Shlomo Barak
email: shlomo@tagapro.com

Space as a Special Frame and Starlight Aberration

Keywords: Starlight aberration, Cosmic microwave background, Lorentz transformation C A Aberration

It is generally accepted that the relevant velocity in the calculation of starlight aberration is the velocity of the Earth in its orbit around the Sun. We contend that, for distant stars or galactic sources which appear fixed over long periods of time, irrespective of their motion, the correct velocity for the calculation is the Earth's velocity relative to space, i.e., relative to the thermal bath of 2.7k Cosmic Microwave Background (CMB). Our result for the starlight aberration constant differs from the commonly accepted value by approximately 0.3 seconds of arc.

Introduction

Einstein [START_REF] Einstein | On the Electrodynamics of Moving bodies[END_REF] derived a relativistic form of the aberration equation. In this equation, which appears in textbooks, the relevant velocity is that of the observer relative to the source, similar to the Doppler shift. This derivation is based on the Lorentz transformation when applied to the issue of addition of velocities.

We contend that when the source is a distant star, or galaxy, which appears fixed over long periods of time, irrespective of its motion, it is the velocity of the observer relative to space which is relevant ("close" and "distant" are quantified below). This velocity, relative to space, is relative to the thermal bath of 2.7k Cosmic Microwave Background (CMB), and measured by the Doppler shift of the CMB.

A Derivation and Calculation

For a detached light pole, we follow Feynman's [START_REF] Feynman | Lectures on Physics I[END_REF] idea for deriving the aberration equation. This derivation is based on a simple vector diagram, as shown in Fig. [START_REF] Einstein | On the Electrodynamics of Moving bodies[END_REF]. Although we get the same equation as the textbooks, the relevant velocity in this case is the velocity relative to space and not the velocity of the observer relative to the source.

We now clarify the term distant source: Say we are expecting a deviation of ~0.3 seconds of arc from the conventional result for the angle of aberration of distant sources and we want a 10% experimental accuracy. The pole of light should then be defined to better than 0.03" during the time of observation.

For a time of observation of, say, 10 years, and a relative tangential velocity of, say, 500 km/sec, the source should be at a distance, d, of at least 10 5 light years, see Fig. [START_REF] Feynman | Lectures on Physics I[END_REF].

Clearly, a source moving at a speed of 1000 km/sec and distant 2.10 5 light years shows the same aberration.

General Case A Polar Star

 v c  c C o s  c S i n   ` v            Cos β Sin γ cos c v γ 1 Sin c ' tg      Cos β 1 Sin γ ' Sin       Cos β 1 Cos β ' Cos c v for γ β c v γ 1 ' tg     c v  ' tg             2 1 β 1 γ c v β

Fig. (1) Aberration of Starlight

Let us consider the simple case of a Polar star, as shown in Fig. [START_REF] Scott | The System of Fundamental Proper Motions in Basic Astronomical Data[END_REF]. S t is the space system and light from a polar star comes along the z-axis. S0 is the solar coordinate system attached to the Sun. S0 moves with respect to S t at speed V ~400 km/sec along the y and y' axes, which are in the directions from the Aquarius galaxy and the Leo-Virgo galaxies.

v A | = | V | + | v | | v C | = | V | -| v | 2 2 D B, v V v  
Taking the relativistic equation for the angle of aberration

    g t (1)
where:

  Note that (3) gives the known constant of aberration

  Fig. (2) A Distant Source

 2 )

 2 Using the numerical values: V = 400 km/sec, v = 30 km/sec, c = 300000 km/sec gives the following results for: A ,  C and  A - C ,which are:  A = 295.65"  C = 254.39" and  A - C = 41.26" (This result differs from the result obtained using just the orbital velocity, v, of the Earth around the Sun. By using  lacks circular symmetry. These theoretical results should be compared with astronomical data and, if not conclusive, should lead to the collection of further observational data.

20.495"


Arthur Crenn

Rizwan Ahmed

Khan -Alexandre Meyer -Saida Bouakaz

BODY EXPRESSION RECOGNITION FROM ANIMATED 3D SKELETON

Keywords: Body Expression Recognition, 3D Skeleton, Features Extraction, Animation

We present a novel and generic framework for the recognition of body expressions using human postures. Motivated by the state of the art from the domain of psychology, our approach recognizes expression by analyzing sequence of pose. Features proposed in this article are computationally simple and intuitive to understand. They are based on visual cues and provide in-depth understanding of body postures required to recognize body expressions. We have evaluated our approach on different databases with heterogeneous movements and body expressions. Our recognition results exceeds state of the art for some database and for others we obtain results at par with state of the art.

INTRODUCTION

Many applications would benefit from the ability to understand human emotional state in order to provide more natural interaction e.g video games, video surveillance, humancomputer interaction, artistic creation, etc. Emotion is a complex phenomena. Expression of an emotion could be personal and subjective as two persons could perceive and interpret differently the same expression. Its perception changes from one culture to another. Furthermore, human expresses emotional information through several channels, like facial expression, body movement and sound. Several studies from various disciplines have shown that body expressions are as powerful as those of the face to express emotion [START_REF] Kleinsmith | Affective body expression perception and recognition: A survey[END_REF]. Unfortunately, to the best of our knowledge, few publications have focused on this issues.

This paper presents a method to detect and classify expression through a sequence of 3D skeleton-based poses. The challenge is to find common informations between all the movements of the same expression. And this, while the expression is embedded in the action performed by the person, e.g. nervous person walking pattern contains the action of walking and the emotional state to be nervous. With the growth and ease of accessibility of devices that track 3dimensional body like the Kinect [START_REF]Kinect[END_REF][START_REF] Bailey | A comparison of motion capture data recorded from a vicon system and a microsoft kinect sensor[END_REF] or accelerometer-based motion capture system [START_REF] Tautges | Motion reconstruction using sparse accelerometer data[END_REF], it is easy to get data. Thus many applications will be benefited from real-time analysis of body movements. There are lots of method proposed in literature for facial expressions [START_REF] Bettadapura | Face expression recognition and analysis: the state of the art[END_REF][START_REF] Ahmed Khan | Framework for reliable, real-time facial expression recognition for low resolution images[END_REF][START_REF] Jung | Joint fine-tuning in deep neural networks for facial expression recognition[END_REF][START_REF] Khan | Exploring human visual system: study to aid the development of automatic facial expression recognition framework[END_REF], however, as mentioned above, there is a lack of research for the analysis of body movement to recognize expressions. Early proposed methods for body movements analysis [START_REF] Karg | Recognition of Affect Based on Gait Patterns[END_REF][START_REF] Kleinsmith | An incremental and interactive affective posture recognition system[END_REF] were limited to specific movements or expressions. Taking an approach proposed by choreographer seeking to describe dance movements, Truong et al. [START_REF] Truong | Laban descriptors for gesture recognition and emotional analysis[END_REF] proposed descriptors calculated from the movements in order to recognize various gestures and expressions. Inspired by Truong's work and results of psychological research [START_REF] Kleinsmith | Affective body expression perception and recognition: A survey[END_REF], we have looked to quantify the space posture of the body, during an action, by introducing new set of features to characterize an expression. Besides, its computational simplicity allowing the recognition of expression on heterogeneous body movements in real-time. Our method has the advantage to be reusable in many domains as movement synthesis processes for computer graphics and animation. The paper is organized as follows. Section 2 presents the state of the art of the emotion analysis. Section 3 details the set of features we proposed. Section 4 shows the results obtained on different databases and the comparison with other state of the art's method. Finally, Section 5 concludes the paper.

RELATED WORK

In recent years, researchers have considerably focused on the automatic facial expression recognition (FER) [START_REF] Bettadapura | Face expression recognition and analysis: the state of the art[END_REF][START_REF] Ahmed Khan | Framework for reliable, real-time facial expression recognition for low resolution images[END_REF][START_REF] Jung | Joint fine-tuning in deep neural networks for facial expression recognition[END_REF]. However, computer vision domain is lacking research on the detection of emotion based on human's posture. In analogy afterward we use the term "Body Expressions" to refer to emotion expressed by body posture. While, psychological studies show that the human's posture is as powerful as facial expressions in conveying emotions [START_REF] Mehrabian | Encoding of attitude by a seated communicator via posture and position cues[END_REF]. That's why, psychologists have sought to understand what bodily information is necessary for recognizing the affective state of one person. Psychological studies [START_REF] Atkinson | Evidence for distinct contributions of form and motion information to the recognition of emotions from body gestures[END_REF][START_REF] Hirai | The relative importance of spatial versus temporal structure in the perception of biological motion: An event-related potential study[END_REF] have investigated the part of the body form versus movement in affect perception. These studies conclude that both form and motion information are important for perceiving emotions from body expressions. Finally, after the form and movement features, psychologists have in-troduced two main levels of bodily details which are high and low-level descriptions [START_REF] Kleinsmith | Affective body expression perception and recognition: A survey[END_REF]. The high level description is often based on the Laban approach which describes body expressions in a global way. The low description is another approach to describe body expression by providing more precise features like distance between joints and angle between body segments. Some techniques related to psychology studies focus on very specific actions. Bernhardt and Robinson [START_REF] Bernhardt | Detecting affect from non-stylised body motions[END_REF] proposed a framework to detect implicitly communicated affect of knocking actions. Their method is based on segmentation to divide complex motions into a set of automatically derived motion primitives. Then, they analyzed the parsed motion in terms of dynamic features, i.e. velocity, acceleration and jerk. They obtained a range of 50% to 81% correct classification rate and we are also going to compare our method with their results (refer Section 4 for comparison). Karg et al. [START_REF] Karg | Recognition of Affect Based on Gait Patterns[END_REF] proposed method for gait patterns recognition. They investigated the capability of gait to reveal a person's affective state. According to their study, speed, cadence and stride length are important factors to correctly discriminate different expressions of a human gait. Paterson et al. [START_REF] Patterson | The role of velocity in affect discrimination[END_REF] confirms the role of velocity for the discrimination of affect. They performed visual experiments and concluded that speed plays vital role in the perception of affect.

Below mentioned are few state of the art articles that proposed heterogeneous body movement analysis. Castellano et al. [START_REF] Castellano | Recognising human emotions from body movement and gesture dynamics[END_REF] proposed a method for automated video analysis of body movement and gesture expressiveness. They used movement expressiveness to infer emotions. They also present two methods for the classification. The first one is based on a direct classification of time series whereas the second one uses a meta-features approach. A meta-feature is the statistical calculation on a set of features in order to abstract the time. They obtained correct classification accuracy of 61% on their database which contains four expressions (Anger, joy, pleasure and sadness). Kleinsmith et al. [START_REF] Kleinsmith | An incremental and interactive affective posture recognition system[END_REF] proposed a system that incrementally learns to recognize the body expression. Their system is based on form features (i.e. distance from one joint to another one) and motion features. They obtained a correct classification rate of 79%, we will compare our method with their results (refer Section 4 for comparison). Truong et al. [START_REF] Truong | Laban descriptors for gesture recognition and emotional analysis[END_REF] proposed a new set of 3D gesture descriptors based on the laban movement analysis model for gestures expressiveness. They obtained high recognition rates for action recognition (F-Score: 97%) on Microsoft Research Cambridge-12 dataset [START_REF] Fothergill | Instructing people for training gestural interactive systems[END_REF]. They also tested their classification approach on their own proprietary database which contains 882 gestures and achieved best F-Score of 56.9%.

We can take inspiration from the domain of animation in computer graphics as they also analyze body movement and gesture expressiveness. The researchers working in the domain of animation generation proposed different methods for modification of animation using skeleton transformations. This modification of expression can be achieved by chang-ing the timing, speed and the spatial amplitude of the motions of body part joints. [START_REF] Amaya | Emotion from motion[END_REF][START_REF] Hsu | Style translation for human motion[END_REF]. Some researchers [START_REF] Bruderlin | Motion signal processing[END_REF][START_REF] Unuma | Fourier principles for emotion-based human figure animation[END_REF] have also used methods from signal processing (Fourier transformation, motion wave-shaping, time-warping, etc.) in order to modify the expression of animations. Recently, with the same goal of synthesis expressive animations, Forger and Takala [START_REF] Forger | Animating with style: defining expressive semantics of motion[END_REF] proposed an approach based on the motion signals by using frequency components.

PROPOSED FRAMEWORK

Our motivation was to propose an efficient recognition method of body expressions on heterogeneous movements that rivals state of the art and in real time on a standard computer. Following the foot prints of several previous works [START_REF] Kleinsmith | An incremental and interactive affective posture recognition system[END_REF][START_REF] Truong | Laban descriptors for gesture recognition and emotional analysis[END_REF][START_REF] Forger | Animating with style: defining expressive semantics of motion[END_REF], we propose a set of novel descriptors based on geometry, motion and frequency-based of body part joints. The overview of our approach is given in Figure 1 and in the following three steps. The rest of this Section is dedicated to the presentation of the features proposed by our method.

Our framework computes low-level features for each

frame of the motion capture data. We decomposed our features in three types: geometric features, motion features and Fourier features. The details of these features are described below.

2. Starting from all these low-level features obtained from a time sequence, we compute the meta-features i.e. mean and standard deviations for each feature. Since metafeatures are independent of the time, we avoid the computationally complex time-warping step for synchronizing two animations.

3. The resulting values of these meta-features are fed to the classifier which provides the expression classification of the input motion capture data.

The low-level features we propose are based on distances between body joints, area of triangle defined by specific joints, angles, velocity, acceleration and frequency of movement of different joints. Table 1 describes the set of all our basic features. We have a total of 68 features. Then, for each feature we compute the meta-features. Thus, our approach leads to a total number of 136 features in order to recognize the body expression. Figure 2 shows the set of meta-features for three expressions. For visual purpose, we are only showing first 76 features from the total of 136 dimensional feature vector. It can be observed in the referred figure that our features have a discriminative trend for these expressions. This discriminative ability is used in the proposed framework to robustly classify body expressions. According to the studies of [START_REF] Karg | Recognition of Affect Based on Gait Patterns[END_REF] and [START_REF] Bernhardt | Detecting affect from non-stylised body motions[END_REF], we have decided to use the following joints for feature extraction: head, pelvis, elbows, shoulders and hands. Experimental results obtained by [START_REF] Karg | Recognition of Affect Based on Gait Patterns[END_REF] showed that head, pelvis, elbow and shoulder joints embed most of the emotion of a movement. Results in [START_REF] Bernhardt | Detecting affect from non-stylised body motions[END_REF] proved that hands are also important in conveying expressions for several action. Thus, analysis of these five joints is most important to recognize body expressions. All the features extracted for body expression analysis are presented in Table 1 and are described below. We used many features to correctly fit to aspects of body expression described by psychological studies, i.e., form and movement, high and low-level descriptions of bodily detail.

The first feature V, is the global space occupy by the skeleton. We use the size of the bounding box of the skeleton in the three directions. The second feature θ is the angle defined between the vertical axis y and the axis binding the center of the hip to the neck. According to studies in psychology, a person tends to extend his body for positive expression whereas for negative expressions a person takes a more compact and forward tilt posture.

The following features are dedicated to correctly capture the configuration of each body part. Distance D between two joints is important feature to analyze body expression. For instance, we use the distance between hand to the shoulder on the same side. This distance gives indirect information about the elbow. We use distances between hands to hips, hands to shoulders and elbows to hips. Furthermore, a new idea introduced by our approach is the use of triangles A to correctly discriminate multiple expressions. The body being symmetric, we take joints on each side of the body, right and left side. The last point of the triangle is chosen on the axis of the body, i.e. either neck or hips. Since the majority of movements is anti-symmetric, the triangle gives lot of information about the expression. For each triangle, we compute its area and the three angles formed by these different triangles. With these four values, we extract information related to shape of the body. For instance one of these triangle-based feature is the area and the angles of the triangle defined by the neck and shoulders. Figure 3 shows the variation of triangles for two different body expressions taken at the same timing of walking. We compute the area and the angle of triangles defined by the hands and the neck; the shoulders and the neck; the elbows and the neck; the hands and the hips.

As mentioned in the state of the art, psychologists have showed that motion is an important characteristic to discriminate expressions for different gestures. Thus, we add to the feature vector the motion features: the velocity v and the acceleration a of the hands, shoulders, hips, head and elbows joints. The velocity is the first derivative of the position of the current joint. Acceleration being the second derivative of this position.

Finally, we use the fast Fourier transformation F to obtained the frequency component of our selected joints. We compute the discrete Fourier transform with the fast Fourier transform algorithm on the signal of the joint angle. Section 4 compares the results by using only geometric features, only motions feature or only the Fourier features on the different databases.

RESULTS AND ANALYSIS

We have tested our method on three databases (refer table 2 for summary of databases) which are presented below. Two of them are acted databases, while the last database consists of synthetic animations generated by the method of Xia et al. [START_REF] Xia | Realtime style transfer for unlabeled heterogeneous human motion[END_REF]. We will refer the last database as SIGGRAPH database in the rest of this paper.

1. Biological Motion [START_REF] Ma | A motion capture library for the study of identity, gender, and emotion perception from biological motion[END_REF]: this database consists of 1356 motions, especially knocking actions for 4 expressions (angry, neutral, happy, sad).

2. UCLIC Affective Body Posture and Motion [START_REF] Kleinsmith | Cross-cultural differences in recognizing affect from body posture[END_REF]: this acted database contains 183 acted animations for 4 expressions (fear, sad, happy, angry).

3. SIGGRAPH database [START_REF] Xia | Realtime style transfer for unlabeled heterogeneous human motion[END_REF]: the SIGGRAPH database is synthetic database generated from 11 minutes of motion capture data. It contains 572 animations with 8 expressions or style (angry, childlike, depressed, neutral, old, proud, sexy, strutting). In above mentioned databases, the SIGGRAPH database includes the largest range of movements: jump, run, kick, walk.

DataBase

Number of movements

Number of expressions UCLIC [START_REF] Kleinsmith | Cross-cultural differences in recognizing affect from body posture[END_REF] 183 4 Biological [START_REF] Ma | A motion capture library for the study of identity, gender, and emotion perception from biological motion[END_REF] 1356 4 SIGGRAPH [START_REF] Xia | Realtime style transfer for unlabeled heterogeneous human motion[END_REF] 572 8

Table 2: Description of the databases used for the test of our method.

Summary of results obtained by our methods using the different sets of features are presented in Table 3. Our proposed approach can run in real-time as it runs at ˜50 fps (on PC running on i7-4710MQ with 8GB of RAM). Extraction of proposed features, except Fourier features, takes 10ms for each frame while the extraction of Fourier features takes 500ms for a sequence of 27 seconds with 1657 frames. Before the classification, we are scaling each attribute of our features to the range [1,+1] to avoid numerical difficulties during the cal- culation. Presented results have been obtained using the support vector machine with a radial basis function kernel (SVM -RBF kernel) method for the classification using a 10-fold cross validation technique. The parameters of the classifier were determined empirically. Proposed features (refer Section 3 for the detailed discussion on proposed features) can be categorized in the following sub-categories.

1. Geometric features: distances, area and angles of triangles.

2. Motion features: velocity and accelerations.

3. Fourier features: magnitude of the spectra for different joints.

4. All features: combines all features mentioned above.

The best result is obtained with the combination of the different proposed features (see Table 3). It is interesting to observe the fact that, correct classification accuracy does not degrade significantly when we used only geometric features.

On the two databases, SIGGRAPH and Biological Motion, geometric features achieved only one percent less correct classification accuracy than the best achieved results. On UCLIC database the recognition rate for the geometric features is 12% less than the combination of all features. This is probably due to the fact that this database is significantly smaller in sample size (183 actions) and presents worst case scenario for machine learning algorithm. Proposed framework achieved best results on the synthetic database (SIG-GRAPH) which is due to the fact that synthetic animations presents exaggerate expressions with high inter-class variations.

Table 4 shows that our method is competitive against state of the art on the UCLIC database with similar recognition rate. In the Biological Motion Database, movements are mainly knocking at a door (≈ 1200 animations out of 1356 animations). The state of the art approach [START_REF] Bernhardt | Detecting affect from non-stylised body motions[END_REF] uses this particularity to compute the average movement of knocking at a door and then subtracting this movement before running the recognition in order to emphasis the expression. Their recognition rate for this biased method is 81%. Nevertheless, this trick is possible for very specific movements, when you assume that all movements are similar. They learn a movement's specific bias. Since purpose of our proposed framework is to be robust against heterogeneous movements, we can not apply this assumption. We believe that to evaluate [START_REF] Bernhardt | Detecting affect from non-stylised body motions[END_REF] and our approach, their unbiased recognition rate of 50% is to be compared with our approach that obtained correct classification accuracy of 57%. Finally, to the best of our knowledge, no method in literature on body expression analysis has tested the SIGGRAPH database.

DataBase

Best results from state-of-the-art Our results

UCLIC 79% [18] 78% Biological

50% unbias [4] 57% SIGGRAPH -93%

Table 4: Comparison of our methods using all features mentioned in this paper to the state of the art methods.

CONCLUSION

We have presented novel approach for automatic recognition of body expressions through 3D skeleton provided by motion capture data. Taking inspiration from psychology domain state of the art, we have proposed simple and representative features to detect body expression from temporal 3D postures, even in complex cases: jump, run, kick etc. We have evaluated our approach on three databases that contain heterogeneous movements and expressions and obtained results that exceeds state of the art. Secondly, our proposed approach runs in real time due to its computation simplicity. Thus, opening up possibilities for human-computer interaction applications. One such application example is new generation of video games that can benefit from real time body expression analysis to adapt its content on run time.

As future work, we will aim at extending the proposed method to use more semantic meta-features reinforcing the recognition of body expressions. For instance, we will seek to fit the low-level features on analytic curves in order to use the curve parameters in the classification. And, we will compute incrementally the low-level features to achieve continuous recognition over time. An improvement of the validation will be to test our approach on multi-simultaneous actions and by cross-validating our method on several databases.

Fig. 1 :

 1 Fig. 1: Overview of our framework.

Fig. 2 :

 2 Fig. 2: Features used for different expressions. These histograms show the discriminative property of our features.

  Id. Type of feature Description V Space of the skeleton Size of the bounding box of the skeleton θ Angle The three angles induces by the triangle formed by both shoulders and neck Angle between the vertical direction y and the axis binding the center of the hip and the head D Distance Right hand to the hips Left hand to the hips Right hand to the right shoulder Left hand to the left shoulder Right elbow to

  (a) First frame of the depressed walking animation. (b) First frame of the proud walking animation.

Fig. 3 :

 3 Fig. 3: Frames of the same action but with different body expressions. This figure show the variations of the triangle area formed by the both shoulders and the neck.Figure is color coded for the ease of visualization i.e. triangle formed by same joints in two figures are shown in similar color.

Table 1 :

 1 List of set of features that we propose to extract from the human postures for the classification of body expressions.

		the hips
		Left elbow to the hips
	A Area	Triangle defined by both hands and neck
		Triangle defined by both shoulders and neck
		Triangle defined by both hands and hips
		Triangle defined by both elbows and neck
	v Velocity	Hands
		Shoulders
		Hips
		Head
		Elbows
	a Acceleration	Hands
		Shoulders
		Hips
		Head
		Elbows
	F Frequency	Change of angle with respect to time of the following joints :
		Hands
		Shoulders
		Hips
		Head
		Elbows

Table 3 :

 3 Our results on the different databases and with different set of features. Classification method is SVM.

	DataBase	Set of features used	Results
	UCLIC	All features	78%
	UCLIC	Only geometric features	66%
	UCLIC	Only motion features	52%
	UCLIC	Only Fourier features	61%
	SIGGRAPH	All features	93%
	SIGGRAPH Only geometric features	92%
	SIGGRAPH	Only motion features	75%
	SIGGRAPH	Only Fourier features	90%
	Biological	All features	57%
	Biological	Only geometric features	56%
	Biological	Only motion features	48%
	Biological	Only Fourier features	46%

The author has requested enhancement of the downloaded file. All in-text references underlined in blue are linked to publications on ResearchGate. The author has requested enhancement of the downloaded file. All in-text references underlined in blue are linked to publications on ResearchGate.


Jean-Michel Dischler
email: dischler@lsiit.u-strasbg.fr

J.-M Dischler

F Zara

Real-time structured texture synthesis and editing using image-mesh analogies

Keywords: Texture, Synthesis, Editing

We present a novel texture synthesis technique designed to reproduce at real-time frame-rates example texture images, with a special focus on patterns characterized by structural arrangements. Unlike current pixel-, patch-or textonbased schemes, that operate in image space, our approach is structural. We propose to assimilate texture images to corresponding 2D geometric meshes (called texture meshes). Our analysis mainly consists in generating automatically these meshes, while synthesis is then based on the creation of new vertex/polygon distributions matching some arrangement map. The output texture image is obtained by rasterizing the previously generated polygons using graphics hardware capabilities, which guarantees high speed performance. By operating in geometry space instead of image/pixel space, the proposed structural approach has a major advantage over current techniques: beyond pure texture reproduction, it allows us to define various tools, which allow users to further modify locally or globally and in real-time structural components of textures. By controlling the arrangement map, users can substitute new meshes in order to completely modify the structural appearance of input textures, yet maintaining a certain visual resemblance with the initial example image.

Introduction

Texture synthesis has proved to be a powerful tool for reproducing automatically and faithfully example texture images, and has thus been extensively studied during the past few years. It has now reached an advanced degree of maturity. Beyond reproduction, new techniques now attempt to grant users more and more control over the synthesis process. These methods essentially focus on the control of feature positions and size, or on techniques to create consistent transitions among different textures (including texture mixing). However, semantic-related structural texture compositions have not been paid much atten-tion yet, though this represents an important visual characteristic of many natural or artificial textures.

In this paper, we propose a structural method designed to address this issue. Our motivation is to allow users a fast, faithful and automatic texture reproduction, but with an interactive control of structural texture compositions: not only shape and position of texture features/elements (called textons according to [START_REF] Julesz | Texton, the elements of texture perception, and their interactions[END_REF]), but also the way the textons are arranged with respect to each other. With our approach, users may, for instance, modify the structural arrangement of an input texture, while maintaining some visual resemblance with the corresponding example image, e.g., exchanging brick arrangements, but not the individual brick patterns. The structural appear-ance is controlled using an arrangement map that can be extracted from images or freely designed by users. Figure 1 depicts an example showing how well our method covers structural texture aspects. The top row shows the input texture (left) and the corresponding texture mesh (right) extracted using image processing techniques. The second row illustrates synthesis: on the left, we show the used arrangement map and on the right the resulting texture synthesis (the synthesis uses the input example, the texture mesh and the arrangement map). Since on the second row the arrangement map matches the initial arrangement of the example texture, we obtain a straight reproduction. The last row illustrates structural control. Another arrangement has been substituted using a different arrangement map, thus modifying the structural composition of the texture. Although the arrangement is different, we maintain a certain visual resemblance with the original model.

To be able to provide efficient interaction tools, our synthesis technique must satisfy a strong constraint: it must run at interactive frame-rates. Our method guarantees such frame-rates by using graphics cards to accelerate the image generation process. More specifically, our technique consists in decomposing textures into sets of connected polygons, which are bounding individual textons. Once the textures have been expressed as 2D texton matching meshes, colors can be ignored. The synthesis operates entirely in geometric space: it consists in reproducing visually similar meshes coarsened by the supplied arrangement map. Once a new mesh has been synthesized (requires a few milliseconds), the corresponding texture image is finally generated in real-time by polygon rasterization.

The paper is organized as follows: the next section briefly presents some related works. Section 3 then explains the preprocessing stage: the automatic generation of texture meshes. Section 4 presents the synthesis of meshes using an arrangement map to control structural as-Fig. 1. Our synthesis is based on mesh extraction (top right) from input images (top left), in combination with arrangement maps (left) to control structural arrangements of resulting textures (right). In both cases, the textures were synthesized in a few milliseconds. Note how the second texture keeps a certain visual resemblance with the example image, though its structural arrangement is different pects. We propose a polygon fitting technique. Section 5 describes how to reconstruct texture images from the previously generated meshes. Finally, before concluding, we present some results, as well as a comparative study with existing synthesis techniques. As will be shown, our method, though not focusing on quality, compares well to current methods, but at a fraction of the computational requirements. In addition, it considerably increases user control concerning structural composition. We further show that our technique not only applies to highly structured textures like brick walls, but also to random patterns such as lawns. The only condition that must be met is that individual textons must be well identified.

Related works and motivation

Seminal texture analysis and synthesis methods were mainly based on histogram analogies using multiscale or spectral approaches [START_REF] Dischler | Anisotropic solid texture synthesis using orthogonal 2D views[END_REF][START_REF] Heeger | Pyramid-based texture analysis/synthesis[END_REF]. But such methods are strongly limited by the fact that they cannot deal with structured patterns. Alternate techniques, based on Markovian processes, have then been proposed. Such techniques generate patterns pixel by pixel, by selecting at each step a color that minimizes an error according to a given neighborhood [START_REF] Efros | Texture synthesis by non-parametric sampling[END_REF]. But the related best pixel match search may require some noticeable time in spite of proposed hierarchical data structures [START_REF] Wei | Fast texture synthesis using tree-structured vector quantization[END_REF]. In addition, semantic-related structures are not addressed well with these methods. Another solution therefore consists in using complete texture pieces [START_REF] Liang | Real-time texture synthesis by patch-based sampling[END_REF] instead. These can be randomly repeated and blended as in [START_REF] Praun | Lapped textures[END_REF]. The quality of patch-based techniques depends on the types of overlap management. Blending, for instance, introduces some new frequencies (overblurring), thus deteriorating visual aspects. Better results are usually obtained using a clever cutting trajectory along the overlap, computed according to an error-minimizing factor [START_REF] Efros | Image quilting for texture synthesis and transfer[END_REF][START_REF] Kwatra | Graphcut textures: image and video synthesis using graph cuts[END_REF]. Recent improvements in the field of texture synthesis focus on recovering even better some featurerelated aspects [START_REF] Wu | Feature matching and deformation for texture synthesis[END_REF] by using additionally Laplacian filters. Other techniques focus on synthesis speed by separating analysis (precomputation step) and synthesis [START_REF] Zelinka | Jump map-based interactive texture synthesis[END_REF] or by using the GPU [START_REF] Lefebvre | Parallel controllable texture synthesis[END_REF].

Fast and faithful texture reproduction remained for a long time a major goal of texture synthesis, but many recent computer graphics-oriented techniques include, in addition to random or uncontrolled high quality reproduction, also the possibility for users to change and constrain some visual aspects. In [START_REF] Bar-Joseph | Texture mixing and texture movie synthesis using statistical learning[END_REF][START_REF] Wei | Texture synthesis from multiple sources[END_REF] different textures can be mixed. In [START_REF] Ashikhmin | Synthesizing natural textures[END_REF] feature distributions can be controlled using a user-drawn feature probability map. In [START_REF] Dischler | Texture particles[END_REF] feature sizes, orientations and so forth can be modified. In [START_REF] Liu | Pattern-based texture metamorphosis[END_REF][START_REF] Zhang | Synthesis of progressively-variant textures on arbitrary surfaces[END_REF], the difficult problem of smooth transitions between different types of textures is addressed. As for texture particles [START_REF] Dischler | Texture particles[END_REF], and the authors of [START_REF] Zhang | Synthesis of progressively-variant textures on arbitrary surfaces[END_REF] consider elementary texture com-ponents (textons) by using texton masks. We therefore call such techniques texton-based. With [START_REF] Zhang | Synthesis of progressively-variant textures on arbitrary surfaces[END_REF], users may also control other feature properties like size and orientation (using an underlying vector-field). More recently, a complete system has been proposed to design new textures from example texture databases [START_REF] Matusik | Texture design using a simplicial complex of morphable textures[END_REF]. In [START_REF] Lefebvre | Parallel controllable texture synthesis[END_REF], a GPU implementation is proposed to produce controlled textures at very fast rates, which allows one to drag-and-drop individual textons at real-time rates. However, this technique uses a pixel-based approach thus failing to capture structural aspects. In [START_REF] Kwatra | Texture optimization for example-based synthesis[END_REF] an optimization technique is used, which allows one to control the synthesis by using underlying flow fields. All of these techniques considerably increase the scope of texture synthesis, especially for computer graphics applications. They provide a wide range of tools, allowing users to design various effects beyond pure texture reproduction. However, none of these techniques ever considered semantic-related structural manipulations. Therefore, there remains an important limitation with respect to user control and free texture design from example images.

The motivation for our technique is to fill this gap. Unlike techniques operating in image space, structural approaches have yet to be studied in detail, because they are known to be restrictive and/or technically more complex. In [START_REF] Lefebvre | Analysis and synthesis of structural textures[END_REF], for instance, the proposed structural method has been limited to specific types of textures such as brick wall patterns and woods. Our technique instead performs a full texture mesh analogy, thus remaining generic. It is only based on the ability to segment and to identify textons in texture images. By using an arrangement map, the user straightforwardly controls the structural aspect of textures for synthesis.

Two-dimensional meshes have been used before in the field of texture synthesis, but to our knowledge not for structural analysis. In [START_REF] Matusik | Texture design using a simplicial complex of morphable textures[END_REF], for instance, simplicial complexes are used to maintain sharpness along interpolations. In [START_REF] Liu | Near-regular texture analysis and manipulation[END_REF], meshes are used to evaluate the distortions of nearregular textures. Here, we extend this concept to characterize the actual structural composition of any type of texture, including irregular ones. In our case, we do not start from rectangular grids, but use image analysis to create 2D texture matching meshes. These are then coarsened to fit an arrangement map.

Our approach mainly extends to the texture particles and texton masks approaches of [START_REF] Dischler | Texture particles[END_REF] and [START_REF] Zhang | Synthesis of progressively-variant textures on arbitrary surfaces[END_REF], respectively, by further bounding individual textons with polygons. Since our polygons may be considered to some extent as cells, our approach comes also close to cellular texture synthesis approaches, which have already been used successfully in the field of pure texture synthesis (that is, without analysis). For example, they have been used for generating brick wall patterns [START_REF] Legakis | Feature-based cellular texturing for architectural models[END_REF][START_REF] Miyata | A method of generating stone wall patterns[END_REF] or noise functions [START_REF] Worley | A cellular texture basis function[END_REF]. Here, we apply this kind of structural classification to the field of texture reproduction and design from example image analysis.

Automatic texture mesh generation

Our first objective is to generate automatically a 2D mesh matching well the structural composition of the input texture. This mesh represents a kind of geometric dual counterpart to the texture image. By viewing only the mesh, one should be able to recover the global structural appearance of the corresponding texture. This mesh will be used later in conjunction with the arrangement map to produce controlled structural arrangements. Mesh reconstruction, for example by analyzing edges in images, is a widely studied area in the field of computer vision and digital image processing [START_REF] Gonzalez | Digital Image Processing[END_REF]; therefore, we will not in detail discuss all related topics here. Indeed, mesh extraction does not represent our core problem. It rather represents a necessary preprocess.

We note that there exists a huge amount of work concerning more generally the creation of triangular, structured, unstructured, hexagonal, etc., meshes from image data (2D or even 3D). We found however that existing methods do not adapt well to the texture analysis and synthesis problem at hand. Therefore, we nevertheless briefly present the major aspects of the method we implemented for generating automatically texture matching meshes. For the sake of time, we will assume that the reader is familiar with morphological operators, such as erosion, dilatation, thinning, and so forth.

As for texton-based techniques [START_REF] Dischler | Texture particles[END_REF][START_REF] Zhang | Synthesis of progressively-variant textures on arbitrary surfaces[END_REF], the first step consists of texture segmentation, which means that we need to identify textons by creating a binary image I s (i, j) from the input texture image I(i, j). In [START_REF] Zhang | Synthesis of progressively-variant textures on arbitrary surfaces[END_REF], such an image is called a texton mask. Figure 2 illustrates our segmentation: (a) represents the input texture I(i, j) and (b) the segmented image I s (i, j).

Gabor wavelets and windowed Fourier transforms [START_REF] Grigorescu | Comparison of texture features based on Gabor filters[END_REF][START_REF] Idrissa | Texture classification using Gabor filters[END_REF] have had wide success in the field of texture segmentation because they unify frequency and spatial analysis and have found to matching the human psycho-physical perception mechanism well. In our case, we apply such filters to the input image, followed by a quantization.

In [START_REF] Zhang | Synthesis of progressively-variant textures on arbitrary surfaces[END_REF], the segmented images (texton masks) are straightforwardly used to control arrangements and to consistently mix couples of textures. In our case, we propose to use this mask to further build a texture mesh (set of polygons). Such a mesh can be automatically and straightforwardly derived from I s (i, j) as described below. Figure 2c-h illustrate the different steps of the procedure. Firstly, we apply a thinning algorithm to the negative of I s (i, j), which consequently enlarges the textons, in such a way that these are separated by no more than one line of pixels (Fig. 2c). Indeed, thinning is a wellknown morphological operation that reduces components in binary images to single pixel-wide branches, while preserving some properties [START_REF] Gonzalez | Digital Image Processing[END_REF]: it does not remove endpoints, it preserves connectedness, and it avoids excessive ero-Fig. 2. Texture segmentation and automatic mesh reconstruction using basic image processing tools sion of regions. Since segmentation often includes some noise, the next step consists in cleaning the image resulting from thinning by removing pending branches due for example to concave textons and by joining very close endpoints. This is again done by iteratively applying specific morphological erosion and dilatation operators. Figure 2d illustrates the result of our cleaning technique. Using this result, one can identify individual cells that are matching some texton distributions. This image often (but not always) needs to be processed again to remove any remaining residual feature. Removal is performed by filling out very small cells, and by reapplying the same procedure. Figure 2e shows the obtained result: we obtain a set of texton-matching cells defined by connected pixel branches. Note that textons on borders (i.e., textons which are incomplete) have been removed in our implementation (if necessary one could keep them). This entire process can be implemented quite easily and we found it to work very well. In fact, we experienced that the main difficulty was not cell generation, but rather to provide a good initial segmentation.

We call the image resulting from thinning and cleaning I c (i, j) because it identifies a set of texton-matching cells. Using the previously computed image I c (i, j), it is now possible to straightforwardly build a corresponding polygonal mesh. We first pick out branching cross-points, which represent the primary vertices of the texture mesh. In Fig. 2f these are represented by green dots. We join these vertices by straight edges according to the branches of image I c (i, j). That is, two vertices are joint only if the corresponding cross-points are also linked together by one branch of pixels. Then, we introduce some new vertices by splitting some edges according to the shape of the corresponding branch. That is, if the straight segment is too distant according to a user selected threshold, we subdivide it to better fit the branch's curvature and shape. This is performed iteratively by introducing new vertices at positions that minimize the average distance of the resulting new edges from the corresponding branch. These new, secondary, vertices are depicted as yellow dots in Fig. 2g. They mainly appear on the borders of the outermost polygons.

Finally, this mesh is again processed to better fit the individual textons of I s (i, j). Indeed, some mesh edges may cross over the textons, which then results in apparent discontinuities during synthesis (see next sections). We therefore have to ensure that mesh edges do not cross over textons, or we must at least minimize such crossings. We apply an iterative procedure that progressively displaces vertices in order to minimize the amount of edges that cross over textons. The final resulting texture mesh is shown in Fig. 2h. It matches the texton distribution of the input texture image well. We note that resulting 2D meshes are not regular, often also non-conformal and may contain polygons that have an arbitrary number of vertices (not necessarily the same number for each polygon).

Synthesis using arrangement maps

In the previous section, we described a technique to generate sets of connected polygons from given input texture images using segmentation and digital image processing. These polygons bound individual textons, so we call them texton-polygons. In this section, we show that meshes can be randomly reproduced to fit a given arrangement map. Our core problem is to be able to generate a new mesh that globally matches (from a visual point of view) this arrangement map, yet includes some elements of the previously generated texture mesh.

We propose a method taking into account two statistical elements: positions and shapes of polygons. We do so by applying consecutively two iterative procedures. The first procedure creates a random arrangement map from a given periodic input arrangement map (Fig. 3), either extracted from example images or designed by users. The arrangement map is, as for the texture mesh, composed of polygons. Each of these map polygons is composed of vertices, which are either conformal or nonconformal. A non-conformal vertex is a vertex belonging to an edge of another polygon. Conformal vertices are exclusively edge extremities. The principle for producing random arrangement maps is straightforward: we first randomly displace vertices. Non-conformal vertices are only displaced along the corresponding edge. Then, we apply an iterative relaxation procedure, aiming at minimizing angular errors to respect initial angles of the input arrangement map. That is, vertices are again progressively displaced in order to match initial edge angles. The user can select the magnitude of randomness by providing a given magnitude coefficient. To keep a perfectly repetitive structure this coefficient may be set to zero.

Figure 3 (left) shows an input arrangement map (same as for Fig. 1), and shows a random perturbation (middle). Note that since all vertices, in this example, are nonconformal, we displaced them only along the corresponding edges, which explains why we keep a sort of stacked linear structure. The last image illustrates the result of relaxation after 50 iterations.

The second procedure (Fig. 4) consists in fitting the texton-polygons into the previously generated arrangement map, which is followed by a second iterative procedure consisting in relaxing the resulting mesh to more or less respect initial texton-polygon shapes (edge angles). We do this in two steps. Firstly, we randomly select for each map-polygon a given texton-polygon. The randomly selected texton-polygon vertices are placed onto the edges and vertices of the map-polygon by following a clock-wise cycle and by optimizing distance ratios with respect to the polygon perimeters (ratios with respect to the global distance around the outside of the polygons). Secondly, the resulting polygon, which is now totally matching the map-polygon is relaxed by an iterative procedure to better fit texton-polygon edge angles. We note that this procedure allows us to make any texton-polygon fit any mappolygon. Even if the texton-polygon contains less vertices than the map-polygon it is possible to duplicate some vertices (considering a null distance edge). Shapes can be also very different. This is illustrated in Fig. 4. The top shows a texton-polygon (extracted from Fig. 1). The two next rows then illustrate the fitting procedure for two different map-polygons (on the left): a rectangle and a triangle. The final result of fitting is shown on the right after 10 relaxation steps.

The same procedure is applied to all map-polygons of the random arrangement map, thus obtaining a new arrangement matching texture mesh. We call this new final mesh the synthesis mesh. We now describe how the latter mesh can be used to create final texture images.

Texture image rasterization

The synthesis mesh resulting from the previously described fitting technique could be, at first glance, straightforwardly used to create texture images. Indeed, the mesh is composed of polygons, which represent basic graphical primitives supported by all current graphics cards. Hence, one may directly associate to each polygon a 2D texture map with texture coordinates that match the initial input texture image I(i, j), thereby letting the final image be generated by fragment rasterization. Two-dimensional texture mapping-based mesh-manipulation tools are commonly and broadly used in nearly all interactive painting and photo-editing systems (e.g., image morphing). However, such a straightforward mesh rasterization approach does not apply well to texture synthesis. Indeed, there are at least two undesirable visual effects resulting from 2D texture mapping: (1) there are visible seams on the borders of the polygons since two adjacent polygons in the synthesis mesh might not have been adjacent in the original texture mesh (thus resulting in discontinuities), and (2) patterns related to textons appear stretched or shrunk, which is due to resampling during rasterization.

To avoid these two undesirable effects, we propose a technique that still consists in using polygonal 2D texture mapping, as supported by graphics cards, but adapted to consider both textons and subtextures together. We now describe what we mean by subtextures and how to define these.

To generate texture meshes (Sect. 3), we have used a binary segmentation based on color quantization. However, it is possible to segment any input texture into more than just two zones (black/white). Therefore, after filtering by Gabor wavelets or Fourier masks, we select a quantization number n q higher than two. Such a quantization is equivalent to performing a pixel classification: each pixel is assigned a class by means of a number (an integer value between 1 and n q ). We call I q (i, j), the image resulting from filtering and quantization. I q (i, j) is composed of sets of connected pixel components C q k (that is, each class k ∈ [1, n q ] corresponds to one or multiple connected pixel sets). Intuitively, these components are clustering pixels that belong to patterns, which have similar filter responses. In other words, it represents a partitioning of I into visually similar zones, that we call subtextures according to [START_REF] Zalesny | Composite texture synthesis[END_REF]. Each texton may now be composed of one or multiple subtextures. Figure 5 shows an example of quantization for the brick wall example of Fig. 1. As visible in this figure, individual textons may be composed of multiple subtextures (each color represents another subtexture on this figure).

We can now generate large texture fields visually matching given subtextures. On Fig. 5, we show an example of subtexture field corresponding to the concrete between the bricks. The arrows show some of the connected components C q k that have been used to generate this subtexture field (Fig. 5 left). The subtexture fields are synthesized in a preprocess by using any existing texture synthesis technique. We used a quilting-like approach. For applying the latter, we straightforwardly use the input image I(i, j) cropped by the corresponding connected component C q k . Once all fields have been generated (as for mesh generation, this needs to be done only once in a preprocess for a given input texture I(i, j)), they can be used in combination with I q (i, j) and with the texton map I s (i, j) to avoid the problems of seams and distortions appearing during rasterization.

The synthesis mesh allows us to create texton distributions by using traditional texture mapping. But, instead of mapping straightforwardly the input image I(i, j) as per usual painting systems, we map the quantized image I q (i, j), further cropped by the texton mask I s (i, j). Figure 6 illustrates the principles of our technique. The top shows traditional texture mapping on a brick texton cropped by its texton mask. On the top right, we further show the same brick stretched horizontally, thus dis-Fig. 5. Identifying subtextures (left) and generating corresponding texture fields (right). Here the subtexture corresponds to the concrete between the bricks of the brick wall texture of Fig. 1 Fig. 6. Using multiple subtextures (middle) for individual texture elements instead of traditional 2D texture mapping (top). We also show the effect of deforming the polygon and subsequently its texton (in this case, we stretched the brick horizontally) torting underlying patterns. The two bottom rows illustrate our technique for an increasing amount of subtextures.

The quantized image I q (i, j) (Fig. 6 left) is used for indexing the corresponding subtextures (it is used as indirection), see middle part of Fig. 6. That is, each polygon is actually rasterized with three 2D texture maps: the texton mask I s (i, j) used to extract only the pixels belonging to textons, the index mask I q (i, j) and the corresponding subtexture field. The texton mask and the index mask produce the shape of the texton (it is resampled according to the shape of the polygon) and the subtexture field the actual colors (small scale patterns). The result is given in Fig. 6 (right). Note how global texton shapes can be deformed, without deforming subtextures.

Figure 7 illustrates a more complete example for the brick wall. In this figure, we show, on the top, traditional texture mapping resulting in visible seams, since Fig. 7. Using texton masks and index masks to avoid seams. The top shows traditional 2D texture mapping with seams and subtexture distortions. The bottom shows our result we have made polygons adjacent that were not adjacent in the initial texture mesh. Below, we show the corresponding texton mask (left). And on the right, we finally show the result obtained by applying our technique combining texton distributions with the corresponding subtextures indexed by I q (i, j). A single rendering pass is necessary: firstly, we initialize the frame-buffer by copying the subtexture field corresponding to the background subtexture (in the case of the brick wall, this is the concrete subtexture of Fig. 5). Then, each polygon is rasterized with its own index mask (a 2D texture map) used to access the corresponding subtexture fields as shown for one single brick in Fig. 6. For practical reasons all subtexture fields are fetched into texture memory once in the form of a 3D texture (the fields are simply stacked). The index value of the index mask then matches the Z coordinate in this 3D texture. In fact, using a 3D texture allows us to bind all subtextures at once in texture memory.

The interesting point addressed by this approach is that texture distortions (according to the shape of the polygon) are only applied to the index and texton mask I q (i, j) and I s (i, j) to modify the shape of the texton accordingly, but not to the subtextures (see the stretched brick of Fig. 6). The reason is that we use two different texture coordinates, e.g., one for the masks and another for the subtexture. This allows for the preservation of subtexture frequencies. Note that instead of using a specific pixel-shader program and 3D texture, it is also possible to use the simpler multitexturing functionality for rasterizing the polygons. However, in this case, multiple passes become necessary, especially if one texton is composed of multiple subtextures (we need one pass for each subtexture).

We note that we generate subtextures only if the size of the corresponding connected component C q k is large enough (we set a minimal size to 200 pixels). Indeed, we experienced that if we use too small components, this results in very noisy subtexture fields, also producing final noisy results. When no subtexture field has been generated for a given texton, the previous procedure then simply indexes the original image I(i, j) as traditional 2D texture mapping (yet still using the texton mask to avoid seams). Figure 6 (last row) illustrates this. On the left quantized image, one can actually see at least 5 classes. Hence, there should be also 5 subtextures. Yet, only 3 were computed as visible in the middle part of the figure. This is because the corresponding connected components were found to be too small.

For smoothly varying or non-stationary texton contents, the use of subtextures can cause incorrect results (we show this in the results section). In such cases, one must use a large number of classes, resulting in very small connected components. This, in turn, causes traditional texture mapping to be implicitly used (we do not compute subtexture fields if the components are smaller than a given number of pixels), which might result in visible pattern distortions.

To generate the final texture image from the previously generated synthesis mesh, one simply has to rasterize each polygon using the texture mapping procedure that we just described. This is usually extremely fast (real-time) since graphics cards now reach high rasterization performances. Since the synthesis mesh technique is also very fast (few iterations are usually sufficient) textures can be synthesized at interactive frame-rates. Users may also interactively edit the synthesis mesh by displacing vertices or by dragging some specific textons on some specific mappolygons.

Results

In this section, we present some results obtained with the previously described texture synthesis and editing technique. The major limitation of our method is illustrated in Fig. 8. Figure 9 illustrates an example of the synthesis result. The top row shows from left to right: the input, the resulting cells and the corresponding mesh. The second row shows the arrangement map and the resulting Fig. 8. Texture examples that cannot be processed with our technique, since textons cannot be segmented Fig. 9. An example of synthesis for different amounts of subtextures Fig. 10. Comparison with texture quilting [START_REF] Efros | Image quilting for texture synthesis and transfer[END_REF], the feature matching synthesis technique of [START_REF] Wu | Feature matching and deformation for texture synthesis[END_REF], the parallel technique of [START_REF] Lefebvre | Parallel controllable texture synthesis[END_REF] and the per-pixel jump map technique of [START_REF] Zelinka | Jump map-based interactive texture synthesis[END_REF] (middle). Left is input, right is our result synthesized mesh as well as the corresponding texton mask. The last row is the resulting texture for a low (left) and high (right) amount of classes. Using a high amount of classes causes connected components to be very small, which results in nearly no computed subtextures.

Figure 10 illustrates a comparative study. The left column represents the model, the middle shows existing techniques (from top to bottom: texture quilting [START_REF] Efros | Image quilting for texture synthesis and transfer[END_REF], the feature matching synthesis technique of [START_REF] Wu | Feature matching and deformation for texture synthesis[END_REF], the parallel technique of [START_REF] Lefebvre | Parallel controllable texture synthesis[END_REF] and the per-pixel jump map technique of [START_REF] Zelinka | Jump map-based interactive texture synthesis[END_REF]), the right column shows our result. Our objective was to compare both quality and speed. Therefore, we took two high quality techniques and two high speed techniques. In our case, the synthesis took from top to bottom 16 ms, 123 ms, 78 ms and 57 ms on a laptop with Pentium M processor 2.00 GHz and 1 GB RAM. The graphics hardware is a NVidia Quadro FX Go 1400. These times include both the synthesis of the mesh and the rasterization. In all cases, the preprocessing time (required only once for a given texture) was below 5 min (this includes segmentation, texture mesh generation and subtexture field synthesis). The number of computed subtexture fields was kept low (an average of 2 fields per texton, except for the second row where we used about 5 fields per texton, which also explains the somewhat increased noise). As demonstrated by this figure, our technique provides sufficiently good results at times comparable to both [START_REF] Lefebvre | Parallel controllable texture synthesis[END_REF] and [START_REF] Zelinka | Jump map-based interactive texture synthesis[END_REF]. Note that since both of these methods are based on per-pixel procedures they fail to greatly capture semantic-related structural aspects. Our method, on the contrary, is designed to address structural textures, so it provides better results in these cases.

Figure 11 illustrates the effect of different arrangement maps on two different textures. The first row shows the input, the second one the reconstructed texture meshes and the third one reproduction. The last two rows illustrate the influence of arrangement maps (depicted in the far left). Note that arrangement maps can contain arbitrary polygons that do not necessarily need to be connected. For the three arrangements, the synthesis time for the lawn was between 16 and 47 ms, and for the panther texture between 14 and 45 ms.

Figure 12 shows some more examples. The right column shows the input, the second one reproduction, and finally a new user-designed arrangement.

The major limitation of our method is illustrated in Fig. 8. This figure shows textures that cannot be segmented into individual textons. In such cases, we cannot build texture meshes and so the method simply cannot be used.

Conclusions and future work

We have presented a new structural approach for texture synthesis and editing. The method is based on a texture Currently, the approach is not suitable for textures that are not characterized by an underlying texton-related structure. In future works, we aim to address this issue. We believe that texture reproduction has now reached an advanced degree of maturity, and that efforts should be focused on increasing user manipulations, including the design of new structural aspects. We also intend to extend this method, in order to edit and manipulate textures at interactive rates directly on arbitrary surfaces.

Fig. 3 .

 3 Fig. 3. Creating random arrangement maps from input arrangement maps using an iterative procedure

Fig. 4 .

 4 Fig. 4. Texton-polygon (top) fitting technique. Of the two bottom rows, the left shows a mappolygon, the middle the clock-wise vertex placement, and the right the final result after relaxation

Fig. 11 .

 11 Fig. 11. Controlling arrangements using the arrangement map (far left)

Fig. 12 .

 12 Fig. 12. More examples of synthesis and controlled arrangements