Edwin Weber
email: edwin.weber@chemie.tu-freiberg.de

Margit Gruner

Tobias ; Gruber

Conrad Fischer

Influence of laterally attached alkyl groups on the conformational behaviour of a basic calix[4]arene: Combined NMR, Molecular Mechanics and X-ray study

Keywords: calixarenes, lateral substitution, synthesis, conformational study, Xray crystal structure calixarenes, lateral substitution, synthesis, conformational study, solution 2D NMR measurements, X-ray crystal structure

Horizontal

broadening: Calix[4]arenes featuring the structural mode of lateral alkyl substituents were prepared. As proven by special ROESY-and EXSY-2D-NMR experiments, the lateral alkyl group substituents are not exercising a decisive influence on the conformational behaviour of the parent calixarene, suggesting a promising approach for horizontal expansion of the calixarene platform.

Introduction

Calixarenes and their derivatives are an important class of compounds that have been extensively investigated regarding their supramolecular recognition properties during the past two decades [START_REF] Gutsche | Calixarenes -An Introduction[END_REF]. Calixarenes have also emerged as very attractive building blocks for the development of highly ingenious functional systems and devices [START_REF] Baklouti | In Calixarenes in the Nanoworld[END_REF]. In both of these respects, much work has been dedicated to the synthesis of calixarenes modified on the upper and lower rims, giving rise to an enormous variety of compound (3). Homocalixarenes (4), thiacalixarenes (5) and others [START_REF] Gutsche | Calixarenes -An Introduction[END_REF] where the bridging methylene units of the conventional calixarene framework are completely replaced by modifying organic groups or hetero atoms, represent further currently studied yet rather well known types of structural modifications of the calixarene family (6). By way of contrast, calixarenes featuring a substitution of only one of the methylene bridges are presently rare (7), although these laterally substituted calixarenes may open interesting aspects of calixarene chemistry including linked constructions of oligotopic receptors (8) as well as systems distinguished by particular anchoring of the calixarene to a specific target or support [START_REF] Baklouti | In Calixarenes in the Nanoworld[END_REF]9). As a result, the conformational behaviour of this particular compound type is also studied only fragmentary in a few cases of modified tetrahydroxycalix [4]-and -calix [5]arenes (7c-d). This warrants to deal with the conformational property of laterally monosubstituted calixarenes more broadly.

Hence, a series of calixarenes that feature a lateral substitution of alkyl groups of different chain length and includes a well-known parent compound was considered for this purpose. The concrete system of compounds which was chosen for this study, as specified in Fig. 1, covers the tetra-tert-butyltetramethoxycalix [4]arene [START_REF] Gutsche | Calixarenes -An Introduction[END_REF] as the reference and 2-5 as the test compounds. This shows an advantage since the conformational behaviour of 1 is known rather detailed from previous work (10).

Moreover, for the synthesis of 2-5 one can follow a literature method elaborated for the calixarene 2 by Scully (7a). The conformational properties of 2-5, which are described here, were determined from a detailed solution NMR study. This involves measurements at various temperatures and uses special 2D NMR techniques to yield a full description of the conformer distribution and the free activation energies of conformational interconversion. We also report on the crystal structure of the corresponding laterally ethyl monosubstituted calixarene 2, being the first crystal structure of a laterally monosubstituted tetramethoxycalix [4]arene.

Results and discussion

Synthesis

The calixarene 1, which is the basic compound for the synthesis of 2-5, was obtained from two-stage methylation reaction of 5,11,17,23-tetra-tert-butyl-25,26,27,28tetrahydroxycalix[4]arene (11) using in a starting phase-transfer process sodium hydroxide, dimethyl sulphate and tetrabutylammonium bromide to yield the intermediate compound with two distal methyl groups, followed by treatment with sodium hydride and iodomethane in a final methylation step (12). A corresponding onestep methylation method of the parent tetrahydroxycalixarene with sodium hydride and iodomethane, described in the literature (10a, 13), did not prove competitive in its result. The target calixarenes 2-5 featuring different laterally substituted alkyl groups were prepared by deprotonation of 1 with n-butyllithium and reaction with respective alkyl halides following the procedure described by Scully (7a).

Conformational study

Conformational predominance and conformational flexibility are important structural parameters of a calixarene molecule, being decisive of its supramolecular behaviour both in solution and solid state [START_REF] Gutsche | Calixarenes -An Introduction[END_REF][START_REF] Baklouti | In Calixarenes in the Nanoworld[END_REF](3). While the so-called cone conformation, providing a spaceous cavity structure, is perhaps the most frequent conformation of the existing calixarenes [START_REF] Gutsche | Calixarenes -An Introduction[END_REF]14), the other types of molecular conformations, including partial cone, 1,2-and 1,3-alternate conformation, are somewhat more rarely found though not less important for a designed purpose (15). As a rule, these conformations are mainly determined by the ring size or the nature and the space required of the substituents being (7c-d).

A well-known molecular structure is that of the tetra-tertbutyltetramethoxycalix [4]arene [START_REF] Gutsche | Calixarenes -An Introduction[END_REF], which was chosen as the parent compound for the test. According to the NMR data (10), 1 in a solution of CDCl 3 exists in an equilibrium of all four conventional conformers of which the partial cone conformation is the preferred one. A partial cone conformer is also reported for the solvent free calixarene 1 (16) as well as for the furan (17) and dichloromethane (18) inclusion compounds in the solid state, while a corresponding sodium complex shows a cone conformation both in the crystal structure and in CDCl 3 /CD 3 CN solution due to coordination of the sodium ion (10b). Thus, it is clear that a potential change of the conformational behaviour in the present cases of calixarenes, in comparison with 1, is attributed to the laterally substituted alkyl groups.

A complex pattern of signals in the NMR spectra of the alkyl substituted Detailed 2D NMR measurements using COSY-, 1 H/ 13 C-correlated HSQC (19) and HMBC (20) as well as NOESY and ROESY experiments gave a full determination of conformers (specified in Fig. 3; 1 H and 13 C chemical shifts are summarized in Tables Depending on the alignment of the four arene units with reference to the lateral substituent, there are 16 different conformational isomers possible (Fig. 4). Six of them are mirror images of each other resulting in identical NMR spectra. The 2D experiments

show that the laterally substituted n-alkyl calixarenes, studied here, exist mainly in one partial cone conformation (pacoD in Fig. 4), with an equatorial substituent between two syn orientated arene units, and also as 1,2-alternate (alt2C in Fig. 4) and cone (coneB in Fig. 4) conformers (Scheme 1), revealed in the region of the OCH 3 groups of the HSQC spectrum (Fig. 5). In the ROESY spectrum (Fig. 6), all conformers possess stronger positive cross peaks between the axial methine H-1 protons in the bridge and the near H-8 protons of the methoxy groups than between these protons and the H-3 protons of the same aromatic rings, indicating the vicinity of one of the methoxy groups on the lower rim to H-1. Further characteristic specific interactions between aromatic protons of the calixarene and protons of OCH 3 or tert-butyl groups neighbouring the methylene bridge are marked in Fig. 6. These correlations suggest the orientation of arene units of the calixarene ring for each individual isomer. For example, the paco isomer is characterized by the cross peaks 8 '/11 ', 16 /13 , 16 '/5 ' and 16 '/13 , and the 1,2-alternate species by the 8g/11g and 8g /13g relation.

Furthermore, in Fig. 6, negative cross-peaks between different H-1 proton signals can be observed due to chemical exchange processes in the form of a dynamic interconversion of conformers. To extract the rate constants for the confomational chemical exchange (k chem ), the 2D-EXSY method (21) was used, and thus the free activation energies ∆G # of the interconversion has been calculated (Table 1).

Interestingly, compounds 2-5 display a fast partial cone/cone interconversion involving values of free activation energy rather comparable to the reported ~13 kcal/mol for the laterally unsubstituted prototype calixarene 1 in the same solvent (10a). The observed influence of solvent and temperature on the conformational behaviour is in agreement with the common expectation. In this connection, the conformational reorientation was found to be faster at higher temperature and retarded in solution of the larger and less polar solvent molecules of tetrachloroethane-d 2 (TCl-d 2 ) compared to CDCl 3 .

The conformer distribution of 1 and 2-5, summarized in Table 2, shows that the partial cone conformation predominates the present series of tetra-tertbutyltetramethoxycalix [4]arenes in CDCl 3 , varying only little by introduction of the lateral alkyl substituents, i.e. the predominance of the partial cone conformation is only slightly affected. Nevertheless, its frequency decreases to some extent for the benefit of the rarely occurring cone-and 1,2-alternate structures in the following manner. With increasing chain length, the ratio of partial cone conformation remains nearly unchanged, while the cone conformation decreases and the 1,2-alternate conformation increases. However, as contrasted with the prototype calixarene 1, for none of the studied compounds a 1,3-alternate conformation was detected. This points to a predominance of thermodynamically stable conformers and suggests the avoidance of an isoclinal arrangement of the lateral substituent, presumably for energetic reasons.

MM Calculation

To evaluate the steric influence of the lateral alkyl substituent, relative energies of the different conformers of 2 as a model compound, summarized in Fig. 4, were determined using the MMFF94 force field (22) as implemented in the SYBYL software. As proven by previous mechanistic studies (7d), all conformations with an axial arrangement of the lateral substituent are energetically discriminated due to their higher angle bending 3). Analogously, the frequency and stability of the coneB conformer detected by NMR can be assumed due to its similar low ground state energy. It is also shown that the energy gap between the 1,2-alternate (alt2C) and the 1,3-alternate conformer is small, giving evidence of their potential presence in solution. The fact that only the 1,2-alternate conformer is detected in the NMR could result from its higher energy gap to the lowest energy partial cone conformer (~ 3.8 kcal/mol for alt2C) leading to separate signals, whereas the interconversion to the 1,3-alternate conformer is too fast on the NMR time scale.

Crystal structure of compound 2 •CHCl 3

In order to compare the conformational results from the solution NMR study with the conformational behaviour in the solid state, we tried to obtain suitable crystals of the compounds 2-5 for X-ray study. Unfortunately, we were unsuccessful in getting highquality crystals in the case of 3-5, presumably due to the high flexibility of the rather extended alkyl chains. However, the corresponding laterally ethyl substituted compound 2 yielded colourless crystals (space group Pca2 1 ) from a solvent mixture of methanol and chloroform (2:1) suitable for X-determination (Table 4). The crystals were analyzed to be a stoichiometric 1:1 solvate with chloroform. Not surprisingly, also in the solid state, one low energy partial cone conformer bearing the lateral substituent in an equatorial position between syn orientated arene units is found (Fig. 7). This result is in agreement both with the predominance of the partial cone conformation in solution and the lowest energy conformer (pacoD) from MM calculation. The following main conclusions can be obtained from this study: [START_REF] Gutsche | Calixarenes -An Introduction[END_REF] The lateral attachment of an alkyl residue to one of the central ring methylene groups of the basic calixarene 1 has no substantial consequence on the conformational behaviour. That is, independent of the chain length, a respective substitution of an alkyl group does not hamper the predominance of the partial cone conformation of 1 in chloroform solution, as proven by NMR spectroscopy. This particular conformation was also found to be low energetic in the calculated sterical energies. Moreover, the crystal structure of compound 2 in its solvated form with chloroform is in structural agreement, showing the partial cone conformation in the crystalline state. ( 2) As against the unsubstituted calixarene 1, the free activation energy for the conformational interconversion of 2-5 in solution is found only moderately higher. Hence, it is shown that (3) an alkyl substitution of one of the hydrogen atoms of a methylene group between the flanking aryl residues of the central ring offers a very promising possibility for coupling of a basic tetramethoxy-calix [4]arene structural element to spacer or linker units in order to realize future developments of new complex framework structures without substantial impairment of the initial calixarene conformation, while corresponding modifications at the upper and lower rim sites normally result in distinct changes of the conformational behaviour.

Future work is required to explore the effect of more than one laterally attached alkyl groups or of a substituent containing polar or functional units in the side chain.

Investigations into this direction are aiming work of our group. The n-BuLi (1.6 M in hexane) was purchased from Acros. Analytical TLC was performed on precoated silica gel plates (Merck, 60 F 254 ). Organic solvents were purified by standard procedures [START_REF] Smallwood | Handbook of Organic Solvent Properties[END_REF].

Experimental

Techniques

Melting points were determined with a hot-stage microscope (VEB Dresden Analytik) and are uncorrected. 1 H and 13 C NMR spectra were recorded using a Bruker DRX 500 spectrometer. The chemical shifts (δ) are reported in ppm relative to TMS = 0 ppm.

Mass spectra were recorded with an EI-MS (Finnigan MAT 8200). The elemental analyses were performed with a Heraeus CHN rapid analyzer.

Synthesis of 5,11,17,23-tetra-tert-butyl-25,26,27,28-tetramethoxycalix[4]arene (1)

A mixture of 5,11,17,23-tetra-tert-butyl-25,26,27,28-tetrahydroxycalix[4]arene (11), NaOH (aqueous, 50 p.c.), dimethyl sulphate and tetrabutylammonium bromide in toluene was reacted following a known procedure (12). Recrystallization from MeOH/CHCl 3 (1:1) yielded 60% of intermediate 5,11,17,23-tetra-tert-butyl-26,28dihydroxy-25,27-dimethoxycalix[4] The synthesis of the products 2-5 follows the protocol described by Scully et al. (7a).

To a stirred solution of 1 (1.0 mmol) in dry THF (30 ml), n-BuLi (1.6 N in n-hexane, 2.9 ml, 4.6 mmol) was added at room temperature under argon. After having stirred for 30 min, the respective 1-halogenalkane (8.0 mmol) was added via syringe to the solution, causing a change of its color from red to yellow. Stirring was continued for 1 h. The solvent was removed under reduced pressure and the residue partitioned into water/dichloromethane (1:1, 60 ml). The organic layer was washed with water (2 x 30 ml), dried (MgSO 4 ) and evaporated under reduced pressure. Recrystallization from MeOH yielded the products as colorless solids. Experimental, MS and elemental analysis data of the individual compounds are specified below. For the detailed 2D

NMR experiments, all substances were dried for 24 h under vacuum at 50 °C. The respective NMR data of 2-5 are given in the Supplementary Materials (Tables S1-S4).

The NMR data for 2 correspond to the literature (7a). 5,11,17,[START_REF] Sheldrick | SHELXL-97: Program for Crystal Structure Refinement[END_REF]27,arene [START_REF] Baklouti | In Calixarenes in the Nanoworld[END_REF] 1-Bromoethane was used. Yield 0.42 g (57%), mp. 183-185 °C [lit. (7a) 184-186 °C]. ,11,17,[START_REF] Sheldrick | SHELXL-97: Program for Crystal Structure Refinement[END_REF]27, 5,11,17,[START_REF] Sheldrick | SHELXL-97: Program for Crystal Structure Refinement[END_REF]27,arene ( 4) 5,11,17,[START_REF] Sheldrick | SHELXL-97: Program for Crystal Structure Refinement[END_REF]27,arene ( 5) (63), 407 (42), 177 (32).

5

1

X-ray crystallography

Crystals of 2 suitable for X-ray diffraction analysis were obtained by slow recrystallization from methanol/chloroform (2:1) solution. The intensity data were collected on a Bruker APEX II diffractometer with MoK α radiation (λ = 0.71073 Å)

using ωand ϕ-scans. Reflections were corrected for background and Lorentz polarization effects. Preliminary structure models were derived by application of direct methods [START_REF] Sheldrick | SHELXL-97: Program for Crystal Structure Refinement[END_REF] and were refined by full-matrix least squares calculation based on F 2 for all reflections [START_REF] Sheldrick | SHELXL-97: Program for Crystal Structure Refinement[END_REF]. All hydrogen atoms were included in the models in calculated positions and were refined as constrained to bonding atoms. Relevant crystal data together with the refinement details are listed in Table 4.

Crystallographic data for the structural analysis have been deposited with the (d, H-3) 7.07 (d, 4 J=2. 4 Hz, 2H, H-5) 7.04 (d, 4 J=2. 3 Hz,2H, 6.86 (d, 4 J=2. 4 Hz,2H, 6.78 (H-13) 6.78 (H-3) 6.75 (H-5) 4.47 (t, 3 J=7.9 Hz, H-1)

4.73 (t, 3 J=8.2 Hz, 1H, H-1) 4.57 ((t), H-1) 4.18 (d, 2 J=12.8 Hz, H-9a) 3.86 (d, 2 J=14.0 Hz, H-17a) 3.84 (d, 2 J=13.0 Hz, H-9a') 3.83 (d, 2 J=14.2, H-17b) 3.80 (d, 2 J=13.8 Hz, H-9b') 3.17 (d, 2

  Mechanics and X-ray study Margit Gruner a , Conrad Fischer b , Tobias Gruber b and Edwin Weber b * a Institut für Organische Chemie, Technische Universität Dresden, Mommsenstr. 13 D-01062 Dresden, Germany; b Institut für Organische Chemie, Technische Universität Bergakademie Freiberg, Leipziger Str. 29, D-09596 Freiberg/Sachs., Germany

calixarenes 2 - 5

 25 in both CDCl 3 and tetrachloroethane-d 2 (TCl-d 2 ) at various temperatures indicates that the compounds exist in different conformers, as demonstrated exemplary for the lateral propyl derivative 3 in Fig. 2. To minimize the signal broadening and separate the overlapping region of methine and methylene signals, we carried out the NMR experiments at an optimized temperature of 269 K, yielding three different signals for the methine protons between 4.47 and 4.79 ppm in CDCl 3 for compounds 2-5.

  of the Supplementary Information). A special denotation of the calixarene scaffold in the three observed conformations is illustrated in Fig.3, indicating similarities in the chemical shift for different pairs of atoms.

  predominance of the partial cone conformation resulting from the NMR experiments, bearing the lateral substituent in an equatorial position between syn orientated arene units in solution (pacoD) may thus be explained with the avoidance of repulsion between the α-C-atom of the lateral alkyl moiety and the neighbouring methoxy groups, indicated by their low sterical energies (Table

1 ,

 1 Selected conformational parameters of the calixarene molecule 2 are summarized in Tab. S5. The opposite phenyl rings A and C differ only little from coplanarity[8.9° (1)], while the aromatic rings B and D are orientated in an angle of 42.8°[START_REF] Gutsche | Calixarenes -An Introduction[END_REF]. Similar to a comparable 2:1 solvate of the lateral unsubstituted calixarene 1 with dichloromethane(18), the methoxy group of ring D points outwards and maintains no interactions with the other rings. In consequence of the compact structure caused by the partial cone conformer, the calixarene does not allow a cavitate inclusion of solvent molecules, which therefore are located interstitially in the crystal lattice. With reference to the crystal packing, the calixarene molecules are orientated translatory staggered along the crystallographic b axis (Fig.8). Corresponding to the nonpolar character of the calixarene, the interactions are limited to weak C-H … π-contacts(23) involving guest and calixarene molecules [d(C1GA … centroid C = 3.569 (1) Å] or the calixarene molecules among each other [d(C33 … centroid B = 3.486 (1) Å] as specified in Tab. S6.ConclusionsAccording to the literature[START_REF] Gutsche | Calixarenes -An Introduction[END_REF]7), calixarenes showing a substitution of a single methylene bridge, especially in the case of an alkyl substitution, are a only the first two members of the potential compound series, i.e. the methyl-and ethyl (2) derivatives have previously been synthesized and preliminarily described regarding their conformational behaviour. With the present calixarenes 3-5 featuring the corresponding mode of lateral substitution but using higher alkyl groups of different chain length, new examples of this particular compound type have now been made available. They enable to perform a first systematic study of the given alkyl groups on the conformational property of the tetramethoxycalix[4]arene system.

1 -

 1 Iodopropane (Fluka), 1-iodopentane (Acros) and 1-bromodecane (Fluka) were used as received.

F

  Selected conformational parameters of the calixarene 2 • CHCl 3 . a Aromatic rings: ring A: C(1)…C(6); ring B: C(8)…C(13); ring C: C(15)…C(20); ring D: C(22) …C(27); b Best plane through atoms C(7), C(14), C(21) and C(28).

  on the physical condition, including type of solvent as well as the presence of a proper guest molecule. However, in no manner, O-alkylated calixarenes that feature an alkyl residue laterally attached to one of the methylene groups of the

				5
	will also depend central ring	have	been	studied	conformationally.	Only	analogous
	tetrahydroxycalixarenes were taken for a corresponding study
	F o r
		P
		e
			e r
				R
				e
				v i e
					w
					O n l
						y

present at the upper and lower rims of the calixarene molecule. Conformational property

General procedure for the synthesis of the laterally monoalkylated calix[4]arenes 2-5

	12
	F o r
	P
	e
	e r
	R
	e
	v i e
	w
	arene as colorless solid, m.p. 235-238°. Following O n l the literature protocol (13), this compound was caused to react with NaH and y
	iodomethane to afford 67% of calixarene 1 as a colorless solid, m.p. 242-244 °C
	(lit.(12) 242-243 °C).

Table 1 .

 1 (a) Rate constants k chem and (b) free activation energies ∆G # of conformational interconversion according to the methine protons H-1 of compounds 2-5 and for comparision of compound 1, calculated by the 2D-EXSY method.

	Cambridge Crystallographic Data Centre, No. CCDC 748215. Copies of this
	information may be obtained free of charge from: The Director, CCDC, 12 Union Road,
	Cambridge, CB2 1EZ, UK. Fax (+44) 1223-336-033; E-mail: deposit@ccdc.cam.ac.uk
	or www: www.ccdc.cam.ac.uk.

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Table 2 .

 2 Mole fractions of conformers for compounds 1-5 in solution.

							Supramolecular Chemistry						Page 20 of 44
	conformer		1				2				3			4	5
		CDCl 3 ,	CDCl 3 ,	TCl-d 2 ,	TCl-d 2 ,	CDCl 3 ,	CDCl 3 ,	TCl-d 2 ,	TCl-d 2 ,	CDCl 3 ,	CDCl 3 ,	TCl-d 2 ,	TCl-d 2 ,	CDCl 3 ,	CDCl 3 ,
		295 K	265 K	295 K	263 K	295 K	261 K	295 K	260 K	295 K	261 K	295 K	260 K	264 K	263 K
	paco ( , ')	85	84	83	84	90	74	88	79	88	72	87	80	73	71
	cone (O)	7	9	6	6	-	17	-	10	-	17	-	10	16	15
	1,2-alt. (M)	8	7	10	9	10	9	12	11	12	10	13	10	11	14

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Table 3 .

 3 Relative energies (in kcal mol -1 ) for possible conformers of ethyl compound 2 obtained by the MMFF94 force field (SYBYL) and calculated populations.

	Conformation	Relative energy	Relative to pacoD	Population
		(kcal mol -1 )	(kcal mol -1 )	(%)
	coneA	225.76	0.01	47.13
	coneB	233.15	7.40	-
	pacoA	233.99	8.24	-
	pacoB	227.77	2.02	1.58
	pacoC	227.58	1.83	2.18
	pacoD	225.75	0.00	47.93
	alt2A	237.02	11.27	-
	alt2B	233.00	7.25	-
	alt2C	229.50	3.75	0.08
	alt3	227.98	2.23	1.11

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Table 4 .

 4 Crystal data and selected details of the data collection and refinement calculations of compound 2 • CHCl 3 .

	Compound	2 • CHCl 3
	Empirical formula	C 51 H 69 Cl 3 O 4
	Formula weight (g mol -1 )	852.4
	Crystal system	orthorhombic
	Space group	Pca2 1
	a (Å)	23.9269(5)
	b (Å)	16.8437(4)
	c (Å)	12.6634(3)
	α (°)	90.00
	β (°)	90.00
	γ (°)	90.00
	V (Å 3 )	5103.6(2)
	Z		4
	F(000)	1832
	D c (Mg m -3 )	1.109
	µ (mm -1 )	0.219
	Data collection
	Temperature (K)	93(2)
	No. of collected reflections	57108
	within the θ-limit (°)	1.21-28.10
	Index ranges ±h, ±k, ±l	-31/31, -22/21, -16/10
	No. of unique reflections	9944
	R int		0.0968
	Refinement calculations: full-
	matrix least-squares on all F 2
	values
	Weighting expression w a	2 )+(0.1788P) 2 + [σ 2 (F o 4.6405P] -1
	No. of refined parameters	537
	No. of F values used [I>2σ(I)]	8817
	Final R-Indices
	R(=Σ|∆F| / Σ|F o |) wR on F 2	0.0843 0.2405
	S (=Goodness of fit on F 2 )	1.092
	Final ∆ρ max /∆ρ min (e Å -3 )	0.000
	a P =(F o	2 + 2F c 2 )

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Table S1b .

 S1b 13C-NMR-spectrum of 2 in CDCl 3 at 264 K.

	paco ( , ')	1,2-alternate(O)	cone(M)
	154.84 (C i -15)
	154.59 (C i -7)

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Table S1c .

 S1c H-NMR-spectrum of 2 in TCl-d 2 at 263 K.

			Page
	paco ( , ')	1,2-alternate(O)	cone(M)
	7.06 (s, br, 1H, H-11')	7.06 (s, br, H-3)	7.09 (H-11)
	7.05 (s, br, 1H, H-13')	6.92 (s, br, H-5)	6.6-6.7 (H-3, 5,
	6.92 (s, br, 1H, H-3')	6.90 (d,br, 2H, H-11)	13)
	6.87 (s, br, 1H, H-11)	6.74 (d,br, 2H, H-13)
	6.83 (s, br, 2H, H-13,5')
	6.59 (s, br, 1H, H-3)
	6.52 (s, br, 1H, H-5)
	4.25 (t, 3 J=7.8 Hz, H-1)	4.43 (t, 3 J=7.8 Hz, 1H, H-1)	4.3 (t, br, H-1)
	4.06 (d, 2 J=12.5 Hz, H-9a)	3.96 (d, 1H, H-17a)	4.14 (br, H-9a)
	3.75 (d, H-17a)	3.73 (d, 2H, H-9a)	3.03 (br, H-9b)
	3.69 (d, H-17b)	3.64 (d, 2H, H-9b)	4.00 (br, H-17a)
	3.09 (d, 2 J=12.4 Hz, H-9b)	3.02 (d, 1H, H-17b)	3.05 (br, H-17b)
	3.73 (d, 2 J~10 Hz, H-9a')
	3.70 (d, 2 J~10 Hz, H-9b')
	3.48 (s, 3H, H-8)	2.96 (s, 6H, H-8)	3.74 (H-8)
	3.39 (s, 3H, H-8')	2.76 (s, 6H, H-16)	3.71 (H-16)
	3.25 (s, 3H, H-16)
	1.60 (s, 3H, H-16')
	1.25 (s, 9H, H-12b')	1.15 (s, 18H, H-4b)	1.29 (H-12b)
	1.12 (s, 18H, H-4b´,12b')	1.12 (s, 18H, H-12b)	1.11 (H-4b)
	0.90 (s, 9H, H-4b)
	1.96 (m, 1H, H-18a)	1.93 (m, 1H, H-18)	not discriminable
	1.89 (m, 1H, H-18b)	0.86 (t, 3H, H-19)
	0.90 (t, 3H, H-19)

1

34 of 44 URL: http:/mc.manuscriptcentral.com/tandf/gsch Email: suprachem@mail.cm.utexas.edu Supramolecular Chemistry F o r P e e r R e v i e w O n l yTable S1d .

 S1d

Table S3a .

 S3a 1 H-NMR-spectrum of 4 in CDCl 3 at 265 K.

	paco ( , ')	1,2-alternate(O)	cone(M)
	7.21 ((d), 1H, H-11')	7.26
	7.20 ((d), 1H, H-11')
	6.98 (((d), 1H, H-5')
	6.97 ((d), 2H, H-3')
	6.97 ((d), 1H, H-13)
	6.94 ((d), 1H, H-11)
	6.81 ((d), 1H, H-3)
	6.72 ((d), 1H, H-5)

40 of 44 URL: http:/mc.manuscriptcentral.com/tandf/gsch Email: suprachem@mail.cm.utexas.edu Supramolecular Chemistry F o r P e e r R e v i e w O n l yTable S3b .

 S3b J=13.0 Hz, H-9b) 4.08(d, 2 J=13.3 Hz, 1H, H-17a) 3.87(d, 2 J=14.7 Hz, 2H, H-9a) 3.75(d, 2H, H-9b)

			Page
			4.30 (br, H-9a)
			3.17 (br, H-9b)
			not discriminable
	3.55 (s, 3H, H-8)	3.11 (s, 6H, H-8)	3.88 (H-8)
	3.55 (s, 3H, H-8')	2.89 (s, 6H, H-16)	3.83 (H-16)
	3.40 (s, 3H, H-16)
	2.00 (s, 3H, H-16')
	1.36 (s, 9H, H-12b')	1.27 (s, 18H, H-4b)	not discriminable
	1.20 (s, 9H, H-4b')	1.23 (s, 18H, H-12b)
	1.20 (s, 9H, H-12b)
	1.07 (s, 9H, H-4b)
	1.97 (m, H-18)	2.03 (m, H-18)	1.97 (m, H-18)
	1.41 (m, H-19)	1.34 (m, H-19)	not discriminable
	1.39 (m, H-20)	1.39 (m, H-20)
	1.32 (m, H-21)	1.31 (m, H-21)
	0.87 (t, 3 J=7.0 Hz, 3H , H-22)	0.82 (m, H-22)

Table S6 .

 S6 Distances und angles of possible hydrogen-bond type interactions of 2.

						Page 44 of 44
		Compound	2 • CHCl 3
		Interplanar angles (°) a
		mpla b /A	83.68 (1)
		mpla/B	43.73 (1)
		mpla/C	87.43 (1)
		mpla/D	86.46 (1)
		A/C	8.90 (1)
		B/D	42.77 (1)
		Atoms involved	Symmetry	Distances (Å)	Angles (°)
				D•••A	H•••A	D-H•••A
		C1G-H1G … centroid(C) a	x, y, z	3.8855 (10)	2.90 (1)	170
		C33-H33A … centroid(B) a	-x, 1-y, ½+z	3.4855 (10)	2.62 (1)	147
		C1GA-H1GA … centroid(C) a	x, y, z	3.5692 (10)	2.63 (1)	157
	a	Centroid means center of gravity of the respective aromatic ring: ring A: C(1)…C(6); ring B: C(8)…C(13); ring C:
		C(15)…C(20); ring D: C(22)…C(27).

URL: http:/mc.manuscriptcentral.com/tandf/gsch Email: suprachem@mail.cm.utexas.edu Supramolecular Chemistry

URL: http:/mc.manuscriptcentral.com/tandf/gsch Email: suprachem@mail.cm.utexas.edu Supramolecular Chemistry

Acknowledgements

This work was supported by the German Federal Ministry of Economics and Technology (BMWi) under grant No. 16IN0218 'ChemoChips'. The authors are also grateful to Dr. I. Thondorf for help with the MM calculation.

Supplementary materials

1 H and 13 C NMR data of 2-5 in CDCl 3 and tetrachloroethane-d 2 , selected conformational parameters and geometric parameters of potential hydrogen bond type interactions from the crystal structure of 2 • CHCl 3 are available as Supplementary Materials, available online.

URL: http:/mc.manuscriptcentral.com/tandf/gsch Email: suprachem@mail.cm.utexas.edu Supramolecular Chemistry

F o r P e e r R e v i e w O n l y

Table S2a.


Srikrishna Bhat

Marie-Odile Berger
email: berger@loria.fr

Frédéric Sur
email: sur@loria.fr

Visual words for 3D reconstruction and pose computation

Visual vocabularies are standard tools in the object/image classification literature, and are emerging as a new tool for building point correspondences for pose estimation. This paper proposes several visual word based methods for point matching, with structure from motion and pose estimation applications in view. The three dimensional geometry of a scene is first extracted with bundle adjustment techniques based on the keypoint correspondences. These correspondences are obtained by grouping the set of all SIFT descriptors from the training images into visual words. We obtain a more accurate 3D geometry than with classical image-to-image point matching. In the second step, these visual words serve as 3D point descriptors robust to viewpoint change, and are then used for building 2D-3D correspondences for a test image, yielding the pose of the camera by solving the PnP problem. We compare several visual word formation techniques w.r.t robustness to viewpoint change between the learning and test images and discuss the required computational time.

Introduction

Camera Pose Estimation is a challenging problem with numerous applications [START_REF] Lepetit | Monocular model-based 3d tracking of rigid objects: A survey[END_REF]. In this paper, we consider an approach in which the pose of a moving camera is estimated using the location information of the 3D points previously extracted from a training video sequence. Point matching is involved in each step of the process and still presents challenging difficulties. Building the 3D model (here, an unstructured 3D point cloud, also called a 3D map) from the training sequence calls for keypoint correspondences across the views. Then, with the model at hand, estimating the pose via the Perspective-n-Points (PnP) camera pose estimation needs correspondences between the 3D points and the keypoints from the training image.

In this paper, we investigate visual word techniques for point matching, both 2D-2D and 3D-2D. While visual vocabularies are now standard tools for object or image classification and recognition [START_REF] Nister | Scalable recognition with a vocabulary tree[END_REF][START_REF] Sivic | Video Google: A text retrieval approach to object matching in videos[END_REF], they are still emerging techniques for Structure from Motion (SfM) and pose estimation problems. The standpoint is not the same: in the first situation visual words are used to build image signatures, whereas in the SfM problems visual words are used as local photometric descriptors to ease point-to-point matching. The standard tool for building point correspondences in SfM problem with Bundle Adjustment (BA) techniques is undoubtedly keypoint matching with e.g. SIFT [START_REF] Lowe | Object recognition from local scale-invariant features[END_REF]. This approach is used for example in Snavely's Bundler [START_REF] Snavely | [END_REF], or in [START_REF] Gordon | Scene modeling, recognition and tracking with invariant image features[END_REF], where a relatively limited set of reference images is used to build the 3D model from BA. Now, attaining a good precision in Bundle Adjustment estimation needs tracks of 2D correspondences between images spanning a large viewpoint change. This is endangered by the lack of invariance of SIFT descriptors to these changes. That is why we use visual word clustering from the set of all images of the learning sequence: the idea is that this sequence should contain smoothly varying aspects of the same objects, thus clustering should group the descriptors associated to the same 3D point into the same visual word.

Related Work

Usual image matching techniques with visual vocabularies have been recently successfully used in 3D reconstruction for multimedia application [START_REF] Agarwal | Building rome in a day[END_REF], location recognition and loop closure detection [START_REF] Angeli | Fast and incremental method for loop-closure detection using bags of visual words[END_REF], or pose computation [START_REF] Engels | Integration of tracked and recognized features for locally and globally robust structure from motion[END_REF][START_REF] Gordon | Scene modeling, recognition and tracking with invariant image features[END_REF][START_REF] Hsiao | Making specific features less discriminative to improve point-based 3d object recognition[END_REF][START_REF] Xiao | Structuring visual words in 3d for arbitrary-view object localization[END_REF].

Our paper shares idea with these four latter papers. In [START_REF] Xiao | Structuring visual words in 3d for arbitrary-view object localization[END_REF], visual word matching is used to define a 3D model from several views of an object through SfM techniques and manual annotation. Each point of the 3D model is then associated with the visual words from the associated 2D points, permitting to build 2D/3D correspondences from a new image (and estimate its pose), after some ad-hoc segmentation and robustification. As mentioned earlier, in [START_REF] Engels | Integration of tracked and recognized features for locally and globally robust structure from motion[END_REF] the SIFT correspondences are used to build a 3D model with BA. The 3D points are associated with the SIFT descriptors attached to their projection in the learning views. Then, the camera pose is estimated in a new video sequence by matching the SIFT keypoints from the test images to these sets of SIFT descriptors, which can be seen as visual words describing the 3D points. In [START_REF] Hsiao | Making specific features less discriminative to improve point-based 3d object recognition[END_REF], visual words are also used as descriptors of 3D points, and a clever algorithm is used to draw 2D-3D correspondences with wide viewpoint changes (thanks to viewpoint simulation [START_REF] Morel | ASIFT: A new framework for fully affine invariant image comparison[END_REF]) and repeated patterns. The approaches from [START_REF] Gordon | Scene modeling, recognition and tracking with invariant image features[END_REF] and [START_REF] Xiao | Structuring visual words in 3d for arbitrary-view object localization[END_REF] are somewhat mixed together in [START_REF] Engels | Integration of tracked and recognized features for locally and globally robust structure from motion[END_REF]. In this latter paper, visual word matching is indeed used in addition to local feature tracking. Local feature tracking enables to estimate pose from frame to frame, while visual words permits longer range matching and stabilizes the estimation. Submaps are built on-line and when the reprojection error becomes too high, a new submap is initiated, and linked to old submaps via visual word matching. Remark that Lepetit et al.'s paper [START_REF] Lepetit | Point matching as a classification problem for fast and robust object pose estimation[END_REF] is also relevant to this work, since it considers point matching as a classification problem: points of interest are associated with artificially generated descriptors under affine or homography hypothesis. To some extent these sets of descriptors can be seen as visual words. As in our framework, the aim is to ease wide baseline matching.

Unlike existing techniques for obtaining 2D/3D correspondences, where the training images are either captured from constrained views of the environment [START_REF] Gordon | Scene modeling, recognition and tracking with invariant image features[END_REF] or deal only with specific objects [START_REF] Xiao | Structuring visual words in 3d for arbitrary-view object localization[END_REF][START_REF] Hsiao | Making specific features less discriminative to improve point-based 3d object recognition[END_REF], we aim at achieving a similar objective from a training video sequence in a large environment. Hence, scalability and robustness of the visual words to pose variations between training and testing images are all the more relevant in our case.

Organization of the paper

Our work involves building a 3D model of the target environment from training images and using the model to compute pose in a test image. In section 2, we present our framework for using the visual word techniques to obtain 2D matches across images during training stage and to represent 3D points for testing stage. In section 2.2 we describe different visual word methods in the literature which will be used in our experiments. Section 2.3 contains the main contribution of this paper, where we present adaptive transitive closure method for computing visual words. In section 2.4 we describe the way in which we match test features with the visual words from the training stage and perform pose computation with the 2D/3D correspondences thus obtained. We separately evaluate the performance of different visual words for 3D model building and pose estimation. In section 3 we describe our data and performance measure for this purpose. The experimental results presented and discussed in section 4 show that our proposed method gives many advantages in terms of speed and quality of the 3D map. Finally, we draw conclusions based on the results and mention our plans for future work in section 5.

Visual word based framework for 3D model building and pose estimation

A Visual Word v is defined by a region R v in Feature Vector Space F , whose elements are identified as representing the same visual image pattern. A feature vector f extracted from a 2D location of an image is said to belong to v if f ∈ R v . We use visual word based framework to represent 3D points in an environment.

Let S = {f 1 .....f N } be the set of SIFT descriptors extracted from the training images. A visual word formation technique partitions S based on some similarity measure on the features, where each partition forms a visual word. In section 2.2, we present different visual word formation techniques used in our experiments. Some of the visual words obtained from S (for e.g. visual words containing features corresponding to repeated patterns in the environment) may not be suitable to uniquely identify 3D points. By employing a pruning strategy (section 2.1) we select suitable elements from the set of visual words computed from S. After this step, a word can be considered as a set of features in physical correspondences and form a track of 2D point matches across respective training images. We then obtain Structure from Motion (SfM) by applying Bundle Adjustment algorithm (Snavely's Bundler, see [START_REF] Snavely | [END_REF]), which computes 3D points corresponding to some of these tracks by minimizing the reprojection error. The 2D tracks with high reprojection error will be discarded by SfM and will not produce any 3D points.

At the end of SfM, we obtain camera pose for the training images and a set of 3D points in the environment. Each such 3D point is uniquely associated with the visual word which was used as input to SfM1 . Hence, we can detect these 3D points in a test image by matching the SIFT features to these visual words, thus providing 2D/3D correspondences for pose estimation. The process of matching a test feature vector with the visual words is explained in section 2.4. Finally, in section 2.5, we mention some of the inherent properties of each type of visual word which are relevant to the pose computation problem.

Pruning visual words

As we are interested in 3D reconstruction and pose computation, our goal is to remove, to a large extent, words which contain features of different 3D physical points. After computing the set of visual words from training video of the target environment, we prune the set to remove false correspondences as much as possible. Figure 1 shows one of the training images and the 2D locations in the image (marked by green '+') corresponding to the SIFT features belonging to the visual words containing the highest number of feature vectors. In [START_REF] Schaffalitzky | Automated location matching in movies[END_REF], patterns occurring more than 5 times in the same image are a priori discarded, in order to handle burstiness [START_REF] Jégou | On the burstiness of visual elements[END_REF] of visual elements. We also apply a similar strategy in a stricter sense. We discard the visual words which appear multiple times in a single training image. We also discard visual words with less than 4 feature vectors, since they are likely to be unstable for reliable detection.

Types of visual words

Currently, the different ways of forming the visual words can be broadly classified into four categories, which are described in the following subsections. In our experiments, we have applied visual words from each category on SIFT features with Euclidean distance d(x, y) based similarity measure.

Type1:k-means based clustering

In the training step, the set of feature vectors extracted from the training images is divided into a pre-determined k number of groups by clustering [START_REF] Sivic | Video Google: A text retrieval approach to object matching in videos[END_REF][START_REF] Nister | Scalable recognition with a vocabulary tree[END_REF]. A Voronoi region corresponding to the cluster center of a group forms a visual word. In our experiments, we apply integer k-means algorithm [START_REF] Vedaldi | VLFeat: An open and portable library of computer vision algorithms[END_REF] to cluster the SIFT features extracted from training images.

Type2:Proximity based matching

The training features are grouped together based on the proximity to each other as in [START_REF] Angeli | Fast and incremental method for loop-closure detection using bags of visual words[END_REF]. In our experiments, we apply range based transitive closure (TC) technique [START_REF] Bhat | Transitive closure based visual words for point matching in video sequence[END_REF]. Two SIFT features x 1 , x 2 are said to be similar if d(x 1 , x 2 ) < r 1 . This similarity relation is reflexive and symmetric. Transitive closure operation is performed on this similarity relation. Each equivalence class in S obtained in this way, represents a visual word. Hence a TC visual word v is represented by a set of feature vectors {f v1 , .., f vn } in the equivalence class.

Type3:Mean-shift (MS) based clustering

Training features are grouped based on the modes of the estimated probability density function. Iterative gradientascent is performed on the estimated probability function starting at each training vector [START_REF] Cheng | Mean shift, mode seeking, and clustering[END_REF]. The vectors which converge to the same mode are grouped into a single visual word. In our implementation, the gradient ascent iteration is stopped when the updated vector lies within a distance 1 from the previous position. After performing mean-shift iterations on all the training vectors, the modes within a distance 2 are merged and represented by their mean (as in the implementation of [START_REF] Georgescu | Mean shift based clustering in high dimensions: a texture classification example[END_REF]). We use values 1 = .1 and

Type4:Visual words from SfM

Instead of clustering the whole set of training features, in this method, initial matches between each pair of training images is established based on standard SIFT keypoint matching [START_REF] Lowe | Object recognition from local scale-invariant features[END_REF], that is to say nearest neighbor matching, provided the ratio between the distances to the nearest and to the second nearest neighbor is below 0.6. The matches which satisfy geometric constraints for the respective pair of images are used to compute 2D tracks. SfM is applied on these 2D tracks to obtain 3D points. The features in the 2D track of a 3D point form the visual word. We use the matching process integrated with the Bundler software [START_REF] Snavely | [END_REF] to establish initial matches between each pair of images. There is no pruning step involved for this type of visual word.

Adaptive TC visual words

For SfM, it is preferable to have longer 2D tracks with multiple views of the same 3D point with significantly varying viewpoint, in order to obtain better quality 3D model. We may have to increase the range value r 1 in range based TC method (section 2.2.2), in order to obtain matches between the features with significant pose variation. As we increase r 1 from a value a to a significantly higher value b, it will definitely retain the existing matches and may even establish new matches between elements of two or more different visual words. Consequently, those visual words will be merged together through transitive closure operation, producing visual words which are supersets of the original sub-words with r 1 = a. Depending on the characteristics of the visual pattern around 3D points or equivalently the region of the pattern in the feature vector space (different visual patterns may vary differently w.r.t. varying pose), this increment in r 1 may lead to some wrong matches. This problem is illustrated in figure 2. It shows portions of two training images and positions of 5 training SIFT features (marked by green '+' and numbered from 1 to 5). By closely observing the local image pattern around these points, we can see that locations 3 and 2 in image (a) match with 4 and 5 in image (b) respectively. Apparently there is no other match among these points. When we compute TC visual words with r 1 = 100, it combines 2 and 5 correctly, but 3 and 4 belong to different visual words. If it is increased to r 1 = 150, then we obtain both the matches, but the feature vector at location 1 gets wrongly merged with the visual word of the feature vector at location 2. The pruning step (section 2.1) will reject the visual word containing 1 and 2 due to its repetition in the same image. Hence, TC visual word with matching range fixed to one of the above values will definitely loose one of the matches. This can be prevented if we can adaptively compute the visual words for locations 3 and 4 with r 1 = 150 and for 2 and 5 with r 1 = 100. Essentially, what we do is to compute visual words for both the values of r 1 and perform pruning on visual words with higher range value r 1 = 150. If a visual word is rejected, then we look for its sub-words in the set of visual words with r 1 = 100 and perform pruning again. This adaptive strategy can retain both the matches shown in the image.

We extend the above strategy for multiple values of r 1 and design a recursive top down approach for obtaining visual words. We obtain TC visual words for multiple values of r 1 = {a 1 > a 2 ... > a k }. This does not add much computational overhead because the range search for the highest value r 1 = a 1 retrieves all the required candidates for other lesser range values. Let V 1 , V 2 ...V k be the corresponding set of visual words. The set of visual words V which finally will be used for building 2D tracks for SfM, is initialized empty. Starting with the set of visual words having highest range value i.e., V 1 , we recursively select candidate visual words which are accepted by the pruning process and add to V . If a visual word v i ∈ V i is rejected while pruning due to repeated occurrence in some images, then we look for its sub-words in V i+1 . Pruning is applied on each sub-word. Successful sub-words are added to V and will be used for building 2D tracks. Unsuccessful ones will in turn lead to pruning of their sub-words in the next level, till we reach sub-words in V k .

Our strategy relies on the assumption that if a matching range value r 1 is significantly high for a particular kind of visual pattern p in the training set of features, in a sense that it will match p with regions which are dissimilar to p, then the visual word containing p along with wrongly matched patterns will repeat in at least one of the training images and will be rejected by pruning process. If this assumption is valid up to the level of accuracy required for the RANSAC based 3D model building process, then we obtain the visual words whose matching range is adapted to the characteristics of the visual patterns represented by them. Even if we do not have any conclusive evidence at present, it will be interesting to investigate the practical effectiveness of this strategy in contrast to the standard SIFT keypoint matching where it is assumed that in each pair of training images, a wrong nearest neighbor match to a keypoint will have, in most of the cases, the second nearest neighbor within a ratio of the distance to the first nearest neigbhor.

Matching and pose computation on test image

During testing, we mainly perform range based matching with the elements in each visual word. A feature vector f from a test image is said to match with visual word v if the nearest neighbor f N N ∈ S to f belongs to v and d(f, f N N ) < r 2 . We run experiments with different values for r 2 . For MS visual words, we run additional experiments where matching is performed by executing the mean-shift iterations. Starting at each test vector, the same mean shift iterations as in the training step, are executed with 1 convergence criteria. A test vector f is said to match a visual word v if corresponding modes lie within a distance of 2 (the values of 1 , 2 are the same as mentioned in section 2.2.3).

We obtain 2D/3D correspondences for a test image through the test feature vectors which match to visual words associated with 3D points. We use a camera of known focal length f . Our intrinsic parameter matrix is K = [f 0 0; 0 f 0; 0 0 1]. We assume that the distortion parameters are zero. We apply EPnP algorithm [START_REF] Lepetit | EPnP: An Accurate O(n) Solution to the PnP Problem[END_REF] to compute the camera pose [R T ] such that the reprojection error of the projection matrix P = K[RT ] is minimal on the set of 2D/3D correspondences. Let Q = {(U i , u i )} be the set of pairs of associated 3D and 2D points in the test image. Due to the presence of possible erroneous matching, we use a RANSAC based pose computation algorithm. Given any set of four 2D/3D correspondences, we first compute an ini-tial guess of the pose using 500 random 4-element subsets of Q to obtain 500 projection matrices P j . We select the projection P best , which produces highest number of inliers (points having reprojection error less than 2 pixels) in Q. Finally, we run EPnP algorithm again using only those elements of Q which are inliers with respect to P best .

Visual word parameters and representation

It is worth noting, in the context of the topic of this paper, the fundamental differences between the types of visual words described above due to the inherent characteristics like computation parameters and representation. Unlike the rest, k-means based method produces pre-determined number of visual words, each with a shape of a Voronoi cell. These are disadvantages for computing 3D points because we may not be able to predict the number of 3D points in a training data a priori and the different feature descriptors of 3D points form complex shapes. But the representation is computationally efficient, since we need to store and match only one cluster center per visual word, unlike the rest where we need to store and match all the feature vectors belonging to a visual word in order to detect the corresponding 3D point in a test image. That is why k-means is so popular in the object/image classification literature (see for example [START_REF] Sivic | Video Google: A text retrieval approach to object matching in videos[END_REF]). Range based matching with every element in a visual word, as explained in the beginning of section 2.4, can represent visual words with complex shapes at the cost of additional space and time complexity for matching.

Experimental Framework

Data Description

For our experiments we capture data inside a room using a camera whose intrinsic parameters are known. We have 7 different short video sequences, out of which 6 training sequences (TD1 to TD6) are captured while manually moving the camera and the last one is a Test sequence captured by fixing the camera at a particular orientation on a robotic table which is instructed to move in a circular path. The radius of the circular path is approximately 42.5 centimeters. Using the robotic measurements we obtain relative positions of the camera in each test image. A rough sketch of the tracks are shown in figure 3. The camera tracks of the sequences are marked with curves in various colors. The track corresponding to each training sequence TDi is tagged with TDi--N where i ∈ {1, 2, 3, 4, 5, 6} and N is the number of images in the sequence. The arrows indicate camera orientation at subsampled positions on the track. T D1 and T D4 have maximum pose variation w.r.t the test sequence. T D5 encircles the test sequence, but the orientations at closest camera positions are such that there is less than 50% view overlap with the test sequence. There are three 2D surfaces in the room on which we have pasted pictures which contain texture information. Some of the pictures are repeated in order to introduce ambiguity. The distance between the cen- ter of the circular robotic trajectory and the angular meeting point of the planar surfaces is approximately 275 centimeters

Evaluation

We have designed an experimental framework for evaluating the goodness of visual words from the 3D model we obtain by applying SfM on the 2D matches established by the visual words. For T D2, we manually mask the two planar regions in all the images. Using these masks we identify the SIFT features extracted from the 2D locations of each surface. For each flat surface in T D2, we identify those 3D points which are associated with at least one SIFT feature lying on the surface. Ideally, all such 3D points should lie on a 2D surface. We compute a plane from these 3D points using RANSAC based least square fit. The goodness measure can be the root mean square distance of the 3D points from the plane. But we cannot apply this measure across different 3D models, unless they are represented in the same scale. To normalize the scale, we manually mark few 2D correspondences in the training images. We compute the 3D positions of these locations in each 3D model by triangulation. Then we manually measure the actual distances between those manually marked points in the environment. Using the ratio of the ground truth distance to the corresponding distance in the 3D model for these points, we can normalize the scale.

For evaluating the accuracy of pose estimation, we use the ground truth 3D camera positions in the test sequence.

Let C gt = {p 1 , p 2 ...p n } and C est = {q 1 , q 2 ...q n } are ground truth and estimated 3D camera positions respectively. Using the closed form solution in [START_REF] Horn | Closed-form solution of absolute orientation using unit quaternions[END_REF], we find the optimal transformation (translation, rotation and scale) of points in C est which minimizes the sum of distances between the respective elements of C gt and C est . We measure the error of C est as

n i ||pi-qi|| nR
, where R is the radius of the circular trajectory of the camera positions in the test sequence.

Experimental Results

We extract SIFT features from the images. For training images we obtain around 200 to 250 features per image. For the test sequence we enable the option to double the size of the image during feature extraction which produces nearly 800 key points per image. We compute the different visual words for range of parameters on training feature vectors. We run k-means with k = {1000, 2000, ..., 9000}, Gaussian mean-shift with σ = {50, 60, ..., 120}, uniform meanshift with w = {125, 150, ..., 250} and range based TC with r 1 = {125, 150, ..., 250}. For our adaptive TC technique proposed in section 2.3, we use the TC visual words with range values of {200, 175, ..., 75} in all experiments. For obtaining visual words directly through standard keypoint match based SfM, we did not need to give any parameter to Bundler software.

Due to lack of space, while presenting the values in tabular form in sections 4.1 and 4.2, we represent the type of visual word and the corresponding parameters as follows. We use letters G, U, T, A, B, K to represent Gaussian meanshift, Uniform mean-shift, range based TC, adaptive TC, visual words obtained directly from Bundler and k-means based visual words respectively. 'X x 1 /x 2 ' represents visual word of type 'X' with x 1 as training parameter and x 2 as testing parameter. If there is no parameter required for training, like for B, or the parameters do not vary, like for A, then we leave it blank, for e.g. 'A /x 2 stands for adaptive TC based visual word with testing parameter x 2 . For MS visual words x 2 is left blank when the matching is performed thorugh mean-shift iterations with the same x 1 used for training. This will avoid confusion with the cases where x 2 is used as range search parameter.

SfM

Table 1, shows the result of evaluation of SfM process on T D2. The first column shows the type of visual word and the parameter. The second columns shows the % of training features which belong to visual word associated with a 3D point. Since the 3D points, during test stage, are detected through the training features, increase in this portion of the training features associated with 3D points will increase the chances of detection of 3D points. The third column shows the % of feature vectors which correspond to the 3D points

Pose Estimation

The top view of the 3D map and the estimated test trajectory on TD2 for 'A /200' is shown in figure 4(a). There is significant view-point change between the train and test sequences. We can see that the deviation in the estimated circular trajectory is small compared to the distance between camera positions and the planar surface. The camera orientation (shown by the arrows at subsampled camera positions) in the test sequence is as expected, since the camera is moving in a circular path while keeping a fixed orientation. We have good reconstruction of the 3D points (red dots in the figure) on the planar surface. There are some scattered 3D points, most of which are from the ceiling (and hence do not belong to the planar region) as marked by blue ellipse in figure 4(b), in a different view obtained by rotating the 3D point cloud by 90 degrees in clock-wise direction around an axis in the direction from the planar region to the test camera positions.

The deviation of the estimated camera positions of the test sequence from the best fit ground truth positions (as explained in section 3.2) is given in table 2. The first column shows the type of visual word and the parameters. The various combination of parameters for training and testing, leads to hundreds of entries for performance values. Due to space limitations, we display the values only for those parameters which provide the best results for their category of visual word on at least one dataset. For some parameters we were not able to perform pose computation on the test sequence due to extremely poor quality of the 3D model built during the training stage. Red bold faced values correspond to the best result on a training data. The best result within a type of visual word for a training data is displayed in red.

The values corresponding to T D1 and T D4 which have large pose difference with the test sequence are given in the last two columns. The quality of the estimated test trajectory is very poor in these cases and consequently, the optimal transform [START_REF] Horn | Closed-form solution of absolute orientation using unit quaternions[END_REF] to the ground truth is not reliable. The only case of slight interest is the entry corresponding to adaptive TC method with matching range 225 for T D4, which is 0.32. None of the other entries are close to it.

By looking at the results corresponding to the rest, i.e., T D2, T D3, T D5 and T D6, we can say that no method is absolutely best in all the cases, but the performance of adaptive TC visual word method is the most stable across various matching parameters. It provides a result very close to the best result (with a maximum gap of .05 times the radius of the ground truth track). Stability of the performance across different training data for a particular value of the parameters is an important factor in our case because we do not have any mean to guess the best parameter value for an environment without ground truth information.

The results indicate that there is no improvement in performance of MS visual words by executing mean-shift iterations during test stage when compared to range based matching.

The poor performance of pose estimation in some of the cases on T D2 is due to the bad quality of the 3D model built during SfM. Even if we ignore the values on T D2, 'A 225' provides the second best average performance (with average deviation 0.15) in the other three cases with a gap of .01 from U 225 (with average deviation 0.14). Apart from stability of performance, adaptive TC visual words are much faster to compute than MS visual words, which makes it more suitable for training in large environments.

Conclusion and Future Work

In this work we have presented a framework for using visual words to represent 3D points in an environment and evaluated the performance of different visual word techniques for representing 3D points in an environment. Our experiments show that the adaptive TC visual words are better in many ways when compared to other techniques. We obtain the best or close to the best performance with an additional advantage of stability of performance across differ- ent parameters and relatively lesser time required during the training stage. One of the drawbacks of our 3D point representation is the space complexity. Multiple feature vectors need to be stored for representing a single 3D point. We need to come up with techniques for approximate matching during training and compact representation for the 3D points during testing, in order for our approach to be efficient in large environments. We were not able to obtain reasonably good results for huge view-point variation between train and test sequences (i.e., for TD1 and TD4). We want to investigate whether ASIFT based view-point simulation [START_REF] Morel | ASIFT: A new framework for fully affine invariant image comparison[END_REF] can help to obtain better results for such cases. Besides, at present, our pose estimation algorithm treats the reprojection error on each detected 3D points with equal weight. We want to investigate how we can improve pose accuracy. Incorporating reconstruction uncertainty on the 3D maps could certainly help us to only consider relevant 3D points in pose computation.

Figure 1 :

 1 Figure 1: Sift features belonging to the three largest visual words (marked by green '+'). Clusters are computed by range based transitive closure method on TD1.

Figure 2 :

 2 Figure 2: Range selection for matching in TC.

Figure 3 :

 3 Figure 3: Camera tracks in the sequences captured for experiments.

Figure 4 :

 4 Figure 4: (a)Estimated circular trajectory in test and train sequence for A /200 on TD2. The arrows show the orientation at subsampled camera positions. The red dots are the 3D points computed through SfM. (b)Points in the blue ellipse belong to the ceiling.

Table 1 :

 1 Result for SfM.

	Param	% Train % of inliers	RMS	Mean Number
		Features	in	Distance Word	Of 3D
		in 3D	plane	of inliers	Size	Points
	T 125	33.0	90.9	3.11	16.43	759
	T 150	26.6	69.8	4.84	15.89	634
	T 175	28.8	87.3	2.84	16.87	646
	T 200	27.0	86.0	3.60	18.52	551
	T 225	24.2	85.7	3.21	21.37	429
	G 50	38.0	98.3	2.36	14.58	985
	G 60	39.8	98.2	2.27	15.18	992
	G 70	32.6	96.0	2.34	14.75	835
	G 80	29.8	98.0	2.23	14.83	760
	G 90	32.1	98.4	2.01	15.61	777
	G 100	25.9	85.7	4.33	15.62	627
	G 110	21.3	82.4	4.39	15.11	534
	G 120	20.8	97.5	2.32	15.89	495
	U 125	35.0	71.9	4.94	13.23	1001
	U 150	38.0	89.3	3.26	13.55	1061
	U 175	27.9	87.7	3.41	12.55	841
	U 200	24.9	67.8	4.44	12.86	733
	U 225	27.3	84.1	3.68	14.42	716
	U 250	25.6	88.8	3.02	16.63	583
	A	62.5	99.2	1.96	20.56	1150
	B	61.6	98.6	2.35	14.81	1571
	K 1000	15.9	78.7	4.68	27.67	217
	K 2000	39.7	96.7	2.72	17.68	848
	K 3000	48.1	71.5	5.13	12.97	1402
	K 4000	46.9	50.9	5.28	10.25	1730
	K 5000	56.5	86.4	3.95	8.92	2396
	K 6000	51.2	74.4	4.92	7.77	2490
	K 7000	50.4	76.2	5.23	7.13	2670
	K 8000	51.2	82.1	4.39	6.64	2914
	K 9000	41.9	54.4	5.25	6.21	2555
	lying within 10 centimeters from the best fit plane (as ex-
	plained in section 3.2). They are the inliers for RANSAC
	based plane fit. The fourth column shows the root-mean-
	square (RMS) distance of these inliers from the plane in
	centimeters. The fifth column shows the average size of the
	visual words associated with the 3D points. The last col-
	umn shows the total number of 3D points computed from
	T D2. From the values in the first 3 columns, it is clear that
	the adaptive TC method performs best closely contended
	by SfM based visual words from Bundler. The entries in
	the fifth column for these two methods indicate that the
	adaptive TC method produces 3D points from longer vi-
	sual words which are split into multiple 3D points by the
	other, resulting in more number of 3D points in the last col-
	umn. In a similar way, Gaussian MS performs better than
	uniform MS and TC visual words which are relatively more
	sensitive to the parameter values. Visual words based on k-
	means are highly unstable with respect to the k parameter,
	and produces least number of inliers for planar 3D points in
	most of the cases. Hence we ignore it in the pose estimation

Table 2 :

 2 Result of pose estimation for each training set.

	Params	TD2	TD3	TD5	TD6	TD1	TD4
	T 125/225	0.13	0.10	0.13	-	1.00	1.07
	T 150/225	0.85	0.13	0.11	0.24	1.04	0.93
	T 175/200	0.19	0.15	0.13	0.23	0.93	1.02
	T 175/225	0.12	0.12	0.13	0.23	0.96	1.08
	T 225/225	0.71	0.12	0.15	0.21	1.05	0.44
	T 250/225	-	-	0.17	0.18	-	0.50
	G 50/150	0.56	0.10	0.19	-	-	-
	G 80/200	0.11	0.14	0.19	0.24	0.99	0.58
	G 90/200	0.08	0.16	0.11	0.29	0.95	1.07
	G 100/200	0.79	0.14	0.10	0.23	0.95	1.06
	G 100/225	0.79	0.13	0.10	0.25	0.86	1.09
	G 110/225	0.98	0.14	0.16	0.22	0.95	0.73
	U 150/225	0.10	0.10	0.18	-	1.02	0.90
	U 200/	0.70	0.10	0.13	0.23	0.85	1.08
	U 200/225	0.75	0.10	0.12	0.25	0.77	0.92
	U 225/	0.21	0.12	0.12	0.19	0.86	1.06
	U 250/225	0.17	0.20	0.15	0.32	0.84	0.43
	A /175	0.14	0.09	0.14	0.29	0.89	0.73
	A /200	0.12	0.09	0.15	0.28	1.15	0.68
	A /225	0.13	0.09	0.14	0.23	1.04	0.32
	B /150	0.67	0.10	0.12	0.33	1.00	1.00
	B /175	0.50	0.09	0.12	0.31	1.05	1.10
	B /200	0.42	0.10	0.12	0.29	0.86	1.07
	B /225	0.37	0.11	0.12	0.37	0.91	1.00

SfM algorithm may create multiple 3D points for some

2D tracks. We discard those 3D points. In our experiments, the number of such 2D tracks is negligible, typically around 1% of the total number of tracks).

= 1. We experiment with two types of kernels: (1)Uniform, i.e., K(x) = 1 for x ≤ w and K(x) = 0 for x > w and (2)Gaussian, i.e., K(x) = e -(x 2 /σ 2 ) . Uniform kernel has compact support, i.e., we have to explicitly provide a bandwidth parameter w, beyond which the kernel has zero value. Gaussian kernel has infinite support, but for practical reasons, we derive w, beyond which the value of the kernel is negligible[START_REF] Comaniciu | Mean shift: A robust approach toward feature space analysis[END_REF]. For variance σ of the Gaussian kernel, our w is such that, if x > w, then e -(x 2 /σ 2 ) <[START_REF] Agarwal | Building rome in a day[END_REF] 128 , where 128 is the dimension of SIFT features. We use kdtree based exact range search (i.e. without any approximation for range search) algorithm[START_REF] Mount | ANN: A library for approximate nearest neighbor searching[END_REF], for speeding up mean-shift iterations.