Representing junctions through asymmetric tensor diffusion

Gradient-based junctions form key features in such applications as object classification, motion segmentation, and image enhancement. Asymmetric junctions arise from the merging of an odd number of contour end-points such as at a 'Y' junction. Without an asymmetric representation of such a structure, it will be identified in the same category as 'X' junctions. This has severe consequences when distinguishing between features in object classification, discerning occlusion from disocclusion in motion segmentation and in properly modeling smoothing boundaries in image enhancement.Current junction analysis methods include convolution, which applies a mask over a sub-region of the image, and diffusion, which propagates gradient information from point-to-point based on a set of rules.A novel method is proposed that results in an improved approximation of the underlying contours, through the use of asymmetric junctions. The method combines the ability to represent asymmetric information, as do a number of convolution methods, with the robustness of local support obtained from diffusion schemes. This work investigates several different design paradigms of the asymmetric tensor diffusion algorithm. The proposed approach proved superior to existing techniques by properly accounting for asymmetric junctions over a wide range of scenarios

Compressed Optical Imaging

We address the resolution of inverse problems where visual data must be recovered from incomplete information optically acquired in the spatial domain. The optical acquisition models that are involved share a common mathematical structure consisting of a linear operator followed by optional pointwise nonlinearities. The linear operator generally includes lowpass filtering effects and, in some cases, downsampling. Both tend to make the problems ill-posed. Our general resolution strategy is to rely on variational principles, which allows for a tight control on the objective or perceptual quality of the reconstructed data. The three related problems that we investigate and propose to solve are 1. The reconstruction of images from sparse samples. Following a non-ideal acquisition framework, the measurements take the form of spatial-domain samples whose locations are specified a priori. The reconstruction algorithm that we propose is linked to PDE flows with tensor-valued diffusivities. We demonstrate through several experiments that our approach preserves finer visual features than standard interpolation techniques do, especially at very low sampling rates. 2. The reconstruction of images from binary measurements. The acquisition model that we consider relies on optical principles and fits in a compressed-sensing framework. We develop a reconstruction algorithm that allows us to recover grayscale images from the available binary data. It substantially improves upon the state of the art in terms of quality and computational performance. Our overall approach is physically relevant; moreover, it can handle large amounts of data efficiently. 3. The reconstruction of phase and amplitude profiles from single digital holographic acquisitions. Unlike conventional approaches that are based on demodulation, our iterative reconstruction method is able to accurately recover the original object from a single downsampled intensity hologram, as shown in simulated and real measurement settings. It also consistently outperforms the state of the art in terms of signal-to-noise ratio and with respect to the size of the field of view. The common goal of the proposed reconstruction methods is to yield an accurate estimate of the original data from all available measurements. In accordance with the forward model, they are typically capable of handling samples that are sparse in the spatial domain and/or distorted due to pointwise nonlinear effects, as demonstrated in our experiments

An improved representation of junctions through asymmetric tensor diffusion

Abstract. Junctions form critical features in motion segmentation, image enhancement, and object classification to name but a few application domains. Traditional approaches to identifying junctions include convolutional methods, which involve considerable tuning to handle non-trivial inputs and diffusion techniques that address only symmetric structure. A new approach is proposed that requires minimal tuning and can distinguish between the basic, but critically different, ‘X ’ and ‘T ’ junctions. This involves a multi-directional representation of gradient structure and employs asymmetric tensor diffusion to emphasize such junctions. The approach combines the desirable properties of asymmetry from convolutional methods with the robustness of local support from diffusion.

Analyse / synthèse de champs de tenseurs de structure : application à la synthèse d’images et de volumes texturés

This work is a part of the texture synthesis context. Aiming to ensure a faithful reproduction of the patterns and variations of orientations of the input texture, a two-stage structure/texture synthesis algorithm is proposed. It consists of synthesizing the structure layer showing the geometry of the exemplar and represented by the structure tensor field in the first stage, and using the resulting tensor field to constrain the synthesis of the texture layer holding more local variations, in the second stage. An acceleration method based on the use of Gaussian pyramids and parallel computing is then developed.In order to demonstrate the ability of the proposed algorithm to faithfully reproduce the visual aspect of the considered textures, the method is tested on various texture samples and evaluated objectively using statistics of 1st and 2nd order of the intensity and orientation field. The obtained results are of better or equivalent quality than those obtained using the algorithms of the literature. A major advantage of the proposed approach is its capacity in successfully synthesizing textures in many situations where traditional algorithms fail to reproduce the large-scale patterns.The structure/texture synthesis approach is extended to color texture synthesis. 3D texture synthesis is then addressed and finally, an extension to the synthesis of specified form textures using an imposed texture is carried out, showing the capacity of the approach in generating textures of arbitrary forms while preserving the input texture characteristics.Cette thèse s’inscrit dans le contexte de la synthèse d’images texturées. Dans l’objectif d’assurer une reproduction fidèle des motifs et des variations d’orientations d’une texture initiale, un algorithme de synthèse de texture à deux étapes « structure/texture » est proposé. Il s’agit, dans une première étape, de réaliser la synthèse d’une couche de structure caractérisant la géométrie de l’exemplaire et représentée par un champ de tenseurs de structure et, dans une deuxième étape, d’utiliser le champ de structure résultant pour contraindre la synthèse d’une couche de texture portant des variations plus locales. Une réduction du temps d’exécution est ensuite développée, fondée notamment sur l’utilisation de pyramides Gaussiennes et la parallélisation des calculs mis en oeuvre.Afin de démontrer la capacité de l’algorithme proposé à reproduire fidèlement l’aspect visuel des images texturées considérées, la méthode est testée sur une variété d’échantillons de texture et évaluée objectivement à l’aide de statistiques du 1er et du 2nd ordre du champ d’intensité et d’orientation. Les résultats obtenus sont de qualité supérieure ou équivalente à ceux obtenus par des algorithmes de la littérature. Un atout majeur de l’approche proposée est son aptitude à synthétiser des textures avec succès dans de nombreuses situations où les algorithmes existants ne parviennent pas à reproduire les motifs à grande échelle.L’approche de synthèse structure/texture proposée est étendue à la synthèse de texture couleur. La synthèse de texture 3D est ensuite abordée et, finalement, une extension à la synthèse de texture de forme spécifiée par une texture imposée est mise en oeuvre, montrant la capacité de l’approche à générer des textures de formes arbitraires en préservant les caractéristiques de la texture initiale