Espace d'échelle | EPFL Graph Search

La théorie de lEspace d'échelle () est un cadre pour la représentation du signal développé par les communautés de la vision artificielle, du , et du traitement du signal. C'est une théorie formelle pour manipuler les structures de l'image à différentes échelles, en représentant une image comme une famille d'images lissées à un paramètre, la représentation d'espace échelle, paramétrée par la taille d'un noyau lissant utilisé pour supprimer les structures dans les petites échelles. Définition Soit f : \R^n \rightarrow \R un signal. On appelle représentation d'une fonction f en espace d'échelles linéaire la fonction L telle que : ::L : \R^n \times \R \rightarrow \R ::L(x,0) = f(x) \forall x \in \R^n ::L(x,t) = g_{\sqrt{t}} * f(x) \forall x \in \R^n, \forall t \in \R^+ où ::: - g_{\sqrt{t}}(x) = \frac{1}{(2 \pi t)^\frac{n}{2}} e ^\frac{-x^Tx}{2t} ::: - * est l'opérateur de convolu

Exploring stabilisation techniques for the reduced basis approximation of avection-diffusion PDEs

Christèle Marie Zbinden

In this thesis, we explore possible stabilisation methods for the reduce basis approximation of advection-diffusion problems, for which the advection term is dominating. The options we consider are mainly inspired by the Variational Multiscale method (VMS), which decomposes the solution of a variational problem into its coarse scale component, from a coarse scale space, and a fine scale component, from a fine scale space. Our stabilisation proposals are divided into three classes. The first one groups methods that rely on a stabilisation parameter. The second class uses VMS at the algebraic level to attempt stabilisation. Finally the third class is also inspired by VMS at the algebraic level, but with the additional constraint that the fine scale space is orthogonal to the coarse scale space. Numericals tests reported in this thesis show that the methods of the first class is not viable options as the best stabilisation parameter among those tested is the stabilisation parameter that is used at the high fidelity level. Although the stabilisation methods of the second class give accurate results when applied to stable problems, they were also dismissed by the numerical tests, as they did not improve the accuracy of the already stabilised problem. The third class also performs well when applied to stable problems. It has been shown in [7] one of those methods can improve accuracy. However in the current implementation, this result was not achieved here.

2016

Unsupervised multiscale image segmentation

Ana Dimitrijevic

In the early stages of visual information processing one of the most fundamental and complex task is segmentation. This process is used to divide images or image sequences into meaningful regions or objects. Such a representation is definitely needed to go from the first rough description of the scene (i.e. light intensity) up to the semantic level, where one is able to discriminate shapes and other high-level visual primitives. The biological visual system performs this extremely difficult task with such ease that is still a major challenge for computer vision to reach this level of speed and accuracy. It is by now widely believed that a method inspired by biological vision has the best chances of accomplishing this goal. Therefore, our main goal in this thesis is to step on biologically inspired schemes to propose new and efficient techniques to solve the image segmentation problem. The starting point and key concept in this research, is the multiresolution paradigm. Indeed, the fact that the Human Visual System (HVS) processes the information in a multiresolution fashion is now well established. Several techniques have been introduced to model this behaviour. Scale-space is one of them and we will thus focus on such a formulation of the segmentation problem. Such a representation is composed by a stack of successive versions of the original data set at coarser scales. It is assumed that, the bigger the scale, the less information referred to local characteristics of the input data will appear. We also impose that general information applying to large scales will last through scale. Taking that into account, it is reasonable to think that local and high resolution scale information can be related to general and low resolution information. This will enable us to extract image structures. We thus propose to link the multiresolution approach to a computational model based on the analysis of the entire range of significant information across scales. The inherent multiscale image structure of the non-linear scale-space guides a coarse to fine segmentation using different strategies. The first one might be termed extrinsic because the non-linear scale-space is analyzed by an external process of linking information through scales. This leads to a completely adaptive scheme that can then be coupled to a labeling procedure in order to define a genuine segmentation. The second one could be labeled intrinsic because it adapts to the image through its inner properties and incorporate this in the labeling step of the main algorithm. These two approaches are particular examples of multiscale image segmentation. We also apply the same scale-space concept to define a segmentation variational formulation that leads to a region merging segmentation. In order to illustrate the proposed segmentation schemes, we apply our algorithms to gray-scale, noisy, color and texture images. Finally, it should be mentioned that the main problem addressed in this thesis, general image segmentation, plays an important role in the image understanding process, especially those that involve natural scenes rich in color and texture. The potential applications of the algorithms are thus numerous: medical image analysis, interactive multimedia developments, object based coding and compression, surveillance applications, image content based browsing and retrieval, etc.

EPFL2006

Matching pursuit-based shape description and recognition in active contours

François Mendels

This thesis is dedicated to the study of a new framework linking image segmentation and shape recognition processes in the image processing domain. Image segmentation process aims at separating an image into homogenous regions, the homogeneity measure depending on the feature chosen, such as color, texture. The goal of a shape recognition process is to identifying object(s) present in an image whose shape is similar to a chosen model, with respect to e.g. given rigid transformations that do not modify the intrinsic nature of the shape. As these kinds of process are nowadays integrated in industrial applications for automation purposes (e.g. detecting a defect on manufactured tools), it is necessary to have flexible, and evolving processes that remain robust in adverse conditions. These two processes are usually realized separately, thus one does not benefit from both approach advantages, and thus, can not automatically correct each other errors. In this work, we wish to add a priori information, such as a given shape of an object, into a segmentation framework, here the active contour framework. Using this framework, we focus on segmenting multiple objects belonging to the same shape space. Up to now, the models including a shape prior in the active contour models, by modifying their energy functional, are unable to solve this problem directly. We choose here to integrate the shape prior in two different ways: we modify the external field, in which the active contour propagates, or we use the a priori information as new initial conditions. In order to obtain a shape prior having both local and global conditions, we introduce a new shape descriptor relying on an analytical low-level representation of images, based on a generic framework using sparse representation algorithms. This continuous shape description is obtained by a decomposition process, here the Matching Pursuit (MP) algorithm using an affine invariant dictionary of basis functions. This description is then used in the shape recognition process. In the learning phase, a template object is decomposed, and the extracted subset of basis functions, called meta-atom, gives the description of our object. We then extend naturally this description into the linear scale-space using the definition of our basis functions, and thus bringing a more general representation of our object. We use this enhanced description as a predefined dictionary of the object to conduct an MP-based shape recognition (MPSR) task into the linear scale-space: we extract iteratively each object belonging to the given shape space. We introduce two different methods to realize this MPSR process in the linear scale-space: a coarse-to-fine approach where the solutions found at higher scales are propagated to lower scales, and a stack scale-space approach where the extraction is realized at all scales at once. The introduction of the scale-space approaches improves the robustness of our method, and permits to avoid local minima problems encountered when minimizing a non-convex energy function. The shape prior is build as the sum of the solutions resulting from the MPSR process. We propose three different ways to introduce the a priori information in the active contour, reflecting three different segmentation goals. At first, we consider the shape prior as the new external field, thus this enables us to deal with occlusion problems. The second proposal combines the influence from the prior information and the original external field, and lead to let the active contour converge towards real boundaries close to the shape prior. The third proposal sums the variable actions of the shape prior and the external field: in this case, the shape prior is strong at the beginning of the process, and it is relaxed during the process to let the active contour converge to the existing boundaries present in the target image. This enables us to extract objects having large deformations when compared to the shape model. We then show results for the detection and segmentation of complex synthetic shapes, as well as natural (aerial and medical) images, for all these approaches, in coherence with the expected segmentation goals. The global approaches remain resistant to noise presence.

EPFL2004