Anisotropic Diffusion Partial Differential Equations in Multi-Channel Image Processing : Framework and Applications

We review recent methods based on diffusion PDE's (Partial Differential Equations) for the purpose of multi-channel image regularization. Such methods have the ability to smooth multi-channel images anisotropically and can preserve then image contours while removing noise or other undesired local artifacts. We point out the pros and cons of the existing equations, providing at each time a local geometric interpretation of the corresponding processes. We focus then on an alternate and generic tensor-driven formulation, able to regularize images while specifically taking the curvatures of local image structures into account. This particular diffusion PDE variant is actually well suited for the preservation of thin structures and gives regularization results where important image features can be particularly well preserved compared to its competitors. A direct link between this curvature-preserving equation and a continuous formulation of the Line Integral Convolution technique (Cabral and Leedom, 1993) is demonstrated. It allows the design of a very fast and stable numerical scheme which implements the multi-valued regularization method by successive integrations of the pixel values along curved integral lines. Besides, the proposed implementation, based on a fourth-order Runge Kutta numerical integration, can be applied with a subpixel accuracy and preserves then thin image structures much better than classical finite-differences discretizations, usually chosen to implement PDE-based diffusions. We finally illustrate the efficiency of this diffusion PDE's for multi-channel image regularization - in terms of speed and visual quality - with various applications and results on color images, including image denoising, inpainting and edge-preserving interpolation

Robust local approximation of scattered data

In this paper, we modify the robust local image estimation method of R. van den Boomgaard and J. van de Weijer for the approximation of scattered data. The derivation of our knot and data dependent approximation method is based on the relation between the Gaussian facet model in image processing and the moving least square technique known from approximation theory. Numerical examples demonstrate the advantages of our robust scattered data approximation

Morphological bilateral filtering

International audienceA current challenging topic in mathematical morphology is the construction of locally adaptive operators; i.e., structuring functions that are dependent on the input image itself at each position. Development of spatially-variant filtering is well established in the theory and practice of Gaussian filtering. The aim of the first part of the paper is to study how to generalize these convolution-based approaches in order to introduce adaptive nonlinear filters that asymptotically correspond to spatially-variant morphological dilation and erosion. In particular, starting from the bilateral filtering framework and using the notion of counter-harmonic mean, our goal is to propose a new low complexity approach to define spatially-variant bilateral structuring functions. Then, in the second part of the paper, an original formulation of spatially-variant flat morphological filters is proposed, where the adaptive structuring elements are obtained by thresholding the bilateral structuring functions. The methodological results of the paper are illustrated with various comparative examples

Bilateral filter in image processing

The bilateral filter is a nonlinear filter that does spatial averaging without smoothing edges. It has shown to be an effective image denoising technique. It also can be applied to the blocking artifacts reduction. An important issue with the application of the bilateral filter is the selection of the filter parameters, which affect the results significantly. Another research interest of bilateral filter is acceleration of the computation speed. There are three main contributions of this thesis. The first contribution is an empirical study of the optimal bilateral filter parameter selection in image denoising. I propose an extension of the bilateral filter: multi resolution bilateral filter, where bilateral filtering is applied to the low-frequency sub-bands of a signal decomposed using a wavelet filter bank. The multi resolution bilateral filter is combined with wavelet thresholding to form a new image denoising framework, which turns out to be very effective in eliminating noise in real noisy images. The second contribution is that I present a spatially adaptive method to reduce compression artifacts. To avoid over-smoothing texture regions and to effectively eliminate blocking and ringing artifacts, in this paper, texture regions and block boundary discontinuities are first detected; these are then used to control/adapt the spatial and intensity parameters of the bilateral filter. The test results prove that the adaptive method can improve the quality of restored images significantly better than the standard bilateral filter. The third contribution is the improvement of the fast bilateral filter, in which I use a combination of multi windows to approximate the Gaussian filter more precisely

Scale-invariance in local heat kernel descriptors without scale selection and normalization

Today, only a small fraction of Internet repositories of geometric data is accessible through text search. Fast growth of these repositories makes content-based retrieval one of the next grand challenges in search and organization of such information. Particularly difficult is the problem of \emph{shape retrieval}, as geometric shapes manifest a vast variability due to different scale, orientation, non-rigid deformations, missing data, and also appear in a variety of different formats and representations. One of the biggest challenges in non-rigid shape retrieval and comparison is the design of a shape descriptor that would maintain invariance under a wide class of transformations the shape can undergo. Recently, heat kernel signature was introduced as an intrinsic local shape descriptor based on diffusion scale-space analysis. In this paper, we develop a scale-invariant version of the heat kernel descriptor. Our construction is based on a logarithmically sampled scale-space in which shape scaling corresponds, up to a multiplicative constant, to a translation. This translation is undone using the magnitude of the Fourier transform. The proposed scale-invariant local descriptors can be used in the bag-of-features framework for shape retrieval in the presence of transformations such as isometric deformations, missing data, topological noise, and global and local scaling. We get significant performance improvement over state-of-the-art algorithms on recently established non-rigid shape retrieval benchmarks

Modélisation statistique du Speckle en OCT : application à la segmentation d'images de la peau

Cette thèse porte sur la segmentation d'images OCT cutanées. Cette modalité d'imagerie permet de visualiser les structures superficielles avec une profondeur de l'ordre du millimètre. En dermatologie, elle permet d'explorer l'épiderme et sa jonction avec le derme. Cependant, les images OCT sont sévèrement affectées par le bruit speckle. Ce phénomène conjugué à la complexité inhérente aux structures de la peau rend l'interprétation des images difficile même pour des experts. L'approche classique consiste à filtrer le speckle avant de faire des traitements de segmentation. A l'inverse, dans cette thèse nous exploitons exclusivement le bruit comme information pour segmenter. Notre approche repose sur la modélisation statistique du speckle. La segmentation se fait par classification des paramètres de ce modèle probabiliste. Ainsi, - On montre que le speckle ne suit pas une loi Rayleigh, comme cela est établi analytiquement. - On ajuste plusieurs lois de probabilité à l'amplitude OCT; et on montre que celle-ci est distribuée selon la loi Gamma généralisée. - On établit que les paramètres de cette loi discriminent statistiquement les couches de la peau. - On conçoit une méthode de segmentation par classification des paramètres locaux du speckle. Les nombreuses expérimentations faites sur plusieurs corpus d'images in-vivo confirment la validité de notre approche. ABSTRACT : This thesis deals with the segmentation of skin OCT images. This modality provides the means to visualize superficial structures down to a millimeter depth. In dermatology, it is used to examine the epidermis and its junction with the dermis. However, OCT images are severely affected by the speckle noise. This random phenomenon added to the complexity of human skin structures makes the visual interpretation of images very difficult. Classical image processing techniques filter this noise prior to any segmentation step. In this thesis, we rely exclusively on the properties of the speckle to perform segmentation. Our approach is based on the statistical modeling of the speckle. Images are segmented by classifying parameters of the statistical model. Therefore, - We show that speckle does not follow the Rayleigh distribution, as developed analytically in the literature. - We fit various probability laws to model OCT signal amplitude ; we show that Generalized Gamma has the best goodness of fit. - We establish that statistical parameters of this distribution discriminate skin layers with good variability. - We develop a segmentation method based on the classification of local statistical parameters. The various experimental results with a number of in-vivo images reported in the thesis confirm the validity of our approac