 78.9 %

Table 6 :

 6 Size of Lexicons (restricted to nouns, verbs, adjectives and adverbs)

Table 7 :

 7 Lexicons relative coverage (% of categorized inflected forms)

Table 8 :

 8 PsychoGLÀFF/Lexique correlations with respect their normalized frequency values

			Subtitles Books
		Frantext	.68	.81
	PsychoGLÀFF	LM10	.62	.59
		FrWac	.67	.62

http://fr.wiktionary.org

GLÀFF and PsychoGLÀFF are freely available from the REDAC website: http://redac.univ-tlse2.fr/lexicons/

WiktionaryX, is an XML version of the English and French editions of Wiktionary, freely available at http://redac.univ-tlse2.fr/lexiques/wiktionaryx.html

For a more comprehensive description of the Wiktionnaire, see[START_REF] Navarro | Wiktionary and NLP: Improving synonymy networks[END_REF]) and[START_REF] Sajous | Semi-automatic Endogenous Enrichment of Collaboratively Constructed Lexical Resources: Piggybacking onto Wiktionary[END_REF][START_REF] Sajous | Semi-automatic enrichment of crowdsourced synonymy networks: the WISIGOTH system applied to Wiktionary[END_REF].

Anton Pérez, L., Gonçalo Oliveira, H., and Gomes, P. (2011). Extracting Lexical-Semantic Knowledge from the Portuguese Wiktionary. In Proceedings of the 15th Portuguese Conference on Artificial Intelligence, pp. 703-717, Lisboa, Portugal. Baayen, R. H., Piepenbrock, R. and Gulikers, L. (1995). The CELEX lexical database (CD-ROM). Philadelphia: Linguistic Data Consortium. Baroni, M., Bernardini, S., Ferraresi, A. and Zanchetta, E. (2009). The WaCky wide web: a collection of very large linguistically processed web-crawled corpora. Language Resources and Evaluation, 43(3): 209-226. Boula De Mareuil, P., Yvon, F., D'Alessandro, C., Aubergé, V., Vaissière, J., and Amelot, A. (2000). A French Phonetic Lexicon with variants for Speech and Language Processing. In Proceedings of the Second International


Jean-Marie Mirebeau

Jérôme Fehrenbach

Laurent Risser

Shaza Tobji

Shaza Tobji Anisotropic

Anisotropic Diffusion in ITK

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

A digital image is usually a large two or three dimensional array of pixel values (typically scalars or vectors). Image processing methods based on Partial Differential Equations (PDEs) regard images as approximations of continuous objects, namely functions from an image domain to a pixel space, to which physics-inspired evolution rules can be applied. Among them, Non-Linear Anisotropic Diffusion (NLAD) is a variant of the heat equation, generalized in two regards: Non-Linearity and Anisotropy.

Anisotropy in diffusion means that the smoothing induced by the PDE can be favored in some directions and prevented in others. This is specified by local eigenvectors and eigenvalues of the diffusion tensor field (see §2). Diffusion coefficients are thus location and direction dependent, generalizing the approach of Perona and Malik [START_REF] Perona | Scale-space and edge detection using anisotropic diffusion[END_REF] which is only location dependent. Importantly, efficient schemes for anisotropic diffusion have been recently made possible by the breakthrough in [START_REF] Fehrenbach | Sparse Non-negative Stencils for Anisotropic Diffusion[END_REF]. This has motivated the development of the ITK module presented in this paper.

Non-Linearity in diffusion means that diffusion tensors are automatically generated from the processed image. We implemented the strategies of Weickert [START_REF] Weickert | Anisotropic diffusion in image processing[END_REF] and we give a simple framework for designing extensions and variants, see §3. The implemented filters and their parameters are described in §4. Figures 2 and3 illustrate their effect on 2D images; Figures 4 and5 on 3D images; Figures 6 and7 on color and vector images.

A possible application of NLAD is to enhance a fingerprint image by smoothing tangentially to the lines. Evidence is also plentiful for NLAD relevance in many other image processing applications, but its use has been limited by technical aspects so far. We intend to alleviate such limitations with the present contribution.

Notations: Let d ∈ {2, 3} denote the image dimension, let Ω ⊂ R d be the image domain, and let V be the pixel space (e.g. [0, 1] for grayscale, [0, 1] 3 for color, R d for vectors). Throughout the paper, we informally consider an idealized cartoon image model, involving a set Γ ⊂ Ω of image contours of dimension d -1. The processed image u : Ω → V is smooth on Ω \ Γ, but has discontinuities across Γ, and is overall corrupted by e.g. by additive white noise. A key feature of NLAD is its ability to detect the set Γ and smoothen tangentially to it.

Linear Anisotropic diffusion

Linear Anisotropic Diffusion1 (LAD), in divergence form, is an elliptic PDE which reads

∂ t u = div(D ∇u), (1)
where D : Ω → S + d is a given field of symmetric positive definite diffusion tensors. Eigenvectors of these tensors define preferential diffusion directions, and the eigenvalues their corresponding coefficients. Evolution rule (1) is complemented with an initial condition u(0, •) = u 0 at time t = 0. If u 0 has pixels of vector type, then their components are treated independently. We use Neumann2 conditions on the domain boundary ∂Ω, as is common in image processing. LAD is formally a continuous gradient descent for the elliptic energy

E(u) := Ω ∇u(x) 2 D(x) dx. (2)
Qualitative effects of LAD strongly depend on the chosen field D of diffusion tensors. Choosing D = Id identically on Ω yields the standard heat equation, which qualitative properties are well known in image analysis: any noise present in the image u is quickly eliminated, but in the meanwhile all image sharp features are blurred. This undesirable side effect can be limited with a proper choice of diffusion tensors D : Ω → S + d . Indeed LAD smoothes primarily the image features which contribute strongly to the energy (2). In the spirit of Perona and Malik, one can introduce an isotropic but variable conductivity D(x) = c(x) Id, with c(x)

1 for all x close to the image contours Γ, see introduction. Smoothing is prevented in the neighborhood of Γ, which preserves the contours sharpness, but also traps some noise along them, see Figure 2 (IV). A more elaborate approach is to construct anisotropic diffusion tensors D(x), which favor diffusion tangentially to the contours curves Γ, but simultaneously prevent diffusion transversally to these curves and between different image regions. All noise is eliminated, yet image discontinuities are preserved, see Figure 2 (II).

Numerical schemes for LAD are in general non-trivial due to interaction between the anisotropic geometry of the diffusion tensors, and the cartesian structure of the pixel grid. The authors recently developed [START_REF] Fehrenbach | Sparse Non-negative Stencils for Anisotropic Diffusion[END_REF] a numerical scheme which handles this interaction using special tools from discrete geometry, named Lattice Basis Reduction (LBR). It provides strong mathematical guarantees (consistency, stability, maximum-principle) for a limited numerical cost.

3 Non-Linear Anisotropic Diffusion.

Linear Anisotropic Diffusion, discussed in §2, requires two main inputs: an image u 0 serving as an initial condition, and a field of diffusion tensors. In order to reduce user input, the diffusion tensors D can be defined in terms of the filtered image u. The resulting PDE is called non-linear anisotropic diffusion

∂ t u = div(D u ∇u), (3)
complemented, again, with Neumann boundary conditions. Perona and Malik [START_REF] Perona | Scale-space and edge detection using anisotropic diffusion[END_REF] suggested to use the following non-linear isotropic (i.e. proportional to the identity matrix) tensors

D u (x, t) := c u (x, t) Id, with c u (x, t) := 1 1 + ∇u(x, t) 2 /λ 2 , (4)
where λ > 0 is a user specified constant. Diffusion is prevented where the conductivity c u (x, t) is small, in other words where ∇u(x, t) is large, such as along the image contours Γ. Perona-Malik diffusion is already available3 in ITK. It has been the subject of considerable academic and industrial interest revealing that, in spite of its numerous qualities, it is mathematically ill posed, unstable, often leads to unsightly "staircasing" visual artifacts, and is not adequate for oscillating patterns as in Figure 3. We describe in the following Coherence Enhancing Diffusion (CED) and Edge Enhancing Diffusion (EED), which are based on more complex tensor constructions introduced by Weickert [START_REF] Weickert | Anisotropic diffusion in image processing[END_REF]. Our first ingredient is the Gaussian convolution kernel: given a standard deviation σ > 0

K σ (x) := 1 σ d K 1 x σ , where K 1 (x) := 1 (2π) d exp -x 2 2 . ( 5
)
The structure tensor S u : Ω → S + d , defined below, is a robust estimator of the gradient direction in an image u, even if this image has oscillating textures. It depends on two small positive parameters: the noise scale σ, and the feature scale ρ. We denote by * the convolution operator, and by v ⊗ v = vv T the self outer product, which yields a semi-definite symmetric matrix.

S u := K ρ * (∇u σ ⊗ ∇u σ ),
where

u σ := K σ * u. ( 6
)
If u is an image with vector pixels, then S u is the sum of the structure tensors associated to the components of u. Assume that u is a scalar image, fix a time t and a point x ∈ Ω, and denote S := S u (x, t), v := ∇u(x, t). Let also λ 1 ≤ • • • ≤ λ d denote the eigenvalues of S, sorted by increasing magnitude, and e 1 , • • • , e d the corresponding unit eigenvectors. If u is sufficiently smooth, then the largest eigenvalue approximates the gradient squared norm: λ d ≈ v 2 , while the corresponding eigenvector approximates the gradient direction: e d ≈ ± v v . Weickert's diffusion tensors D := D u (x, t), are defined in terms of this eigen-analysis of the structure tensor S := S u (x, t):

D = 1≤i≤d µ i e i ⊗ e i , where S = 1≤i≤d λ i e i ⊗ e i . (7)
Smoothing is promoted in the direction e i if µ i is large, and prevented if µ i is small, for any 1 ≤ i ≤ d. Weickert's classical constructions are presented in (8) and (11). One should not shy away of designing more complex and application dependent variants; for instance one may want to enhance filaments and tubular structures in 3D data. Three very simple variants (9), ( 10) and ( 12) are presented for illustration. All depend on three parameters λ, m, α. The main one, λ > 0, is an edge detection threshold. The exponent m is typically 2 or 4. The small parameter α, typically 1/100, determines the condition number of the diffusion tensors.

• Edge Enhancing Diffusion (EED) aims to avoid significant diffusion across the set Γ of image contours, but to allow it anywhere else. Note that for 3D images discontinuity planes will be enhanced, rather than edges. The first diffusion tensor eigenvalue is µ 1 = 1, because the eigenvector e 1 is orthogonal to the image (approximate) gradient direction e d , hence never transverse to Γ. Other eigenvalues satisfy µ i ≈ α 1 if λ i -λ 1 λ, and µ i ≈ 1 otherwise. The condition λ i -λ 1 λ indeed suggests that the eigenvector e i points through an image contour. Precisely4 : (note that µ 1 = 1)

µ i := 1 -(1 -α) exp - λ λ i -λ 1 m . ( 8
)
The choice of Weickert, to set µ 1 = 1, may lead to undesired effects: one always performs diffusion in at least one direction. An undesirable side effect is that the image is blurred close to the angles of its contour set Γ. We believe that such salient features should be preserved, hence we introduce a Conservative variant of EED (cEED) for which µ 1 can be small, when appropriate, so as to prevent diffusion around the angles of Γ, see Figure 8 for a comparison. Precisely

µ i := 1 -(1 -α) exp - λ λ i m . (9)
If all eigenvalues are set equal µ 1 = • • • = µ d , then the diffusion tensors are isotropic, in other words scalar multiples of the identity. The following isotropic variant of EED is close in spirit to the Perona-Malik model: diffusion is prevented in the neighborhood of the image contours Γ, regardless of direction. This construction is implemented purely for comparison with the anisotropic ones, and does not take advantage of the innovative numerical scheme developed by the authors

µ i := 1 -(1 -α) exp - λ λ d m . (10)
• Coherence Enhancing Diffusion (CED) prevents diffusion except along local image structures which have a coherent direction. The diffusion tensor eigenvalues satisfy µ i ≈ α 1, unless

µ i := α + (1 -α) exp - λ λ d -λ i m . ( 11
)
The above formula often leads to false positives: at a position with large gradients, but without a clear preferred direction, one may very well have λ d -λ i λ (for instance if λ d = 100λ and λ i = 95λ). A more reliable coherence detector is λ m -λ i λ + λ i , which leads to a Conservative variant of CED (cCED), see Figure 8 for a comparison. Precisely: (note that µ d = α)

µ i := α + (1 -α) exp - λ + λ i λ d -λ i m . ( 12
)
We emphasize that the distinction between EED and its conservative variant cEED (resp. CED and cCED) is rather subtle, and mostly located around image contour corners, as evidenced on Figure 8. In other illustrations, we only show the conservative variant, which is slightly better at preserving detail.

Implemented filters and their parameters

Our contribution to ITK consists of the following four image filters, which implement the mathematical notions presented in §2 and §3. The figures are produced with the last filter, which implements CED, EED and their variants described §3. The first three filters are its building blocks, but they may be of independent interest for other applications. All filters are multithreaded.

For each filter, the processed image pixels can be of scalar or vector type. In the latter case, the underlying floating point type needs to be specified via the second template parameter of the filter, see Figure 1 (bottom right). Pixels of integral type (resp. RGB pixels) must be cast to floating point (resp. Vector ) types, see Figure 1. The image dimension must be 2 or 3.

Linear Anisotropic Diffusion (LAD). The filter LinearAnisotropicDiffusionLBRImage-

Filter , requires two inputs: a processed image and a tensor image. Note that non-linear diffusion is achieved through successive linear diffusions, over multiple small time intervals, with regularly updated diffusion tensors. Parameters:

• MaxDiffusionTime specifies the target physical time for the LAD evolution PDE [START_REF] Fehrenbach | Sparse Non-negative Stencils for Anisotropic Diffusion[END_REF]. The filter has early abort options, as discussed in the next point, hence one should check the EffectiveDiffusionTime at termination.

• MaxNumberOfTimeSteps, RatioToMaxStableTimeStep. Explicit numerical schemes for diffusion are subject to a Courant-Friedrichs-Levy (CFL) condition, which limits the largest stable time step. This time step, which depends on the input diffusion tensors, is automatically computed by the filter, and the requested time interval [0, MaxDiffusionTime] is split accordingly. Early abort occurs if this splitting exceeds the specified MaxNum-berOfTimeSteps.

Structure tensor. Filter StructureTensorImageFilter . Parameters:

• NoiseScale σ, and FeatureScale ρ, see (6). Suggested ranges: σ ∈ [0.5, 3], λ ∈ [2, 10], assuming a unit pixel spacing. The lower bounds of these intervals are recommended, unless noise is extremely strong.

• RescaleForUnitMaximumTrace. If on, the structure tensors are rescaled: S u = αS u , where α > 0 is the largest constant such that Trace(S u (x)) ≤ 1 for all x ∈ Ω. (The trace is the sum of the eigenvalues

λ 1 + • • • + λ d , see (7)
.) This option is meant to ease the choice of the edge detection threshold λ in CED, EED. One may want to check the variable PostRescaling = α at termination.

Non-Linear Anisotropic Diffusion (NLAD). Filter AnisotropicDiffusionLBRImageFilter . This class (I) computes structure tensors by invoking the previous filter, (II) performs their eigen-analysis, (III) changes them into diffusion tensors via (7), (IV) runs linear diffusion with the constructed tensors by invoking the first filter. After a limited number of time-steps of linear diffusion, the steps (I-II-III-IV) are repeated so as to update the diffusion tensors, until exhaustion of the prescribed diffusion time. Parameters:

• DiffusionTime for which the evolution rule (3) is applied.

• Adimensionize. If on, the filter ignores the image pixel spacing information, and sets on the RescaleForMaximumUnitTrace option for structure tensor generation. This is intended to ease the choice of DiffusionTime, and of the edge detection threshold λ in CED, EED, and variants.

• MaxTimeStepsBetweenTensorUpdates is self descriptive. NoiseScale and FeatureScale are passed for structure tensor generation.

• EigenValuesTransform is a virtual method used to construct the diffusion tensor eigenvalues (µ i ) d i=i from those of the structure tensors (λ i ) d i=1 , which are sorted increasingly for convenience. The method must be redefined in a subclass, as in the next filter, else it triggers an exception.

Coherence-Enhancing diffusion and Edge-Enhancing diffusion. The two PDEs, and their variants, are implemented in the same filter CoherenceEnhancingDiffusionFilter , which subclasses the Non-Linear Anisotropic Diffusion filter. Parameters:

• Enhancement allows to switch between EED, cEED, CED, cCED and Isotropic (10) tensor constructions, by redefining the superclass virtual method EigenValuesTransform.

The relevant choice depends on the type of image structures that one wants to enhance.

• Lambda= λ, Exponent= m, Alpha= α are the parameters involved in tensor design (8) -(12).

• Suggested parameter ranges. Adimensionize=True. DiffusionTime ∈ [0.5, 5], although larger values can be relevant for very strong noise or artistic effects. Edge detection

  Finally, let S + d denote the collection of symmetric positive definite d × d matrices, and let Id be the identity matrix. To each D ∈ S + d we associate the norm e D := e, De , e ∈ R d , where •, • denotes the standard scalar product on R d .

Figure 1 :

 1 Figure1: The provided filters expect image pixels of scalar or vector pixel type. A preliminary cast is required for integral pixel types (left), or non-Vector pixel types such as RGB (right). The provided executable (or ".cxx" file) performs these casts automatically.

Figure 2 :

 2 Figure 2: I: Source image. II: cEED is the best pick. III: cCED only affects the directionally coherent parts, the image region contours, which is clearly inadequate. IV: Isotropic (10, Perona-Malik like) diffusion leaves some noise trapped along the image contours. Parameters: T = 20, λ = 0.05, σ = 3, others default.

Figure 3 :

 3 Figure 3: I: Source image. II: cEED is not advised, since it blurs the junctions of the fingerprint lines. III: cCED is the best pick, since it enhances the fingerprint lines, and does not blur the more complex regions. IV: Isotropic (10, Perona-Malik like) diffusion either fails to remove noise, or blurs the fingerprint lines, depending on the image region. Parameters: T = 20, λ = 0.02, others default.

Figure 4 :

 4 Figure 4: Left: Volume plot and slice of an FMRI of the human skull, with artificially added Gaussian noise of variance 0.01 (data range: [0, 1]). In the volume plot, values below 0.08 are shown transparent. Right: Effect of cEED. Parameters: T = 5, λ = 0.003.

Figure 5 :

 5 Figure 5: Synthetic function cos( x 3 ), x ∈ [0, 1] 3 , corrupted with Gaussian noise of variance 0.5. Left: level lines, and slice {x = 0.1}. Right: effect of CED. By construction, CED barely affects the neighborhood of the origin (0, 0, 0), where no specific coherent direction can be determined. Parameters: T = 10, λ = 0.02, σ = 4, ρ = 10.

Figure 6 :

 6 Figure 6: I: Detail of the Lena image. II: cEED removes noise and preserves most image detail. III: cCED enhances the flow structure of the hat plumes, without much affecting the rest of the image. In particular it does not remove noise. IV: Isotropic diffusion (10, Perona Malik like) removes noise in the interior of the image regions, but leaves some noise close to image contours such as the border of Lena's cheek. Parameters: T = 2, λ = 0.003, m = 4, others default.

Figure 7 :

 7 Figure 7: Left: Directions and norms (black=0, white=1) of the vector field v(x) := sign( x -1) x ⊥ / x on [-1.3, 1.3]2 , degraded by gaussian noise of variance 2, on a 50 × 50 grid. Norms of these vectors (black=0, white=1). Right: Effect of cEED. Note that the streamlines are better reconstructed, and that the norms vanish along the (approximate) circle x = 1 where v(x) changes sign so that there is a cancellation effect (and likewise close to the vector field singularity at the center). Parameters: T = 10, λ = 0.05, others default.

Figure 8 :

 8 Figure 8: Left: (I) source image, (II) effect of cEED, (III) effect of EED. Note that the triangle corners are better preserved with cEED. Parameters: T = 5, λ = 0.03. Right: (I) source image, (II) effect of cCED, (III) effect of CED. Note that cCED better preserves contrast along where the two fronts meet. Parameters: T = 20, λ = 0.05.

University Paris-Dauphine, Laboratory Ceremade, CNRS.

Institut de Mathématiques de Toulouse, Université Paul Sabatier, CNRS. Young researcher ANR program: Numerical Schemes using Lattice Basis Reduction. NS-LBR ANR-13-JS01-0003-01

We use here the terminology of Weickert[START_REF] Weickert | Anisotropic diffusion in image processing[END_REF]. Perona-Malik diffusion, which uses an adaptive scalar tensor field similar to (4), is in contrast a Non-Linear Isotropic Diffusion equation.

Neuman boundary conditions must take into account the geometry defined by the diffusion tensor field. They take the form ∇u(x), D(x)n(x) = 0, where n(x) denotes the unit outward normal at x ∈ ∂Ω.

Under the name (misleading with our conventions) GradientAnisotropicDiffusionImageFilter .

Actually, Weickert uses µ1 = 1 together with (9) for i > 1. This results in discontinuous diffusion tensors, which is not advisable from a mathematical standpoint, hence the formula (8).


Antoine Petit

Eric Marchand

Rafiq Sekkal

Keyvan Kanani

3D object pose detection using foreground/background segmentation

This paper addresses the challenge of detecting and localizing a poorly textured known object, by initially estimating its complete 3D pose in a video sequence. Our solution relies on the 3D model of the object and synthetic views. The full pose estimation process is then based on foreground/background segmentation and on an efficient probabilistic edge-based matching and alignment procedure with the set of synthetic views, classified through an unsupervised learning phase. Our study focuses on space robotics applications and the method has been tested on both synthetic and real images, showing its efficiency and convenience, with reasonable computational costs.

I. INTRODUCTION

The scope of this paper deals with 3D initial pose estimation of a single known 3D object in a monocular image sequence, with a focus on the case of a space object, such as a satellite or a debris moving in outter space. Solving this issue is a key requirement to initialize a robust and accurate frame-by-frame 3D tracking phase, for instance for space autonomous rendezvous and space debris removal applications.

In the field of monocular 3D object recognition, detection and pose estimation, different classes of approaches can be considered among the large literature. Some methods (single or multi class) are based on global template matching using real training templates of the object. Some of them consider appearance [START_REF] Hinterstoisser | Dominant orientation templates for real-time detection of texture-less objects[END_REF], or shape [START_REF] Olson | Automatic target recognition by matching oriented edge pixels[END_REF][START_REF] Gavrila | Real-time object detection for smart vehicles[END_REF][START_REF] Holzer | Distance transform templates for object detection and pose estimation[END_REF] to represent the object. Many others are based on learning local or semi-local features described by descriptors such as SIFT [START_REF] Lowe | Distinctive image features from scale-invariant keypoints[END_REF], region descriptors such as HOG [START_REF] Dalal | Histograms of oriented gradients for human detection[END_REF], extracted from real training images of the object. The online recognition and detection phase can then provide, potentially besides the object class, pose or viewpoint estimates, through a pose computation step based on 2D-3D point correspondences with the 3D model [START_REF] Lepetit | Keypoint recognition using randomized trees[END_REF], using a voting process method [START_REF] Lowe | Distinctive image features from scale-invariant keypoints[END_REF][START_REF] Thomas | Towards multi-view object class detection[END_REF][START_REF] Rodrigues | 6D pose estimation of textureless shiny objects using random ferns for bin-picking[END_REF]. But in our context, these methods, based on real training images, are not suitable since natural images of space objects can hardly be obtained prior to the mission itself. Besides, space objects are often poorly textured or prone to specular effects (for instance due to the insulating film on satellites), making the description of templates or the extraction and description of local features complicated.

Using the 3D model of the object: instead, we propose to rely on another class of approaches which learns the A. Petit was with Inria Rennes, France. He is now with Universita degli Studi di Napoli Federico II, Napoli, Italia, antoine.petit@unina.it E. Marchand is with Université de Rennes 1, IRISA, Lagadic Team, France, Eric.Marchand@irisa.fr R. Sekkal was with INSA Rennes, IRISA, Lagadic Team, France K. Kanani is with Astrium, Toulouse, France geometry or the shape of the 3D model of the object, which is assumed to be known and present in the image. We deal with industrial objects (spacecrafts, satellites or parts of them), for which accurate geometrical CAD models can be available. Some template matching methods [START_REF] Ulrich | Cad-based recognition of 3d objects in monocular images[END_REF][START_REF] Reinbacher | Pose estimation of known objects by efficient silhouette matching[END_REF], sparse 2D-3D edge feature matching techniques [START_REF] Lowe | Three-dimensional object recognition from single twodimensional images[END_REF][START_REF] Strzodka | A graphics hardware implementation of the generalized hough transform for fast object recognition, scale, and 3d pose detection[END_REF] or multiview learning frameworks based on part or region descriptors [START_REF] Liebelt | Multi-view object class detection with a 3d geometric model[END_REF][START_REF] Stark | Back to the future: Learning shape models from 3d cad data[END_REF], suggest to use and learn the 3D model of the target object and its projection. However, approaches such as [START_REF] Lowe | Three-dimensional object recognition from single twodimensional images[END_REF][START_REF] Strzodka | A graphics hardware implementation of the generalized hough transform for fast object recognition, scale, and 3d pose detection[END_REF], based on matching geometrical primitives such as lines, can be computationally prohibitive, due to the large search space. Furthermore, they face problems when extracting the considered geometrical primitives from edges in the image with degraded conditions such as noise, blur, or background clutter. Region or part descriptor based methods [START_REF] Liebelt | Multi-view object class detection with a 3d geometric model[END_REF][START_REF] Stark | Back to the future: Learning shape models from 3d cad data[END_REF] have recently proposed to overcome the issue of computational costs by efficiently learning the 3D model with shape descriptors. But these solutions, which are more suited for object class detection, still require a certain amount of supervision during the learning step and are restricted to a coarse set of viewpoints.

Towards template matching: Here we design an unsupervised method for single class object pose detection, precise enough to correctly initialize a frame-by-frame tracking process, while keeping computational costs reasonable. We propose to follow the idea of template matching. Some efficient edge or shape based global similarity measures [START_REF] Olson | Automatic target recognition by matching oriented edge pixels[END_REF][START_REF] Steger | Occlusion, clutter, and illumination invariant object recognition[END_REF][START_REF] Belongie | Shape matching and object recognition using shape contexts[END_REF] have been considered to cope with occlusion, clutter, noise, and specular effects... Our idea is thus to match an exhaustive set (over the 6D pose parameters), of non photorealistic synthetic views of the object. With the issue of the large search space, we propose to efficiently learn the set of views. In this sense, we rely on the concept of aspect or view graph [START_REF] Cyr | A similarity-based aspect-graph approach to 3d object recognition[END_REF][START_REF] Toshev | Shape-based object recognition in videos using 3d synthetic object models[END_REF] or of hierarchical view graph [START_REF] Ulrich | Cad-based recognition of 3d objects in monocular images[END_REF][START_REF] Reinbacher | Pose estimation of known objects by efficient silhouette matching[END_REF], leading to sets of reference views of the object. Our pose estimation process can then be performed by matching the input image with these graph structures.

Benefiting from foreground/background segmentation: the considered single object is assumed to be moving with respect to its background. Thus, we suggest to take advantage of a foreground/background segmentation technique, as in [START_REF] Toshev | Shape-based object recognition in videos using 3d synthetic object models[END_REF].

For computational efficiency and robustness concerns, we propose to spread our object localization process over a sequence of successive input images. Only reasoning on the first frame could indeed result in a too coarse pose estimate, or would require a more exhaustive and costlier searching process over the pose parameters. With our system, the retrieval of the pose is then based on progressively matching and aligning the synthetic views with a short image sequence. At the end of the process the most likely view is determined and selected, along with the stored pose used to render it. Combining this pose with estimated in-plane rotation, translation and scaling parameters to align the view in the image allows us to compute the pose. Indeed, with our applications the dimensions of the object can be assumed to be small (∼ 10m) relatively to its distance from the camera (∼ 100/1000m), a weak perspective projection model can be assumed: an isotropic scaling (equivalent to a translation along the optical axis) precedes an orthographic projection.

In this work we propose an accurate edge-based distance function which is made robust to segmentation errors, by involving both the segmented and the original images. We also suggest to use the image in-plane translation, rotation and scale of the segmented silhouette to coarsely estimate the similarity transformation of the considered tested view to guide the matching process and compute the pose. This framework would thus result in a fast process, and would be less sensitive to local minima, in contrast to [START_REF] Ulrich | Cad-based recognition of 3d objects in monocular images[END_REF][START_REF] Toshev | Shape-based object recognition in videos using 3d synthetic object models[END_REF], which rely on a costlier coarse-to-fine search [START_REF] Ulrich | Cad-based recognition of 3d objects in monocular images[END_REF], or an exhaustive probabilistic inference over these parameters [START_REF] Toshev | Shape-based object recognition in videos using 3d synthetic object models[END_REF].

Contributions: As main contributions, this paper suggests a novel probabilistic matching and edge-based alignment framework between the views and the image to retrieve the full 6 DoF pose. A novel foreground/background segmentation method suited for the targeted application combining color statistical modeling and motion-based compensation is also proposed.

Overview of the approach: our method can be outlined by the following steps:

• Learning step : based on generated synthetic views of the object, it aims at building a hierarchical model view graph leading to some reference views of the model. • Pose estimation step along the image sequence :

-Foreground/background segmentation of the object. By computing binary moments of the extracted silhouette, an initial estimate of the image inplane translation, rotation and scale transformation parameters of the reference views in the image can be determined. -With the aim of refining these parameters, particle filtering is performed with respect to them, for each reference view, along the input image sequence. -We then determine the most likely model view and an associated estimate of the image similarity transformation of the view in the image, providing the complete pose, along the input image sequence. -Finally the matched view and the pose and refined by traversing through the hierarchical view graph.

II. FOREGROUND/BACKGROUND SEGMENTATION

We deal with a single object moving in an input image sequence. The aim of this segmentation task is to extract a foreground layer, corresponding to the object silhouette in the image, in the presence of a potentially cluttered and dynamic background. The information provided by the extracted sil-houette will further be used in the pose estimation step (see Section IV-E).

Among the vast literature addressing the issue of segmentation, classical approaches rely on background modeling and substraction [START_REF] Stauffer | Adaptive background mixture models for real-time tracking[END_REF] but these methods requires a prior knowledge of the background and are limited to static or weakly dynamic backgrounds. Other methods [START_REF] Criminisi | Bilayer segmentation of live video[END_REF][START_REF] Sheikh | Background subtraction for freely moving cameras[END_REF] have based their solution on the assumption that foreground and background layers have different motion patterns. The general idea is then to automatically extract and classify these patterns and build models of both layers. Segmentation can then be efficiently achieved using graph cuts [START_REF] Boykov | Fast approximate energy minimization via graph cuts[END_REF].

Since the apparent motions of both the foreground (the moving object) and the background can potentially be identified, our basic idea is also to use a statistical foreground/background modeling technique. In our application, we can assume that, locally, the Earth is a rigid body at rest in space, and that the apparent motion of the background is due to the camera selfmotion, the processing time of the algorithm being negligible with respect to the Earth self rotation period. For this reason we rely on the idea suggested in [START_REF] Sheikh | Background subtraction for freely moving cameras[END_REF], consisting in automatically identifying the background and the foreground layers and then to statistically model them.

As in many layer segmentation methods, we use an energy minimization framework, based on statistical models of the foreground and the background.

A. Energy Minimization formulation

For an image I k , we denote by α = {α i } N i=1 the set of the unknown binary labels of the set of pixels {p i } N i=1 of I k (α i = 0 for the background pixels, α i = 1 for the foreground). Estimating the values α of the labels for an entire image can be formulated as the minimization of an energy-based Markov Random Field objective function E(α), with respect to α:

E(α) = E data (α) + γE smooth (α) (1) with E data (α) = i U i (α i ) (2)
E data is the "data" energy term, with U i (α i ) a unitary term accounting for the observation probability p(p i | α i ) of pixel p i to belong to the foreground or to the background, based on some image "data" (intensity, color, location...) observed in the image at pixel p i , using the statistical models previously built for the background and the foreground. More formally, we have

U i (α i ) = -log(p(p i | α i )
). E smooth is the smoothness energy term whose goal is to favor smoothness, or spatial coherence within the pixels [START_REF] Criminisi | Bilayer segmentation of live video[END_REF].

In order to compute the optimal solution of this energy minimization problem and to determine α, we employ the graph cuts algorithm [START_REF] Boykov | Fast approximate energy minimization via graph cuts[END_REF].

In our context, we propose to compute the data energy term using two different terms. One term is obtained through foreground and background statistical modeling (E m data , see section II-B). The other term is computed by modeling the motion of the background and using homography-based motion compensation (E c data , see section II-C). Formally, E data can be rewritten as:

E data (α) = βE m data (α) + (1 -β)E c data (α). (3)
β is a weighting parameter (0 < β < 1). p m (p i | α i ) and let us define p c (p i | α i ) as the corresponding observation probabilities for E m data and E c data .

B. Feature tracking, clustering and foreground/background modeling

As in [START_REF] Sheikh | Background subtraction for freely moving cameras[END_REF], we propose to identify and describe both foreground and background layers by processing some feature points that will be tracked over a certain number of frames and will be classified as background or foreground points, consistently with their motions. We choose Harris corner points that are detected on the first frame. By tracking them over the image sequence with the Kanade-Lucas-Tomasi (KLT) tracker, we obtain a set of trajectories on a sliding window. When a frame I k0 is reached, the goal is then to cluster these trajectories into background or foreground trajectories. Since the background is supposed to be stationary in the world frame, we follow the approach of [START_REF] Sheikh | Background subtraction for freely moving cameras[END_REF], which uses the rank-constraint for the background. It means that the matrix formed by the projected trajectories of stationary points in the world frame is a rank three matrix, so that background trajectories must lie in a subspace spanned by three basis trajectories. RANSAC is used in order to robustly determine these basis trajectories from the set of all trajectories, and to finally identify trajectories that lie within the resulting subspace. This method enables to efficiently cluster trajectories and the corresponding feature points into foreground trajectory points or background trajectories. We obtain a set of background trajectory points {p b i } N b i=1 and a set of foreground trajectory points

{p f i } N f i=1 .
We then use these sets to determine the statistical models of both background and foreground layers. For both layers Kernel Density Estimation is employed as probabilistic modeling [START_REF] Sheikh | Background subtraction for freely moving cameras[END_REF], but in our approach, only a color model is used for the background. The foreground model is instead based on both color and spatial information. A reason for this choice is that the foreground layer is likely to be concentrated in the image, making spatial information more discriminative than for the background.

More formally, the background model is based on the set of vectors

{z b i } N b i=1 , where z b i = R i G i B i T , with R i , G i and B i the RGB color coordinates of pixel p b i . The foreground model is based on the set of vectors {z f i } N f i=1 , where z f i = R i G i B i u i v i T , with R i , G i and
B i the RGB components of p f i and u i and v i the pixel coordinates of p f i . Then the probability p m (p i | α i ) for a pixel p i to belong to the background or the foreground is then computed using Kernel Density Estimation, by selecting the appropriate data z i on p i , and using an Epanechnikov kernel function, which is fast to compute. But kernel density estimation is computationally expensive, and both layers are modeled this way only for the first frame I k0 . For the next ones, based on the data provided by this initial segmented frame, the background and the foreground are represented by smoothed color histograms h which are adaptively learned over successive frames.

C. Homography based motion compensation

Relying on the important assumption that the background can be considered as planar, the idea is to evaluate pixel observation probabilities through motion compensation. It is based on the estimation of the homography transformation induced by the motion of the background in successive frames. With this motion compensation framework, the idea is to compensate for errors induced by a poor modeling of foreground and the background layers, due to some misclassifications of the trajectory points.

By using background trajectory points identified at a frame I k , and the same points at frame I k-k H , with k H ≤ k 0 we can compute the homography k H k-k H between the two background planes, with a RANSAC robust procedure. k H k-k H is then applied to the whole frame I k-k H , to compensate for the background motion between I k-k H and I k , and thus to discriminate the foreground layer, which has a different motion, by computing the error e(p i ):

e(p i ) = I k (p i ) -I k-k H ( k H k-k H (p i )) (4)
Likelihoods can then be evaluated by a Gaussian kernel, with a bandwidth σ:

p c (p i | α i = 0) = 1 σ √ 2π e -e(p i ) 2 2σ 2 (5)
p c (p i | α i = 1) = 1 -p c (p i | α i = 0) (6)

III. HIERARCHICAL MODEL VIEW GRAPH

A. Generation of synthetic views

The purpose of our template matching method is to align a sequence of successive initial input images with synthetic views generated from the 3D model. These views are generated on a view sphere centered on the 3D model. This is managed by a 3D rendering engine by setting virtual cameras at uniformly spaced viewpoints (see Figure 1). [START_REF] Cyr | A similarity-based aspect-graph approach to 3d object recognition[END_REF][START_REF] Toshev | Shape-based object recognition in videos using 3d synthetic object models[END_REF][START_REF] Reinbacher | Pose estimation of known objects by efficient silhouette matching[END_REF] process these views as silhouette shapes. Instead we propose to extract both silhouette and internal edges of the rendered views through a Laplacian filter computed on the depth maps, in order to avoid ambiguities between silhouettes (Figure 1). For each generated view V , we store the pose c V M o used to render the 3D model. Besides, we also store the centroid c V = u V v V , orientation α V and area A V of the silhouette of the projected 3D model (Figure 1 right). These parameters are evaluated using image moments.

B. Building a hierarchical model view graph

Since the process of matching the whole set of views with the input images can be computationally challenging, we iteratively cluster the views into a hierarchical view graph, as in [START_REF] Ulrich | Cad-based recognition of 3d objects in monocular images[END_REF][START_REF] Reinbacher | Pose estimation of known objects by efficient silhouette matching[END_REF]. We consider an unsupervised clustering technique based on Affinity Propagation [START_REF] Frey | Clustering by passing messages between data points[END_REF], similar to [START_REF] Reinbacher | Pose estimation of known objects by efficient silhouette matching[END_REF]. At the first level of the hierarchy, we build clusters within disjoint neighborhoods on the sphere. This is done by comparing the views with each other in each neighborhood using a distance function (see Section III-C). A slight overlap is considered between the different neighborhoods to consider inter neighborhood variabilities. The result is a set of clusters, represented by reference views, which define the first level of our hierarchical structure. We proceed in the same way with these views. Since this set has an acceptable size, we do not consider spatial neighborhoods from this level. We can then iteratively build successive hierarchical levels until a reasonable number N r of reference model views is reached. A set {V j } Nr j=1 of reference views is finally obtained.

c V v u α V A V

C. An edge-based distance function between synthetic views

The proposed distance function D, intended to compare two synthetic views, is based on all the extracted edges of the two views, instead of silhouette contours as with the Shape context used in [START_REF] Toshev | Shape-based object recognition in videos using 3d synthetic object models[END_REF], which is based on the silhouette contours. From the sets of edge points {c i k } Ni k=1 and {c j k } Nj k=1

(both silhouette and internal edges) on views V i and V j , we compute an oriented Chamfer distance by looking for the closest edge from one view to the other, so that D i,j = 1 2 (d i,j + d j,i ). d i,j is related to the distance for each edge point c i k of V i to the closest one in V j . It also takes into account the difference between the orientation θ(c i k ) of the edge point c i k and the orientation of the corresponding closest edge point in V j . It results in an accurate and robust discriminative distance function by taking into account distance between edges of the views and the difference between their corresponding orientations.

IV. A PROBABILISTIC FRAMEWORK FOR ALIGNING AND MATCHING REFERENCE VIEWS WITH INPUT IMAGES

Our problem consists in matching and aligning the reference model views to each input image and finding the most likely one. Once a first image is segmented, at time step k 0 , the next input images are used to determine a pose estimate. In order to ensure smooth transitions between the matched and aligned model views, we propose a probabilistic framework to determine the best view. Let us first describe how the pose can be determined from the alignment of a given synthetic view V with an input image I.

A. Rough pose computation assuming a weak perspective model

We assume a weak perspective projection model, justified in our applications by the fact that the dimensions of the target space object are small relatively to the distance from the camera. Based on this assumption, the pose c M o between the camera and the object can be retrieved using the stored pose c V M o used to generate the considered synthetic view V and the similarity transformation which aligns the view V with the image I. This similarity transformation can be represented by four parameters: the in-plane rotation, expressed by a rotation angle β, the 2D translation vector t = t x t y T , and the scaling s. Let R -β denotes the 3D rotation matrix of angle -β around the optical axis z c . The rotation matrix c R o of c M o can then be computed

through c R o = R -β c V R o , with c V R o the rotation matrix of c V M o .
Since synthetic views are generated on a view sphere centered on the 3D model, at a fixed distance d 0 , and since scaling is assumed isotropic, the translation vector c t o of c M o is given by c t o = s d 0 t x t y 1

T .

Next, we present our solution to align each reference view V j r with the input images (section IV-B), giving a fair similarity transformation, and to determine the best matching (or most likely) reference view (section IV-D).

B. Aligning a reference view by refining similarity transformation parameters

Using the segmentation technique presented in section II, the silhouette of the object can be extracted on the first segmented frame I k0 . The centroid c = u v , orientation α and area A of this silhouette can be then evaluated, using the image moments.

Given a reference view V j and using its stored silhouette parameters u j v j α j A j T , we can retrieve the similarity transformation to align V j with I k0 . This similarity transformation can be expressed by vector x j :

x j = t u t v β s (7) = u -u j v -v j α -α j A A j (8)
Based on the process presented in section IV-A, the pose c V j M o (used to generate V j ) and x j can provide us with a pose c M o , for the considered view V j . However, due to some segmentation errors, u v α A T may be too coarsely computed. We thus propose, for each reference view V j , to refine the parameters x j .

C. Refining as particle filtering

With the aim of estimating and refining x j by minimizing a distance function between a reference view and the observed input image, we propose an efficient and robust solution by using particle filtering, which is particularly suited to deal with the non-linearity of this distance function, in contrast to local deterministic minimization techniques such as Gauss-Newton or Levenberg-Marquardt. It is also more optimal and computationally efficient than coarse-tofine searches.

Given a reference model view V j and a first image I k0 , we estimate and refine the corresponding parameters x j using particle filtering, and we propose to use the CONDENSA-TION [START_REF] Isard | Condensation -conditional density propagation for visual tracking[END_REF] formulation of the filter, whose steps are recalled hereafter, and which is illustrated on Figure 2.

In this sense, the similarity transform x j k , for a frame I k , is represented by a finite set {x (i,j) k } Nj i=1 of N j samples, or particles, associated with weights {w

(i,j) k } Nj i=1 , with Nj i=1 w (i,j) k = 1.
Then, after initialization, the process consists in predicting the states of the particles according to a motion model (here a simple Gaussian noise is used), in updating the weights using a likelihood function and in performing a random weighted draw among the particles to avoid degeneracy. The estimate x j k is then the estimator of probability expectation.

Likelihood evaluation: a likelihood function needs to be evaluated for each particle to compute its weight. The function chosen here is derived from the distance function presented in section III-C. For a model view V j , a particle x (i,j) k , an image I k and its corresponding segmented image I seg k , it consists in the distance D(x

(i,j) k
) between the contour points {p i,j l } Mx l=1 extracted from V j translated, scaled and rotated around its centroid with respect to x

(i,j) k ) = ρd(x (i,j) k , I k ) + (1 - ρ)d(x (i,j) k , I seg k ).
ρ is a scalar tuning the balance between the original image and the segmented one. d(x

(i,j) k , I k ) and d(x (i,j) k , I seg k )
are respectively computed in similar ways to d i,j (section III-C). By computing the distance on both the edge maps of the original image and the segmented image, the idea is that edges resulting from a potentially cluttered background can be discarded through the segmented image, whereas potential segmentation errors can be compensated by keeping the original image edges.

Also, due to potential ambiguities in the computation of the image moments and the direction of the principal axis, we actually use the distance D min (x

(i,j) k ) = min(D(x (i,j) k ), D(x (i,j) k,π )), where x (i,j)
k,π is the particle x (i,j) k rotated by π in the image plane. The likelihood π

(i,j) k of x (i,j) k
for a frame I k , with τ a tuning parameter, is thus given by:

w (i,j) k ∝ π (i,j) k = e -τ -1 Dmin(x (i,j) k ) 2 (9) c j α j A j

D. Matching the reference views within a probabilistic framework

Once particle filtering is performed for all the reference views V j for a frame I k , the goal is then to find the most likely view, while ensuring smooth transitions with respect to previous selected views. For this purpose, probabilistic graphical models can be considered. We have chosen to employ Hidden Markov Models (HMM) which define a joint distribution over the sequence of the matched model views and the sequence of observations which are the initial input images.

The sequence of the matched views as a Hidden Markov Model: a HMM supposes that the sequence of matched reference views {V l } k l=k0 follows a hidden Markov process. Besides, each observation I l is assumed to only depend on V l . Based on these assumptions, the joint probability of the sequence {V l } k l=k0 and the sequence {I l } k l=k0 can be written as:

p(V k0:k , I k0:k ) = k l=k0 p(I l |V l )p(V l , V l-1 ) with p(I l |V l = V j ) = 1 A Nj i=1 π (i,j) l , A = Nr j=1 Nj i=1 π (i,j) l (10)
The probability p(I l |V l ) refers to the observation probability of a given matched model view V l , with V j the view corresponding to V l in {V j } Nr j=1 . π

(i,j) l
is the weight of particle x (i,j) l and A is a normalization factor so that we deal with a probability distribution.

p(V l , V l-1 ) is the transition probability between matched views V l and V l-1 . It can be determined offline by:

p(V l , V l-1 ) ∝ e - acos(u l T u l-1 ) 2 2σv 2 (11)
where u l corresponds to the viewpoint vector of the matched view V l in the set {V j } Nr j=1 . This viewpoint vector is related to the azimuth and elevation angles used to generate the synthetic view corresponding to V l . σ v a fixed parameter related to the variance of the viewpoints.

Inference of the HMM: in order to maximize equation [START_REF] Isard | Condensation -conditional density propagation for visual tracking[END_REF] with respect to the sequence of views, in the set {V j } Nr j=1 at each time step k and thus to determine V k (the last element of the estimated sequence), we use the classical Viterbi algorithm on the whole sequence of observations until k. The resulting reference view V j * corresponding to V k is thus chosen as the most likely one.

As an estimate of the similarity transformation parameters, we propose to consider the whole set of reference views to compute a global estimate x k , given their respective probabilities {p(I k |V j )} Nr j=1 and their estimate { x j k } Nr j=1 . It gives x k = Nr j=1 p(I k |V j ) x j k . The particles {x k (i,j) } Nj i=1 of each V j are reweighted with respect to x k , prior to being processed in the particle filters of the different reference views, for the next frame I k+1 .

E. Refinement as graph search and pose computation

Once a certain number of frames k F is reached, the most likely reference model view V k F , serves as a starting point of a best match search among its child views on the hierarchical view graph and among the whole set of its associated particles. More formally, if V reference view corresponding to V k F , the process results in a view V l j * determined at the bottom level on the view graph, and in a best particle x k F . With x k F and V l j * and using the steps described in section IV-A, we can compute a pose c M o k F . This pose is finally directly used to initialize a frame-by-frame tracking algorithm [START_REF] Petit | A robust model-based tracker combining geometrical and color edge information[END_REF].

V. RESULTS

We have evaluated and validated our technique with a focus on space objects. The algorithm has been run, using a standard laptop (2.8GHz Intel Core i7 CPU), on synthetic images featuring a Spot satellite (512 × 512 images are processed). Concerning real sequences, a first one shows the Soyuz TMA-12 spacecraft approaching the International Space Station (ISS). A second one features the Atlantis Space Shuttle performing its pitch maneuver towards the ISS.

B. Segmentation

As explained in Section II, the pose detection process starts by segmenting the initial images of the sequence. Figures 4(a,d,g) shows the Harris corner points being tracked using the KLT tracker (red trajectories) for the different sequences. Blue and green dots represent the dots respectively classified as belonging to the foreground object or the background, spread on regular grids. We observe that the clustering process explained in section III-A is performed correctly, with very few misclassified pixels for Spot (Figure 4(a)) and Soyuz (Figure 4(d)) whereas we find more errors for Atlantis (Figure 4(g)). Figures 4(b,e,h) depicts the mean image between the current image and its homographybased compensated one, enhancing the motion of the object with respect to the background, with the zone featuring the object being blurred (with k H = 5).

Finally, Figures 4(c,f,i) shows both object (colored) and the background (black) layers after the segmentation phase, which starts at k 0 = 8, with satisfactory results, despite the cluttered background. This segmentation step is executed in around 0.6s using kernel density estimation and in 0.38s using histograms. In order to show the advantage the Hidden Markov Model used to match the reference views with the input images (section IV-D), the marginal joint probabilities, provided by the Viterbi algorithm, of the different reference views along the input sequence are plotted.

For sequences on Figure 6(a)-6(d), 7(b)-7(d), 6(f)-6(i) and 5(l)-5(n), we observe that consistent reference views are matched and realigned to the image through particle filtering. The benefit of the HMM is visible through its ability to smooth, by estimating the optimal sequence, the determination of the most likely view at each time step. For the sequence on Figures 6(a)-6(d), three reference views (views 1, 46 and 47) still have similar appearance, despite the hierarchical clustering technique described in section III-A. Thanks to the inference of the HMM, view 1 is progressively rejected, in terms of marginal joint probability, and the marginal probability of view 46 is increasing. A false positive can be observed on the initial match for the sequences on Figures 5(a)-5(d). However, the HMM rapidly discard this inconsistent view and a fair one is finally dominant. Ambiguities can also be observed for the Soyuz sequence (Figures 6(f)-6(i)) between view 6 and view 19.

On Figures 7(b)-7(d) (see also the provided video), due to the coarse segmentation, the orientation of the object in the image is initially not proper, as seen on Figure 7(b), but through the particle filtering framework, the most likely view, which is consistent with the image, is progressively aligned, its marginal probability increasing. Without the alignment procedure, tracking then fails.

The alignment and matching step is executed in around 0.35s per frame. Including segmentation, the process is executed in less than 1f ps.

D. Discussion

An issue regarding our pose detection system to be discussed concerns its reliance on the segmentation process and on image moments. In this study we have dealt with cases for which moments are quite distinct. Besides, potential ambiguities in the determination of the direction of the principal axis of the object are treated by computing the distance function w.r.t both a considered particle and itself rotated by π. However, in the case of more ambiguous moments (a spherical object for instance) or on large segmentation errors, the determination of the image plane rotation could be problematic, despite our robust distance function and alignment procedure, solving the issue to a certain extent. Finally, as another issue and as suggested in the results shown above, ambiguities between different reference views may result in false positives. To improve segmentation, a solution for our applications would be to use the localization information provided by the chaser spacecraft with respect to the earth to provide prior information on the earth apparent motion. Otherwise, some priors on the apparent motion or color of the earth surface could be used. Besides, to relax the reliance on segmentation or to cope with indistinct moments, we could think of integrating in the process some local or region descriptors based learning methods.

VI. CONCLUSION

In this paper we propose a method to address the challenging issue of full-viewpoint detection and initial pose estimation in the case of complex poorly textured known 3D objects such as spacecrafts. The idea is to match and align synthetic views of the 3D model of the known object with successive initial frames. In order to efficiently cover the parameter space, the views are classified into a hierarchical view graph. We also take advantage of a segmentation technique, which guides the probabilistic edge-based matching process to provide a sufficiently precise pose to initialize a classical frame-by-frame tracking.

Fig. 1 :

 1 Fig. 1: Generation of synthetic views on a view sphere centered on the 3D model. Contours are extracted by processing the depth buffer of the rendered 3D model, and silhouette parameters are compute using image moments.

  (i,j) k , and the corresponding closest contour points of both sets {p l,k } N l=1 and {p seg l,k } P l=1 extracted from I k and I seg k using a Canny edge detector. It gives D(x

Fig. 2 :

 2 Fig. 2: Illustration of particle filtering for a reference view. The view is translated, rotated and scaled according to the particles, and the likelihoods are evaluated w.r.t the input image and its segmented frame.

Fig. 3 :

 3 Fig. 3: Some reference views determined at the second level of the view graph.

Fig. 4 :

 4 Fig. 4: Segmentation process. On (a,d,g) are shown the tracked KLT trajectory points, in green those classified as foreground points and in blue as background points. (b,e,h) represent the mean image after homography based motion compensation and (c,f,i) the resulting segmented image.

TABLE I :

 I Parametrization of the view sphere for each object and results of the learning step, with the number of reference determined at each level L of the hierarchical view graph.

A. Learning step

Table I shows the parametrization of the view sphere for the different objects, with sampling steps for both azimuth and elevation angles.

It also presents the results of the building of the hierarchical model view graph and the number of reference views obtained at each level L of the graph. For each object, we have stopped the learning process at level 2 in order to get reasonable numbers of reference views. Some examples of these reference views can be seen on Figure 3.