Simone Frintrop

The High Repeatability of Salient Regions

In this paper, we show that salient regions, detected by a biologically motivated attention system, have a considerably higher repeatability than features detected by standard detectors (Harris-Laplacians and DoG features). If a scene contains a salient region, which differs in one of several possible features from the rest of the scene, the repeatability is close to 100%. In settings in which no especially salient region is present, the repeatability of attention regions is similar to DoG features and considerably higher than Harris-Laplacians.

Introduction

Feature detection is an important task for many applications in computer and robot vision. Usually, the detected features are used to establish correspondences between images. This is important in classical computer vision tasks like object recognition [START_REF] Lowe | Distinctive image features from scale-invariant keypoints[END_REF], wide baseline matching [START_REF] Matas | Robust wide baseline stereo from maximally stable extremal regions[END_REF], and 3D reconstruction [START_REF] Pollefeys | Visual modeling with a hand-held camera[END_REF], but also in tasks for cognitive agents like robot localization [START_REF] Se | Mobile robot localization and mapping with uncertainty using scale-invariant visual landmarks[END_REF], and simultaneous localization and mapping (SLAM) [START_REF] Davison | MonoSLAM: Real-Time Single Camera SLAM[END_REF][START_REF] Frintrop | Attentional landmarks and active gaze control for visual SLAM[END_REF].

Many good and stable feature detectors have been developed during the last decades (see [START_REF] Mikolajczyk | A comparison of affine region detectors[END_REF] for a comparison). An important property of feature detectors is their repeatability: the same feature should be detected if a scene is visited from a different viewpoint or if the illumination changes. Usually, detectors compensate for a lack of repeatability by determining a large amount of features, which naturally increases the repeatability. However, in many applications a few stable features are sufficient and even preferable, since detecting, storing and comparing hundreds of features per frame is costly. Especially cognitive agents which have to share resources between different modules and tasks would profit from such a complexity reduction.

We show here that the human ability to focus on a few, salient regions in a scene can be exploited to achieve a sparse collection of features with very high repeatability. Biologically motivated attention systems mimic the mechanisms of the human visual system to determine the saliency of regions based on strong contrasts and uniqueness in several feature dimensions. Many attention systems have been developed during the last years [START_REF] Tsotsos | Modeling visual attention via selective tuning[END_REF][START_REF] Itti | A model of saliency-based visual attention for rapid scene analysis[END_REF][START_REF] Frintrop | VOCUS: A Visual Attention System for Object Detection and Goaldirected Search[END_REF] and have been evaluated with respect to their ability to simulate human eye movements [START_REF] Parkhurst | Modeling the role of salience in the allocation of overt visual attention[END_REF]. They have been also used as feature detector for computer vision and robotics [START_REF] Frintrop | Attentional landmarks and active gaze control for visual SLAM[END_REF], but to our knowledge, they have not yet been compared to standard detectors. An exception is an entropy-based saliency detector [START_REF] Kadir | An affine invariant salient region detector[END_REF] which was compared with other detectors in [START_REF] Mikolajczyk | A comparison of affine region detectors[END_REF]. 1 It does however not consider the combination of different feature channels. In this paper, we show that regions with a high saliency have a considerably higher repeatability than features detected with standard detectors.

Biologically motivated salient regions

Biologically motivated attention systems base on the ability of humans to detect outliers in a scene. A black sheep in a white herd or a red ball on green grass attract our attention [START_REF] Treisman | A feature integration theory of attention[END_REF][START_REF] Wolfe | Visual search[END_REF]. Here, we use the attention system VOCUS [START_REF] Frintrop | VOCUS: A Visual Attention System for Object Detection and Goaldirected Search[END_REF]. It is in many aspects similar to the well-known system of Itti et al. [START_REF] Itti | A model of saliency-based visual attention for rapid scene analysis[END_REF] (a description of the differences can be found in [START_REF] Frintrop | VOCUS: A Visual Attention System for Object Detection and Goaldirected Search[END_REF]). One advantage of VOCUS is that it is real-time capable (50 ms for a 400 × 300 pixel image, on a 2.8 GHz PC [START_REF] Frintrop | A real-time visual attention system using integral images[END_REF]). Additionally, VOCUS has a top-down part to search for targets [START_REF] Frintrop | VOCUS: A Visual Attention System for Object Detection and Goaldirected Search[END_REF], but this is not considered here.

VOCUS creates a saliency map by computing image contrasts and uniqueness of a feature. The feature computations for the features intensity, orientation, and color are performed on 3 different scales with image pyramids. Two intensity feature maps, for on-off and off-on contrasts, are computed by center-surround mechanisms. Similarly, 4 orientation maps (0 • , 45 • , 90 • , 135 • ) and 4 color maps (green, blue, red, yellow) are computed (cf. [START_REF] Frintrop | VOCUS: A Visual Attention System for Object Detection and Goaldirected Search[END_REF]).

Before the features are fused, they are weighted according to their uniqueness: a feature which occurs seldomly in a scene is assigned a higher saliency than a frequently occurring feature. This is the mechanism which enables humans to instantly detect outliers in a scene. The uniqueness W of map X is computed as W(X) = X/ √ m, where m is the number of local maxima that exceed a threshold and '/' is here the point-wise division of an image with a scalar. The maps are summed up to 3 conspicuity maps I (intensity), O (orientation) and C (color) and combined to the saliency map:

S = W(I) + W(O) + W(C) (1)
The local maxima in S are sorted by saliency value (brightness in S), resulting in a ordered list of salient regions, the VOCUS-ROIs, V i = (V 1 , ..., V k ). Note that V j has a higher saliency than V j+i (i ∈ {1, .., (kj)}). The value of k is usually determined automatically, by considering all V i that have a saliency value of at least p% (e.g. p = 50) of V 1 . In the following experiments, we determine a fixed k to enable a direct comparison depending on the number of features.

Experiments

In our experiments, we show the high repeatability of salient regions and compare it with the repeatability of the standard detectors Harris-Laplace corners [ 1. The repeatability of the strongest feature of ROIs from the attention system VOCUS, Harris-Laplace, and DoG features on the data sets illustrated in Fig. 1.

and Difference-of-Gaussians (DoG) blobs, i.e. extrema in DoG scale space [START_REF] Lowe | Distinctive image features from scale-invariant keypoints[END_REF]. 2 To make the detectors comparable with the VOCUS-ROIs, we reduced the number of points by sorting them according to their response value and considering the same amount of features for each detector. We compared whether this response can be used to obtain a similar result as with salient regions.

As performance measure, we used the repeatability, similar to [START_REF] Mikolajczyk | A comparison of affine region detectors[END_REF]. 3 It is defined as the percentage of features (regions/points) in an image sequence which are detected in subsequent frames. All experiments were carried out on images of size 320 × 240.

Repeatability of strongest feature

In the first experiment, we evaluated the repeatability of the strongest/most salient feature. The experiments were performed on 5 image sequences of 200-400 frames (cf. Fig. 1). In all cases, strong viewpoint changes occur.

The 1st data set shows an artifically created scenery with many white and one green object with the same shape. The artificial set up enabled us to create a typical pop out case in which one object is considerably more salient than the others. Data set 2 and 3 show natural scenes in an office environment which contain objects which were especially designed to be salient for humans: a red circle containing a warning remark and a green exit sign. The last 2 data sets show scenes in which no especially salient object occurs, many regions are equally salient and are used for comparison.

Table 1 shows the repeatability of the most salient VOCUS-ROI V 1 and the strongest Harris-Laplace and DoG feature. For scenes containing especially salient objects (data sets 1-3), the repeatability of VOCUS-ROIs is, as to be expected, very high; it varies between 95 and 100%. The repeatability of Harris-Laplace and DoG features is considerably lower. Naturally, the advantage of attention regions especially shows off if there are salient objects. This is for example useful for a cognitive agent which is able to actively search for salient regions in its environment. Anyway, it is interesting to investigate what happens if there are no particularly salient objects but a normal, cluttered scene. We expected the VOCUS-ROIs to have about the same repeatability as the other detectors here. The last two rows of Table 1 show that the repeatability of VOCUS-ROIs and DoG points is indeed similar. Harris-Laplace corners have generally a much lower value. Note however that Harris-Laplacians have a very high accuracy which is important for some applications.

Repeatability of the k strongest features

In the second experiment, we investigate how the repeatability changes if not only one, but the k most salient features are considered. Naturally, the repeata- bility goes up when considering more features. 4 However, since our concern here is to select few features, we consider small k.

We investigated the repeatability on the first 10 frames of data set 1 for different numbers of k. We investigated values up to k = 11, since this is the average value of VOCUS-ROIs detected in natural environments if k is chosen automatically (cf. sec. 2). The results are shown in Fig. 2. The highest repeatability is, as expected, obtained for k = 1, V 1 is on the same region in each frame. For k ∈ {2, 3, 4}, the VOCUS-ROI repeatability goes slightly down. This is easily explained: in the example, there is one especially salient object, the other objects are identical and have very similar saliency. Therefore, V 2 -V 4 tend to switch regions from frame to frame. For k > 4, the repeatability goes up again.

The repeatability of DoG and Harris-Laplace features is considerably lower, 20 -30% for Harris-Laplace and around 50% for DoG (except for k = 1). These first results illustrate the advantage of salient regions. It will however be necessary to repeat this experiment in future work for the other data sets. It is to be expected that the difference between curves is lower for natural scenes, especially for scenes without particularly salient objects. This goes conform with our claim: salient regions are highly repeatable, for scenes without salient regions the performance is comparable to standard approaches.

Conclusion

In this paper, we have shown the advantages of salient regions: they have a considerably higher repeatability than other image regions. Biologically motivated attention systems are able to capture this saliency from different feature dimensions. If a region pops out from the rest of the scene in at least one of 10 dimensions, its saliency is high. In applications in which a few correspondences between images are sufficient, this provides a significant advantage. One example is the loop closing in visual SLAM scenarios in which a previously seen location has to be redetected [START_REF] Frintrop | Attentional landmarks and active gaze control for visual SLAM[END_REF]. It would also be possible to actively search for expected, salient features by controlling the camera.

In a comparison with standard detectors, we have shown that the salient regions have a considerably higher repeatability. Naturally, this works best if the scene contains especially salient objects. In normal scenes without especially salient parts, the attention regions still show equal or better performance than the other detectors. The presented experiments are first results to illustrate the advantages of saliency. More detailed experiments are planned for the future to investigate how representative the values are in different settings.

Fig. 1 .

 1 Fig. 1. The 5 data sets for the experiments in Tab. 1. 1st col: saliency map for 1st frame. 2-4th col: some frames with the most salient VOCUS-ROI V 1 (red ellipse). Complete sequences on http://www.informatik.uni-bonn.de/∼frintrop/research/saliency.html).

Fig. 2 .

 2 Fig.2. Comparison of the repeatability of VOCUS-ROIs, Harris-Laplace, and DoG features on 10 frames of a sequence with a visually salient object (data set 1, Fig.1).

Table

  16]

			repeatability of strongest feature [%]
	data set # frames VOCUS-ROI Harris-Laplacians DoG features
	1	400	100	8	21
	2	305	95	32	53
	3	259	97	44	59
	4	291	70	47	78
	5	209	82	12	74

The low score in[START_REF] Mikolajczyk | A comparison of affine region detectors[END_REF] may be explained by the comparison method: a large amount of features (200-1600) per frame was considered, and the advantage of a saliency detector naturally shows off rather for a sparse feature representation.

We used the publically available PYRA real-time vision library for both Harris-Laplace and DoG features (http://www.csc.kth.se/∼celle/). Both detectors are, as usual, restricted to gray-scale images.

[START_REF] Pollefeys | Visual modeling with a hand-held camera[END_REF] In[START_REF] Mikolajczyk | A comparison of affine region detectors[END_REF], also the number of correspondences were determined, but since we are interested in a low number, this performance measure is not useful here.

Repeatability rates of about 60% have been reported for Harris-Laplacians in[START_REF] Mikolajczyk | A comparison of affine region detectors[END_REF], with k > 1000.


Michela Romanini

Ivo B Rietveld
email: ivo.rietveld@univ-rouen.fr

Maria Barrio

Philippe Négrier

Denise Mondieig

Roberto Macovez

René Céolin

Josep-Lluís Tamarit
email: josep.lluis.tamarit@upc.edu

Philippe Negrier

Uniaxial Negative Thermal Expansion in Polymorphic 2-Bromobenzophenone, Due to Aromatic Interactions?

INTRODUCTION

Benzophenone (chemical formula C13H10O, Figure 1) and its derivatives exhibit great diversity in biochemical and photophysical properties, which are exploited in a huge number of applications. They are inhibitors of enzymes and possess antimicrobial, anticancer, and antiviral properties. Moreover, they are good absorbers of ultraviolet light and are used to prevent damage in the skin in sunscreen lotions and to avoid photo-degradation of polymers for packaging. Benzophenone derivatives are also used as crosslinking units between polymers, and as photoinitiators among others. [START_REF] Kim | Designing Responsive Buckled Surfaces by Halftone Gel Lithography[END_REF][START_REF] Schlumpf | Endocrine activity and developmental toxicity of cosmetic UV filters-an update[END_REF][START_REF] Costa | Structure Based Design, Synthesis, and Evaluation of Potential Inhibitors of Steroid Sulfatase[END_REF][START_REF] Cuquerella | Benzophenone Photosensitized DNA Damage[END_REF][START_REF] Wu | Structural diversity and bioactivities of natural benzophenones[END_REF][START_REF] Suzuki | Estrogenic and antiandrogenic activities of 17 benzophenone derivatives used as UV stabilizers and sunscreens[END_REF] In pharmaceutical chemistry, the benzophenone scaffold is a basic synthetic building block. [START_REF] Surana | Benzophenone: a ubiquitous scaffold in medicinal chemistry[END_REF] Finally, these molecules are used in light-emitting diodes and in other optoelectronic applications due to their linear and nonlinear optical properties. [START_REF] Hoshino | Electroluminescence from triplet excited states of benzophenone[END_REF][START_REF] Zhao | The important role of the bromo group in improving the properties of organic nonlinear optical materials[END_REF] Benzophenone (BPh) was observed to exhibit polymorphism in the latter part of the 19 th century [START_REF] Gossner | VIII. Untersuchung polymorpher Körper[END_REF] and a short historical review has been given in a paper by Kutzke et al. [START_REF] Kutzke | Metastable β-phase of benzophenone: independent structure determinations via X-ray powder -diffraction and single crystal studies[END_REF] The polymorphism is strongly related to the chiral character of the benzophenone molecule. The chirality is associated with the dihedral angle between the two planes defined by the phenyl rings, which can also be described in terms of the angles of either phenyl group with the central ketone plane, >C-(C=O)-C<, through the two torsion angles O=C-C-C, in which the last carbon atom is part of either one of the phenyl rings. However, the enantiomers (i.e. stereoisomers that cannot be superposed on their mirror image) only materialize in the solid state as both in the liquid and gas phase, the aromatic rings of BPh can turn more or less freely resulting in a dynamically averaged single conformation.

Whereas the crystal structure of the stable polymorph of BPh (orthorhombic, space group P212121) contains only one enantiomer, 12 the metastable polymorph (monoclinic, space group C2/c), obtained by recrystallization from the liquid, which is by its nature racemic, is a racemate. [START_REF] Kutzke | Metastable β-phase of benzophenone: independent structure determinations via X-ray powder -diffraction and single crystal studies[END_REF] In addition, the two polymorphs differ in their molecular conformation characterized by the dihedral angle between the planes of the two phenyl rings, while all other bond lengths and angles remain similar. In the stable phase of BPh, this dihedral angle is 54.4°, whereas in the metastable phase it is 64.5°. [START_REF] Kutzke | Metastable β-phase of benzophenone: independent structure determinations via X-ray powder -diffraction and single crystal studies[END_REF] Both dihedral angles are close to the theoretical optimum angle of 52.5° calculated for the isolated molecule using DFT. [START_REF] Ma | Variable Conformation of Benzophenone in a Series of Resorcinarene-Based Supramolecular Frameworks[END_REF] Because the metastable form of BPh is racemic, a transition on heating from this phase to the enantiomer-pure, stable form would imply a chiral inversion of one of the two enantiomers. This process has not been reported for BPh as it was for 4-methylbenzophenone (Figure 1), [START_REF] Kutzke | Stable and metastable crystal phases of 4methylbenzophenone[END_REF] which may imply that the activation energy for the conversion is too high. Ma and Coppens studied ten supramolecular crystals in which BPh is encapsulated as a guest and determined the distortion energy of the different conformations of BPh as a function of the dihedral angle between the phenyl planes ranging between 42 and 68°. [START_REF] Ma | Variable Conformation of Benzophenone in a Series of Resorcinarene-Based Supramolecular Frameworks[END_REF] They obtained energy differences of up to 25 kJ•mol -1 , which is significant compared to the lattice energy of the stable, -85.9 kJ•mol -1 , and metastable, -83.0 kJ•mol -1 , polymorphs. [START_REF] Kutzke | Metastable β-phase of benzophenone: independent structure determinations via X-ray powder -diffraction and single crystal studies[END_REF] Quantum chemical calculations for BPh on the rotational potential energy surface showed that the dihedral angle between the phenyl rings remains near 60 o along most of the minimum rotational energy path, thus, close to the values found in both stable and metastable structures. This result suggests that steric interactions are more important than conjugation and crystal-packing forces when it comes to the molecular conformation. [START_REF] Gough | Hindered internal rotation in benzophenone[END_REF] The interplay of chirality and polymorphism in the BPh derivatives is diverse. In this work, a study on 2-bromobenzophenone (2-BrBPh, Figure 1) is presented. Introducing a bromine atom at the 2-position causes stronger steric hindrance between the aryl groups in comparison to unsubstituted BPh. The structure of the stable phase (form I) of 2-BrBPh was determined by Baumer et al. in 2005 through single crystal X-ray diffraction and was found to be a racemate (monoclinic, space group P21/a). [START_REF] Baumer | 2-Bromobenzophenone[END_REF] A new metastable phase (form II), obtained by recrystallization from the supercooled liquid, was recently discovered by Baran et al., but its structure remains to be determined. [START_REF] Baran | Discovery of a new polymorphic phase of orthobromobenzophenone[END_REF] Baumer et al., through DFT calculations and quantum chemical modelling on the isolated molecule, demonstrated the existence of two low-energy conformers with different torsion angles (both existing as a pair of enantiomers), while the conformation with the lowest energy was very close to the observed torsion angle in phase I. Because the energy barrier between the two conformations was found to be small, the gas phase at RT should contain about 34% of the other conformation. Thus, they concluded that the crystal packing has a "substantial influence on the conformational parameters" (i.e. the torsion angle) of the 2-BrBPh molecule in the crystalline state. [START_REF] Baumer | 2-Bromobenzophenone[END_REF] However, this must be within the boundaries created by the steric hindrance between the two rings and the bromine atom.

It is interesting to point out that the equilibrium conformation of unsubstituted benzophenone is a "helicoidal" conformer with both phenyl rings tilted with respect to the plane of the carbonyl group. [START_REF] Baraldi | Conformations and internal rotation properties of molecules containing one geminal diphenylgroup: diphenylethylene, diphenylketimine, benzophenone, diphenylether and diphenylmethane[END_REF] Such a geometry favours cross-conjugation between both equivalent phenyl moieties by sacrificing the optimum coplanar geometry which would maximize electronic conjugation of a single phenyl ring with the central carbonyl group. In contrast, in the brominated 2-BrBPh derivative the phenyl ring is coplanar with the carbonyl group. This entails that the large electronegativity of the Br substituent leads to a strong molecular asymmetry which suppresses the energy gain of cross-conjugation between the two aryl moieties, leading to a coplanar geometry that maximizes electron delocalization between the carbonyl group and the unsubstituted ring. A survey of other mono-substituted analogues (Figure 1), such as 2-chlorobenzophenone (2-ClBPh), [START_REF] Pinkus | Crystal structures of 2-chloro-and 2,5-dichloro-benzophenones[END_REF] 4-bromobenzophenone (4-BrBPh), [START_REF] Strzhemechny | Polymorphism of 4-bromobenzophenone[END_REF] or 4-methylbenzophenone (4-methylBPh) [START_REF] Kutzke | Stable and metastable crystal phases of 4methylbenzophenone[END_REF] for which crystal structures of the stable and metastable phases have been described, shows that the interplay between chirality, the structures, and their stability is highly unpredictable. Whereas stable phases of 4-methylBPh (P21/c), 2-ClBPh (P21/c) and 4-BrBPh (P21/c) are centrosymmetric (racemic) crystal structures, metastable phases (when they have been discovered) were found either to contain both enantiomers, i.e. to be racemic crystals, in the case of 4-BrBPh with a P-1 space group, or to contain only one enantiomer, i.e. to be enantiomorph crystals, in the case of 4-methylBPh with a P31 space group. Interestingly, for the unsubstituted BPh, the stable form contains only one enantiomer in the P212121 space group, while the metastable form is the racemic crystal with the space group C2/c. Thus, Wallach's rule [START_REF] Wallach | Zur Kenntniss der Terpene und der ätherischen Oele[END_REF] claiming that racemic crystals have in general a higher density and stability does not seem to be universally true, in particular in the case of BPh.

Intermolecular interactions caused by aromatic systems have received considerable attention. [START_REF] Hunter | The nature of π-π interactions[END_REF][START_REF] Salonen | Aromatic rings in chemical and biological recognition: energetics and structures[END_REF] Often, these interactions are called π-π stacking and three main configurations between two aromatic rings are identified: 23 i) face-to-face, ii) parallel-displaced, and iii) Tshaped edge-to-face (also designated as C-H•••π). Nonetheless, the interpretation of the strengths of these quite different interaction geometries is still not fully understood, while the use of the term π-π stacking to describe aromatic interactions is being advised against. [START_REF] Martinez | Rethinking the term "pi-stacking[END_REF][START_REF] Grimme | Do special noncovalent pi-pi stacking interactions really exist?[END_REF] In particular for small, simple molecules such as benzene direct face-to-face stacking does not increase the interaction between two aromatic rings. [START_REF] Grimme | Do special noncovalent pi-pi stacking interactions really exist?[END_REF] However, larger sized aromatic molecules, electron withdrawing substituents on aromatic rings, parallel-displaced geometries and the T-shaped geometries all lead to more favorable interactions for which the label 'aromatic interaction' is probably too general. [START_REF] Salonen | Aromatic rings in chemical and biological recognition: energetics and structures[END_REF][START_REF] Martinez | Rethinking the term "pi-stacking[END_REF][START_REF] Grimme | Do special noncovalent pi-pi stacking interactions really exist?[END_REF] In addition to the problem of the identity of 'the' aromatic interaction, the directionality of the aromatic interactions is not as straightforward as for example for hydrogen bonds. Thermal expansion studies may allow to obtain information about the directionality; however, such studies related to molecules that are mainly aromatic in nature are fairly rare. The aromatic molecule 1-hydroxypyrene was found to exhibit positive thermal expansion in all directions. [START_REF] Gajda | Crystal morphology fixed by interplay of π-stacking and hydrogen bonds -the case of 1-hydroxypyrene[END_REF] Nonetheless, Saraswatula et al. demonstrate that increasing the strength of the aromatic interactions can decrease thermal expansion in a series of similar aromatic molecules. [START_REF] Saraswatula | Stronger π•••π Interaction Leads to a Smaller Thermal Expansion in Some Charge Transfer Complexes[END_REF] Glipizide is probably one of the earlier examples demonstrating uniaxial negative thermal expansion (NTE), although steric hindrance appears to be the cause of the uniaxial contraction on heating. [START_REF] Burley | Structure and intermolecular interactions of glipizide from laboratory X-ray powder diffraction[END_REF] NTE has been observed for co-crystals with 4-phenylazopyridine, which was ascribed to a rotational movement of the molecules and to the hydrogen bonds present in the co-crystals. [START_REF] Hutchins | Achieving dynamic behaviour and thermal expansion in the organic solid state via cocrystallization[END_REF] Furthermore, NTE has been shown to be generated by oppositely shifting molecular layers, although hydrogen bonding was again involved in this case. [START_REF] Bhattacharya | Steric guided anomalous thermal expansion in a dimorphic organic system[END_REF][START_REF] Bhattacharya | Uniaxial Negative Thermal Expansion in an Organic Complex Caused by Sliding of Layers[END_REF] It is therefore, up to now, not clear whether aromatic interactions are able to directly cause (uniaxial) NTE as hydrogen bonds are known to be capable of.

In the following, the crystal structures of 2-bromobenzophenone are analyzed. It is demonstrated that, despite the existence of two possible conformers for each enantiomer of 2BrBPh, both stable and metastable crystalline phases belong to a centrosymmetric space group and thus, both enantiomers are present. These enantiomers only favor one conformation. Moreover, temperature-resolved X-ray diffraction demonstrates the presence of uniaxial NTE in the presence of mainly aromatic interactions. It is shown that the density of the metastable phase is higher than that of the stable phase and its consequences on the stability relationship between phases I and II as a function of pressure will be analyzed.

EXPERIMENTAL SECTION

Material.

Differential Scanning Calorimetry. Differential scanning calorimetry (DSC) experiments

were carried out with a conventional Q100 thermal analyzer from TA Instruments. It was calibrated using the melting point of indium (Tfus = 429.75 K and ∆fusH = 3.267 kJ mol -1 ). The specimens with sample masses around 10 mg were weighed with a microbalance sensitive to 0.01 mg and sealed in aluminum pans.

High-pressure differential thermal analysis. High-pressure differential thermal analysis (HP-DTA) measurements were carried out with an in-house-constructed apparatus similar to the equipment built by Würflinger [START_REF] Würflinger | Differential thermal-analysis under high-pressure IV. Low-temperature DTA of solid-solid and solid-liquid transitions of several hydrocarbons up to 3 kbar[END_REF] operating between 0-300 MPa. Melting temperatures as a function of pressure were determined of specimens mixed with an inert Perfluorinated liquid (Galden; Bioblock Scientifics, Illkirch, France) to eliminate air while enclosed in tin capsules. The onset of the calorimetric peaks was taken as the melting temperature.

High resolution X-ray diffraction as a function of temperature. High-resolution Xray diffraction as a function of temperature was performed at normal pressure using Debye-Scherrer geometry and transmission mode. CuKα1 (λ = 1.54056 Å) radiation was used in a horizontally mounted INEL diffractometer with a quartz monochromator and a cylindrical position-sensitive detector (CPS-120) with 4096 channels (0.029 o 2θ-angular step). Powder samples were introduced into a 0.5-mm-diameter Lindemann capillary. The temperature was controlled with a 700 series Oxford Cryostream Cooler from Oxford UK Cryosystems.

Lattice parameters as a function of the temperature were determined through isothermal acquisition of X-ray patterns between 100 K and the respective melting points of both forms. External calibration by means of the cubic phase Na2Ca3Al2F4 and cubic spline fitting was used to convert the measurement channels into 2θ. Peak positions were determined using pseudo-Voigt fitting.

Liquid density measurements. The density of the (supercooled) liquid was determined as a function of the temperature with a DMA-5000 Density Meter from Anton Paar. Data were obtained at isothermal steps on cooling from 363.2 K down to 298.2 K with a temperature control of ±1 mK.

RESULTS AND DISCUSSION

Characterization of the polymorphic behavior Thermodynamic study. A DSC curve of a 2-BrBPh sample in a closed pan is presented in Figure 2. Heating from room temperature, the sample (initially purified form I) exhibited a single endothermic effect ascribed to a melting transition with a mean onset at 312.2 ±0.5 K and a mean value of the melting enthalpy of 18.7 ±0.4 kJ•mol -1 (see Table 1). On reheating after quick or slow cooling of the melt to 193 K, a glass transition was observed at 224.8 ±0.5 K (midpoint), followed by an exothermic peak at around 265 K corresponding to the recrystallization of the supercooled liquid into the metastable form II, which melts at 302.2 ±0.5 K, with a lower melting enthalpy, 16.3 ±0.7 kJ•mol -1 , than form I. Crystallographic study. Powder X-ray diffraction (PXRD) patterns of form I as a function of the temperature from 100 K to its melting point have been fitted to the published structure [START_REF] Baumer | 2-Bromobenzophenone[END_REF] and virtually the same results were obtained. An example of the PXRD at room temperature together with the Rietveld refinement is provided in Figure S1. The structure of form I, which contains Z = 4 molecules in the unit cell, with only one molecule in the asymmetric unit (Z' = 1), was reported in the space group P21/a. [START_REF] Baumer | 2-Bromobenzophenone[END_REF] For the sake of comparison with the structure of form II, the structure can be transformed from the space group P21/a (a, b, c, β) to the space group P21/c (a', b, c', β) (a' = c and c' = a).

Although form II was recently discovered by Baran et al., [START_REF] Baran | Discovery of a new polymorphic phase of orthobromobenzophenone[END_REF] the structure and its relative stability with respect to form I have not been resolved. In order to solve the structure, a crystalline powder of form I was introduced into a Lindemann capillary and subjected to the described thermal treatment (see Figure 2). Growth of form II occurred at 280 K. Long acquisition-time high-resolution PXRD patterns were acquired at 200 K as well as at room temperature (293 K). The lattice was indexed using the X-cell software [START_REF] Neumann | X-Cell: a novel indexing algorithm for routine tasks and difficult cases[END_REF] followed by a Pawley profile-fit minimizing the R-factor, Rwp, [START_REF] Pawley | Unit-cell refinement from powder diffraction scans[END_REF] to confirm the space group (P21/c). This procedure enables to refine the lattice parameters, zero-shift, background, and peak profile parameters. To fully determine the structure of form II, rigid body Rietveld refinement was used based on the molecule in form I, thus all bond lengths, including those with hydrogen, are based on the existing molecular geometry of form I. In the Rietveld refinement therefore, only the angles between the cycles and the carbonyl group were adjusted. The fitted diffraction pattern is presented in Figure 3. Results of the Rietveld refinement of form II have been compiled in Table 2 together with the data of form I. A list of refinement parameters for form II can be found in Table S1 in the Supporting Information. 6.24 4.15 a Form I is refined following Baumer et al. [START_REF] Baumer | 2-Bromobenzophenone[END_REF] using data obtained on the same equipment as the data for form II.

For both polymorphs I and II, the space group is centrosymmetric with a single molecule in the asymmetric unit (Z'=1). Both phases have therefore an inversion center, which allows the crystallographic transformation within the structure from one enantiomer to the other.

The Cambridge Crystallographic Data Centre deposit (CCDC 2023202) contains the supplementary crystallographic data for this paper. It can be obtained free of charge from the CCDC via www.ccdc.cam.ac.uk/data_request/cif. The molecular conformations within both phases are quite similar. The subtle differences are related to the relative position of the planes of the phenyl groups towards each other through the torsion angles containing the carbonyl group (see Table 3). For O1-C1-C1A-C6A, the bromine substituted phenyl group, the angles are 68.3(5)° and 66.8(10)° and for O1-C1-C1B-C6B, the unsubstituted phenyl group, the angles are 17.6(6)° and 28.8(9)° for the stable form I and the metastable form II, respectively (see the inset of Figure 5 for the atom labels). As indicated by Baumer et al., these angles demonstrate the highly asymmetric character of 2-BrBPh when compared to similarly substituted compounds, such as 4-BrBPh. [START_REF] Baumer | 2-Bromobenzophenone[END_REF] It is demonstrated here that this asymmetry is maintained in both the stable and the metastable phase. The torsion angle with the brominated ring for either stable, 68.3(5)°, and metastable, 66.8(10)°, phases is quite large, when compared to the unsubstituted benzophenone with values around 27° and 41°. [START_REF] Kutzke | Metastable β-phase of benzophenone: independent structure determinations via X-ray powder -diffraction and single crystal studies[END_REF] Nonetheless, close similarity is found when comparing the central bond angle at the carbonyl group, C1A-C1-C1B, which are 117.8(3) o and 117.7(7) o for 2-BrBPh and 121.4(2) o and 118.9(1) o for BPh for the stable and metastable phases, respectively. As far as the packing is concerned, the structure of the metastable phase is quite different from that of the stable phase. Figure 4 contains the structure of both stable and metastable phases projected on the cb plane (P21/c setting for both structures). Fingerprint plots and Hirshfeld surfaces [START_REF] Turner | CrystalExplorer17[END_REF] are provided in the supplementary materials (Figures S4 andS5).

Table 3. Main characteristic torsion angles of the stable and metastable phases of 2bromobenzophenone a

Torsion

Both the stable phase and the metastable phase exhibit aromatic interactions. In the stable phase, form I, a number of strong aromatic interactions can be found (Figures S2a, b, andc). [START_REF] Macrae | Mercury 4.0: from visualization to analysis, design and prediction[END_REF] They are: i) a T-shaped interaction (C4A-H4A•••π), also observed by Baumer et al., [START_REF] Baumer | 2-Bromobenzophenone[END_REF] with a distance between the hydrogen and the ring of 2.96 Å and a distance of 5.11 Å between the centers of the two rings (Figure S2a), ii) a parallel-displaced interaction between two unsubstituted rings with a center-to-center distance of 4.64 Å and a shortest atom-atom (C4B•••C4B) distance of 3.59 Å (Figure S2b), and iii) a second parallel-displaced interaction between two bromine-containing rings with a center-to-center distance of 4.03 Å (Figure S2c). In total three strong and four moderate aromatic interactions (see for example Figure S2d for a moderate interaction) are found in the stable form by the AI aromatic interaction analyzer in Mercury (see Table S2). [START_REF] Macrae | Mercury 4.0: from visualization to analysis, design and prediction[END_REF] A weak intermolecular hydrogen bond, O1•••H3B, with 2.50 Å (angle 167.7° and O1 -C3B distance 3.412 Å) is present in the structure in combination with an even longer, weaker one, O1•••H6A (angle 153.0° and O1 -C6A distance 3.562 Å), with 2.71 Å.

In the structure of the metastable phase, form II, the shortest hydrogen bond distances have shifted to 2.67 Å for O1•••H4B (angle 166.0° and O1 -C4B distance 3.580 Å), and 2.680 Å for O1•••H5A (angle 119.6° and O1 -C5A 3.237 Å); these are longer than what can be properly considered as a hydrogen bond. [START_REF] Desiraju | The C-H•••O hydrogen bond in crystals: what is it?[END_REF][START_REF] Steiner | Distinction between the weak hydrogen bond and the van der Waals interaction[END_REF][START_REF] Steiner | O hydrogen bonding in crystals[END_REF][START_REF] Desiraju | The Weak Hydrogen Bond In Structural Chemistry and Biology[END_REF] In terms of aromatic interactions, two strong T-shaped interactions exist (Figures S3a andb), one with the C6A-H6A•••π distance of 2.73 Å along the c direction and a center-to-center distance of 5.01 Å (Figure S3a) and a second one with a C4A-H4A•••π distance of 2.96 Å and a center-to-center distance of 5.14 Å (Figure S3b). In addition, eight moderate T-shaped and parallel-displaced interactions (see for example Figures S3c andd) can be found in the metastable form (see Table S3) by the aromatic interaction analyzer in Mercury. [START_REF] Macrae | Mercury 4.0: from visualization to analysis, design and prediction[END_REF] Thus, although the stable form I possesses more strong interactions, the denser form II (Table 2) compensates the lack of stronger interactions by the presence of eight moderate aromatic interactions (compare Tables S2 andS3).

Lattice parameters of both forms have been obtained as a function of the temperature (see Supporting Information Table S4) from 100 K up to the respective melting points. Figure 5 presents the specific volumes of both polymorphs together with that of the liquid phase as a function of the temperature. The results in Figure 5 clearly demonstrate that the specific volume of the stable form I is larger than that of form II at any given temperature, which means that the metastable form II is denser than the stable form I, contrary to the expected behavior according to the density rule of Burger and Ramberger. [START_REF] Burger | Polymorphism of Pharmaceuticals and Other Molecular-Crystals .1. Theory of Thermodynamic Rules[END_REF] This implies that with increasing pressure the relative stability of the denser form II increases and that of form I decreases.

The specific volumes of the three condensed phases have been fitted as a function of the temperature using the least-squares method leading to the following equations: vI (/cm 3 g -1 ) = 11.1(6)•10 -5 T(/K) + 0.6102(4) (1a) vII (/cm 3 g -1 ) = 12.0(4)•10 -5 T(/K) + 0.6055(10) (1b)

vL (/cm 3 g -1 ) = 50.1(2)•10 -5 T(/K) + 0.5559(8) (1c)
With these equations, the volume changes on melting and between the two solids have been determined (Table 1).

Analysis of the thermal expansion

In order to analyze the anisotropy in the intermolecular interactions, lattice parameters (Table S4) were fitted by a standard least-squares method to a polynomial function of the temperature. The polynomial coefficients describing the temperature dependencies have been compiled in Table S5 in the Supporting Information. The thermal expansion tensor of a monoclinic structure is defined by the principal coefficients, α1, α2, and α3, which form an orthogonal system, while the axis related to α2 is parallel to the unit-cell axis b. [START_REF] Salud | Anisotropy of intermolecular interactions from the study of the thermal-expansion tensor[END_REF] The thermal-expansion tensors for the stable form I and the metastable form II are represented in Figure 6 and have also been provided in the form of a table in the supplementary materials with the correlation between the principal tensor directions and the unit-cell axes (Table S6). The thermal expansion tensor at 200 K for the stable (P21/a setting) and metastable (P21/c setting) phases.

Figure 6 shows the eigenvalues as a function of the temperature for the two solid phases as well as a pictorial representation of the thermal-expansion tensor at 200 K. Except for the lowest temperatures, the overall expansivity, αV, (see upper panels of Figure 6) is higher in the metastable form II than for the stable form I. However, negative eigenvalues, implying contraction on heating and therefore called 'hard direction', [START_REF] Salud | Anisotropy of intermolecular interactions from the study of the thermal-expansion tensor[END_REF] are present in the expansion tensors of both phases (α3, see Figure 6).

For the stable phase, the hard direction (within the ac plane) can hardly be a consequence of the C-H•••O hydrogen bonds although they run along the [100] direction, because they are simply too weak distance-wise and donor-wise. As can be seen in Table S4, in the supplementary materials, the angle β decreases with increasing temperature, while the a and c axes increase in length. This can be interpreted as the unit cell being pulled at its origin (in the ac plane) and at the opposite side of the diagonal a + c, which within the crystal, translates into two layers moving in opposite directions as indicated in Figure 7a. While this causes expansion along the diagonal a + c, it diminishes the length of the diagonal c -a, similar to the situation described by Bhattarcharya and Saha. [START_REF] Bhattacharya | Uniaxial Negative Thermal Expansion in an Organic Complex Caused by Sliding of Layers[END_REF] However, contrary to the latter paper, in which the crystal contains several strong hydrogen bonds, [START_REF] Bhattacharya | Uniaxial Negative Thermal Expansion in an Organic Complex Caused by Sliding of Layers[END_REF] the current molecule does not have any hydrogen bonds that could be implicated in NTE and there is no clear reason, why these layers don't expand by moving away from each other. A tentative explanation may be the aromatic interactions, which possess a certain directionality. Although a number of these interactions is located within the moving layers, a strong interaction (according to the aromatic interaction module of Mercury [START_REF] Macrae | Mercury 4.0: from visualization to analysis, design and prediction[END_REF] ) is exactly positioned along the c -a direction that experiences the NTE (Figure 7a double red arrow and Figure S2b). It appears that the distance between the centers of the two aromatic cycles indicated by the red double arrow decrease on heating indicating a possible strengthening of this interaction. It is therefore of interest to investigate more precisely the role of the aromatic interactions and their directionality in this particular NTE. As for the hardest α3 direction of the metastable phase, the mechanism is less clear, because there is less movement in the system. However, again in the ac plane layers can be observed that are solely interconnected by aromatic interactions (Figure 7b, T-shaped interactions). As the angle β again decreases slightly on heating a similar sliding movement of the layers can be expected. The strongest expansion is along the b axis, which lacks any of the stronger aromatic interactions. As the hydrogen bonds are basically nonexistent in this structure, it would once again be of interest to investigate more closely the role of the aromatic interactions in the observed NTE.

It could be argued that in some way steric hindrance may in part cause the NTE through a trellis effect (as the steric interaction itself would be repulsive and therefore cause expansion). However, due to the small size of the 2-BrBPh molecule, scenarios such as found for the much longer glipizide [START_REF] Burley | Structure and intermolecular interactions of glipizide from laboratory X-ray powder diffraction[END_REF] are rather unlikely and it is therefore hard to imagine how steric interactions could cause NTE in the present case. In addition, the clear partitioning of both structures in layers makes it less likely that steric hindrance limits these layers from moving away from each other. Possibly, theoretical calculations, such as DFT, preferably with the effect of temperature taken into account, may provide additional information on the expected strength of the aromatic interactions and its role for this molecule in these two structures.

The experimental slopes, dT/dP, corresponding to the melting of forms I and II, match perfectly with those calculated according to the Clapeyron equation (see Table 1).

High-pressure thermal analysis results demonstrate that the melting temperatures of the two polymorphs approach each other on increasing pressure as the slope dT/dP of the melting of the metastable form II is steeper than the slope of the higher melting form I, which can be seen in the left-hand panel of T-shaped and parallel-displaced aromatic interactions are important in both form I and form II. The latter is the densest of the two even if it is less and exhibits a more pronounced thermal expansion. It is striking, however, to observe that both forms exhibit uniaxial contraction on heating. The NTE can in both cases be explained by layers shifting in opposite directions; however, because of the absence of any significant hydrogen bonding, it is of interest to find out to what level the aromatic interactions both in the stable form I and in the metastable form II are responsible for the NTE behavior. In this respect, theoretical calculations, in particular as a function of the temperature, would be a welcome addition to this experimental study.

Thermodynamic properties at normal and high pressure have been determined for the stable and metastable phases and the pressure-temperature phase diagram has been constructed. While the metastable phase behaves monotropically with respect to the stable phase, with an increase in pressure, the phase relationship between the two polymorphs becomes enantiotropic. The solid-solid equilibrium line, which becomes stable at higher pressure, has a negative slope due to the negative difference in volume and it must be rather steep considering the small value of the dT/dP slope listed in Table 1. This implies that the solid-solid phase transformation is mainly entropy driven.

For Table of Contents only:

Figure 1 .

 1 Figure 1. Molecular structure of benzophenone (A1 = A2 = 'H'), 4-methylbenzophenone (A1 = 'H', A2 = 'CH3'), 2-bromobenzophenone (A1 = 'Br', A2 = 'H'), 2-chlorobenzophenone (A1 = 'Cl', A2 = 'H'), 4-bromobenzophenone (A1 = 'H', A2 = 'Br')

  2-bromobenzophenone ((2-bromophenyl)phenylmethanone) was purchased from Aldrich with a purity of 98%. Most of the experiments were performed after careful purification of the sample through recrystallization in ethanol by the group of Professor A. Jezowski at the Institute of Low Temperature and Structure Research, Wroclaw (Poland).

  (dT/dP) exp / K•MPa-1 0.290 ±0.012 0.322 ±0.012 -* Values for the I to II transition have been calculated; the enthalpy and entropy differences are in principle valid at 307.2 K (the mean of the two melting temperatures), ∆v has been evaluated at 307.2 K leading to a dT/dP slope evaluated at the same temperature. Although the errors are in certain cases larger than the values themselves, the volume difference and the slope must have negative values (see eqs. 1 and text on relative stability below).

Figure 2 .

 2 Figure 2. Differential scanning calorimetry curves of 2-bromobenzophenone recorded at a rate of 10 K min -1 . (1) First heating of the purified form I. (2) Second heating after cooling the melt to 193 K in which a glass transition at Tg (from the glass state, G, to the supercooled liquid, SCL) can be observed (see inset).

Figure 3 .

 3 Figure 3. Experimental (red circles) and Rietveld refined (black line) diffraction patterns along with the difference profile (blue line) and Bragg reflections (vertical bars) of the monoclinic P21/c space group metastable phase II of 2-Br-benzophenone at 200 K. The inset corresponds to a 4.5times-magnified intensity scale in the 40-60 o 2θ range for clarity.

  atom labels see the inset of Figure 5.

Figure 4 .

 4 Figure 4. Projections of the 2-bromobenzophenone structure on the ab plane (P21/a setting) or cb plane (P21/c setting) for the stable phase form I (left) and on the cb plane (P21/c setting) for the metastable phase form II (right)

Figure 5 .

 5 Figure 5. The specific volume of 2-bromobenzophenone as a function of the temperature for the stable form I (solid blue circles, solid line), the metastable form II (open red circles, dashed line), and the liquid phase (open squares, dashed line). The open blue circle corresponds to the single crystal study of Baumer et al. 16 and half-full circles correspond to the X-ray powder diffraction values of the stable form I from Prokhvatilov et al. 41 Inset: Molecular conformations with atom labels of 2-bromobenzophenone in the stable form I (grey) and metastable form II (blue). Brown and red bonds correspond to the C-Br and C=O bonds, respectively.

Figure 6 .

 6 Figure 6. Eigenvalues (bottom) of the thermal-expansion tensor and thermal expansivity αv (top) for stable form I (left) and metastable form II (right) as a function of the temperature. (Insets) The thermal expansion tensor at 200 K for the stable (P21/a setting) and metastable (P21/c setting) phases.

Figure 7 .

 7 Figure 7. Two layers in (a) form I (ac plane, P21/a setting) and (b) form II (ac plane, P21/c setting) moving in opposite direction (green arrows) on heating decreasing the angle β. The NTE is indicated by a purple line, while the strong aromatic interaction is indicated by a red double arrow. The explanation is tentative, in particular for form II, because the NTE displacement is small.

  Relative stability of the crystalline phasesThe high-pressure melting temperatures of both forms are shown in Figure8for a series of pressures. Several examples of high-pressure thermograms are presented in FigureS6for both polymorphs in the Supporting Information. The experimental onset melting temperatures as a function of pressure were fitted with a linear expression leading to: TI-L /K = 0.290(12) P /MPa + 313.4(1.6) (2a) TII-L /K = 0.322(12) P /MPa + 301.2(1.5)

Figure 8 . 8 .

 88 In the center panel of Figure 8, the T and P axes have been exchanged in line with most phase diagrams in the pharmaceutical community. The slopes convert therefore into dP/dT. Due to the inequality dP/dTI-L > dP/dTII-L the melting curves converge at the triple point I-II-L (Figure 8, center panel). This convergence implies that form II possesses a stable domain at high pressure and high temperature above the triple point I-II-L. In addition, because ∆SI-L > ∆SII-L, SI < SII and while vI > vII, the slope of the I-II transition dP/dTI-II should be negative. Accordingly, the topological pressure-temperature phase diagram corresponds to that depicted in the center panel of Figure In summary, the relationship of form II with respect to form I, which is monotropic at normal pressure and up to the triple point I-II-L, becomes enantiotropic for temperatures and pressures above this triple point (see the Gibbs-energy diagrams in the right-hand panels in Figure 8).

Figure 8 .

 8 Figure 8. Left-hand panel: Experimental temperature-pressure phase diagram of 2bromobenzophenone with solid and open circles the melting transitions of form I and form II, respectively. Center panel: Topological pressure-temperature phase diagram of 2bromobenzophenone. Right-hand panel: Isobaric sections of the Gibbs-free-energy-vstemperature diagrams at P=P1 (monotropic behavior, bottom panel), and at P=P2 (enantiotropic behavior, top panel). Solid lines represent stable equilibria (minimum Gibbs free energy)

Table 1 . Enthalpy (∆H), entropy (∆S), and volume (∆v) changes at the observed phase transitions together with the experimental ((dT/dP) exp ) and calculated ((dT/dP) calc ) slopes of the melting temperatures with respect to the pressure

 1

	Property / Phase	I→L	II→L	I→II *
	transition
	T/K	312.2 ±0.5	302.2 ±0.5
	∆H / J•mol -1	18.7 ±0.4	16.3 ±0.7	2.4 ±0.9
	∆S / J•K -1 • mol -1	59.8 ±1.3	53.8 ±2.3	6 ±3
	∆v / cm 3 •mol -1	17.69 ±0.13	17.45 ±0.16	-0.0019
				±0.0025
	(dT/dP) calc / K•MPa -1	0.296 ±0.009	0.324 ±0.017	-0.0003
				±0.0005

Table 2 . Results of the Rietveld refinements of 2-Br-BPh form I a and form II

 2

	Phase	form I	form II
	Formula	C13H9BrO	C13H9BrO
	FW (g•mol -1 )	261.118	261.118
	Crystal system	Monoclinic	Monoclinic
	Space group	P21/a	P21/c
	T (K)	200(1)	200(1)
	Wavelength (Å)	1.54056	1.54056
		a = 7.8160(3) Å	a = 8.4896(19) Å
		b = 16.7374(7) Å	b = 6.5438(8) Å
	Unit cell	c = 8.4654(4) Å	c = 20.253(1) Å
	dimensions	α= 90°	α= 90°
		β = 97.610(4)°	β = 104.452(6)°
		γ= 90°	γ=90°
	Z(Z')	4(1)	4(1)
	V (Å 3 )	1097.68(8)	1089.5(4)
	Dx (g•cm -3 )	1.5801(1)	1.5918(6)
	Rwp (%)	8.27	6.24
	Rp (%)

Acknowledgements

This work was supported by the Spanish Ministry of Science and Innovation (Grant FIS2017-82625-P) and the Catalan Government (Grant 2017SGR-42). We thank A. Jezowski of the Institute of Low Temperature and Structure Research, Polish Academy of Sciences for the purification of the 2-bromobenzophenone sample.


Ali Borji
email: borji@ipm.ir

Majid Nili Ahmadabadi

Babak Nadjar Araabi
email: araabi@ipm.ir

Offline Learning of Top-down Object based Attention Control

Keywords: Top-down attention, object based attention, saliency

Like humans and primates, artificial creatures like robots are limited in terms of allocation of their resources to huge sensory and perceptual information. Serial processing mechanisms are believed to have the major role on such limitation. Thus attention control is regarded as the same solution as humans in this regard but of course with different attention control mechanisms than those of parallel brain. In this paper, an algorithm is proposed for offline learning of top-down object based visual attention control by biasing the basic saliency based model of visual attention. Each feature channel and resolution of the basic saliency map is associated with a weight and a processing cost. Then a global optimization algorithm is used to find a set of parameters for detecting specific objects. Proposed method is evaluated over synthetic search arrays in pop-out and conjunction search tasks and also for traffic sign recognition on cluttered scenes.

Introduction

Both machine and biological vision systems have to process enormous amount of visual information they receive at any given time. Therefore attentional selection provides an efficient solution to this problem by proposing a small set of scene regions worthy further analysis to higher-level cognitive processes like scene interpretation, object recognition, decision making, etc. In this regard visual attention acts as a front end to a more complex vision system.

A model for bottom-up visual attention known as saliency-based model is proposed in [START_REF] Itti | A Model of Saliency-Based Visual Attention for Rapid Scene Analysis[END_REF] by Itti et al., which is an extension and implementation of an earlier model by Koch & Ullman [START_REF] Koch | Shifts in Selective Visual Attention: Towards the Underlying Neural Circuitry[END_REF]. Bottom-up model in its original form is solely datadriven and simply selects some spatial locations without using any feedback mechanism or top-down gains. In [START_REF] Navalpakkam | An Integrated Model of Top-down and Bottom-up Attention for Optimal Object Detection[END_REF], this model is biased toward specific objects by strengthening the saliency of a target object over a distracting background. To this end, they have maximized the signal-to-noise ratio (SNR) between the target and background. In [START_REF] Torralba | Contextual guidance of eye movements and attention in real-world scenes: the role of global features in object search[END_REF], authors have developed a method to account spatial relationships among objects in a Bayesian framework. Their model modulates the basic saliency model by a spatial saliency map that is learnt from probabilities of objects to appear in a scene. That way, for example when looking for a person in a beach scene, areas around the sea are more probable to contain a person (and thus are more salient) than the sky regions. However it is very hard to find an exact formulation for the visual search and object detection, since many parameters are involved. Therefore using an offline approach which could implicitly account such hidden parameters seems to be an appropriate approach. In this work, we use a global optimization algorithm for tuning parameters of the saliency model for object detection. Since main goal of attention is to reduce computational complexity, we have also put costs on features and resolutions of the images in order to find solutions with both low computation and high discrimination power.

Proposed Method

To furnish the saliency model for our purpose, i.e. biasing it for object detection, a dyadic Gaussian pyramid (with six scales) is built in each feature channel of the image by successively filtering the image with a Gaussian low-pass filter and then subsampling it. Then a surround inhibition operation is applied over each scale in the pyramid to enhance those parts of the image which are different from their surroundings. To implement surround inhibition, saliency model reduces finer and coarser scales from each other. Because we would like to also weight different resolutions in the map, we dissociate scales and then apply the surround inhibition over each scale separately. To accomplish surround inhibition, a non-linear filter which compares the similarity of a pixel with the average of its surrounding window and then inhibits the center pixel by an exponential weight was designed. Equation 1shows this filter.

where surround is a spatial n×n mask around pixel I(x,y) excluding the point itself. I ' (x,y) is the new value of the pixel. Output image was later normalized to its initial range. Figure 1 demonstrates surround inhibition operation over some test images. The implementation of the Gaussian pyramid is illustrated in figure 2. Surround modulated images in each scale are upsampled to a predetermined scale and after normalization and weighting are summed to form feature maps.

F x,y in above equation is the map at the scale s of channel x. SI is the surround inhibition operation. N(.) is the iterative normalization operator as defined in [START_REF] Itti | Feature combination strategies for saliency-based visual attention systems[END_REF]. These feature maps are summed over scales and sums are normalized again:

F N ∑ ω S . F ,S , with l L I L C L O L I I , L C RG, BY , L O 0 , 45 , 90 , 135 (3)
In each feature channel, feature dimensions contribute to the conspicuity maps by weighting and normalizing once again, as shown in equation 4.

C N ω . L F , p I, C, O (4)
All conspicuity maps are weighted and combined at this stage into one saliency map:

SM ω . C , k I, C, O (5)
The locations in the saliency map compete for the highest saliency value by means of a winner-take-all (WTA) network of integrate-and-fire neurons. The winning location (x n , y n ) of this process is attended to. Then this point is inhibited for a while (a phenomenon called inhibition of return) to let the attention shift to other locations. After a time constant it will have the chance to become active again and catch the attention focus. The whole process is summarized in figure 3.

In order to reduce the computational complexity of the model, in addition to a weight, a cost is also associated to each feature channel and image resolution. Goal is to find a set of weights which determines the contributions of features (intensity, color, orientation and image resolutions) to detect a specific object in a set of images while taking into account their costs. Therefore the optimum weight vector must satisfy two conditions: 1) it must enable the saliency model to detect an object of interest (maximum detection rate), 2) its associated feature vector must have the minimum cost. Let Img Img , Img , … Img be m training images with target object locations tagged. We use comprehensive learning particle swarm optimization (CLPSO) [START_REF] Liang | Comprehensive learning particle swarm optimizer for global optimization of multimodal functions[END_REF] to search for weight vectors satisfying above properties. An example fitness function satisfying the above two conditions is shown in equation 6.

Fitness ω 1 mpn

dist Saliency Img , ω , t u ω c

In above formula, n is the dimensionality of cost or weight vector, dist j () is the Euclidian distance between j-th salient point generated by the saliency model and the target location t i in i-th image. u(x) is the step function and is one when a feature channel or resolution is used. Saliency is a function which takes an image and a weight vector as input and outputs a vector of p salient points.

Experiments and Results

We evaluated our biased saliency method for traffic sign detection over a dataset of 30 signs. They were bike, pedestrian and crossing signs. We also applied it for saliency detection over synthetic search arrays (pop out and conjunction search tasks). Twenty samples of each signs were used to derive a weight vector. Figure four illustrates achieved weight vectors after CLPSO convergence for a sample run. Table 1 shows the average detection rates using two first detection hits over remaining 10 test images. A detection hit was counted if a salient point was generated in a vicinity of 30 pixels around the target point (center of object). Feature costs were defined based on relative computational cost of model features. Figure 5 shows some example natural scenes with detected traffic signs. Figure 6 shows the average spatial map for each traffic sign. This map could be used as starting point for searching a specifc sign to speed up the detection process.

Conclusions and future works

Our proposed model in this paper is constructed over the basic saliency based model of visual attention and biases it for detecting objects of interest. Weights and costs were associated with features and resolutions of the model and then an optimization algorithm was used to select features (sensors) which had lowest cost and high detection rate. Proposed method was used to detect traffic signs in cluttered road scenes. In order to reduce the cost, algorithm bypassed those channels which were not important in detecting the objects. Since the parameters of the saliency model are continuous-valued, online learning of those parameters degrades performance of any algorithm for learning top-down attention control based on the saliency model. Therefore an offline approach seems reasonable. Learned parameters then could be used online when a complex task demanding perceptual and physical actions has to be done. Therefore, future works in this regard should focus on how to use this knowledge in interactive tasks.

Fig. 1 .

 1 Fig. 1. Surround inhibition using equation one. Window sizes from top-left to bottom-right are: 15×15, 7×7, 15×15, 5×5, 9×9, 11×11. Red circles illustrate the salient locations (γ=.04).

Fig. 2 .

 2 Fig. 2. Gaussian pyramid with surround inhibition. w shows weights of different scales of the pyramid. SI is the surround inhibition operation as in equation 1. The input image is decomposed into three feature channels: Intensity (I), color (C) and orientation (O). Color channels are calculated as follows. If r, g and b are the red, green and blue dimensions in RGB color space normalized by the image intensity I, then R = r -(g+b)/2, G = g -(r + b)/2, B = b -(r +g)/2, and Y = r + g -2 (|r -g| + b) (negative values are set to zero). Local orientations, O θ are obtained by applying Gabor filters to the images in the intensity pyramid I. F I,S N SI I , F RG,S N SI R G , F BY,S N SI B Y , F ,S N SI O ,

  , … ω and C c , c , … c respectively.

Fig. 3 .

 3 Fig. 3. Revised saliency model of visual attention. SIB is the Gaussian pyramid in figure 2.

Fig. 4 .

 4 Fig. 4. Best weights for saliency model after CLPSO convergence.

Table 1 .

 1 Average detection rates of biased and basic saleincy model and average cost of the final best weight vector of CLPSO over five runs. Costs = [3 1 4, 3 3, 4 4 4 4, 6 5 4 3 2 1].

Fig. 5 .

 5 Fig. 5. Sign detection over 5 sample test images. Top row: pedestrian, middle: crossing, bottom: bike. Red circle is the first attended location and yellow one is the second.

Fig 6 .

 6 Fig 6. Spatial map showing the possible locations of traffic signs in the images of the dataset.