A geometric dissimilarity criterion between Jordan spatial mosaics. Theoretical aspects and application to segmentation evaluation

International audienceAn image segmentation process often results in a special spatial set, called a mosaic, as the subdivision of a domain S within the n-dimensional Euclidean space. In this paper, S will be a compact domain and the study will be focused on finite Jordan mosaics, that is to say mosaics with a finite number of regions and where the boundary of each region is a Jordan hypersurface. The first part of this paper addresses the problem of comparing a Jordan mosaic to a given reference Jordan mosaic and introduces the (Epsilon) dissimilarity criterion. The second part will show that the (Epsilon) dissimilarity criterion can be used to perform the evaluation of image segmentation processes. It will be compared to classical criterions in regard to several geometric transformations. The pros and cons of these criterions are presented and discussed, showing that the dissimilarity criterion outperforms the other ones

General Adaptive Neighborhood Image Processing for Biomedical Applications

In biomedical imaging, the image processing techniques using spatially invariant transformations, with fixed operational windows, give efficient and compact computing structures, with the conventional separation between data and operations. Nevertheless, these operators have several strong drawbacks, such as removing significant details, changing some meaningful parts of large objects, and creating artificial patterns. This kind of approaches is generally not sufficiently relevant for helping the biomedical professionals to perform accurate diagnosis and therapy by using image processing techniques. Alternative approaches addressing context-dependent processing have been proposed with the introduction of spatially-adaptive operators (Bouannaya and Schonfeld, 2008; Ciuc et al., 2000; Gordon and Rangayyan, 1984;Maragos and Vachier, 2009; Roerdink, 2009; Salembier, 1992), where the adaptive concept results from the spatial adjustment of the sliding operational window. A spatially-adaptive image processing approach implies that operators will no longer be spatially invariant, but must vary over the whole image with adaptive windows, taking locally into account the image context by involving the geometrical, morphological or radiometric aspects. Nevertheless, most of the adaptive approaches require a priori or extrinsic informations on the image for efficient processing and analysis. An original approach, called General Adaptive Neighborhood Image Processing (GANIP), has been introduced and applied in the past few years by Debayle & Pinoli (2006a;b); Pinoli and Debayle (2007). This approach allows the building of multiscale and spatially adaptive image processing transforms using context-dependent intrinsic operational windows. With the help of a specified analyzing criterion (such as luminance, contrast, ...) and of the General Linear Image Processing (GLIP) (Oppenheim, 1967; Pinoli, 1997a), such transforms perform a more significant spatial and radiometric analysis. Indeed, they take intrinsically into account the local radiometric, morphological or geometrical characteristics of an image, and are consistent with the physical (transmitted or reflected light or electromagnetic radiation) and/or physiological (human visual perception) settings underlying the image formation processes. The proposed GAN-based transforms are very useful and outperforms several classical or modern techniques (Gonzalez and Woods, 2008) - such as linear spatial transforms, frequency noise filtering, anisotropic diffusion, thresholding, region-based transforms - used for image filtering and segmentation (Debayle and Pinoli, 2006b; 2009a; Pinoli and Debayle, 2007). This book chapter aims to first expose the fundamentals of the GANIP approach (Section 2) by introducing the GLIP frameworks, the General Adaptive Neighborhood (GAN) sets and two kinds of GAN-based image transforms: the GAN morphological filters and the GAN Choquet filters. Thereafter in Section 3, several GANIP processes are illustrated in the fields of image restoration, image enhancement and image segmentation on practical biomedical application examples. Finally, Section 4 gives some conclusions and prospects of the proposed GANIP approach

On the linear combination of the Gaussian and student's <i>t</i> random field and the integral geometry of its excursion sets

International audienceIn this paper, a random field, denoted by GTβν, is defined from the linear combination of two independent random fields, one is a Gaussian random field and the second is a student's t random field with v degrees of freedom scaled by β. The goal is to give the analytical expressions of the expected Euler-Poincaré characteristic of the GTβν excursion sets on a compact subset S of R2. The motivation comes from the need to model the topography of 3D rough surfaces represented by a 3D map of correlated and randomly distributed heights with respect to a GTβν random field. The analytical and empirical Euler-Poincaré characteristics are compared in order to test the GTβν model on the real surface

General Adaptive Neighborhood Image Processing. Part I: Introduction and Theoretical Aspects

30 pagesInternational audienceThe so-called General Adaptive Neighborhood Image Processing (GANIP) approach is presented in a two parts paper dealing respectively with its theoretical and practical aspects. The Adaptive Neighborhood (AN) paradigm allows the building of new image processing transformations using context-dependent analysis. Such operators are no longer spatially invariant, but vary over the whole image with ANs as adaptive operational windows, taking intrinsically into account the local image features. This AN concept is here largely extended, using well-defined mathematical concepts, to that General Adaptive Neighborhood (GAN) in two main ways. Firstly, an analyzing criterion is added within the definition of the ANs in order to consider the radiometric, morphological or geometrical characteristics of the image, allowing a more significant spatial analysis to be addressed. Secondly, general linear image processing frameworks are introduced in the GAN approach, using concepts of abstract linear algebra, so as to develop operators that are consistent with the physical and/or physiological settings of the image to be processed. In this paper, the GANIP approach is more particularly studied in the context of Mathematical Morphology (MM). The structuring elements, required for MM, are substituted by GAN-based structuring elements, fitting to the local contextual details of the studied image. The resulting transforms perform a relevant spatially-adaptive image processing, in an intrinsic manner, that is to say without a priori knowledge needed about the image structures. Moreover, in several important and practical cases, the adaptive morphological operators are connected, which is an overwhelming advantage compared to the usual ones that fail to this property

General Adaptive Neighborhood Image Processing. Part II: Practical Applications Issues

23 pagesInternational audienceThe so-called General Adaptive Neighborhood Image Processing (GANIP) approach is presented in a two parts paper dealing respectively with its theoretical and practical aspects. The General Adaptive Neighborhood (GAN) paradigm, theoretically introduced in Part I [20], allows the building of new image processing transformations using context-dependent analysis. With the help of a specified analyzing criterion, such transformations perform a more significant spatial analysis, taking intrinsically into account the local radiometric, morphological or geometrical characteristics of the image. Moreover they are consistent with the physical and/or physiological settings of the image to be processed, using general linear image processing frameworks. In this paper, the GANIP approach is more particularly studied in the context of Mathematical Morphology (MM). The structuring elements, required for MM, are substituted by GAN-based structuring elements, fitting to the local contextual details of the studied image. The resulting morphological operators perform a really spatiallyadaptive image processing and notably, in several important and practical cases, are connected, which is a great advantage compared to the usual ones that fail to this property. Several GANIP-based results are here exposed and discussed in image filtering, image segmentation, and image enhancement. In order to evaluate the proposed approach, a comparative study is as far as possible proposed between the adaptive and usual morphological operators. Moreover, the interests to work with the Logarithmic Image Processing framework and with the 'contrast' criterion are shown through practical application examples

Caractérisation géométrique et vélocimétrique d'empilements granulaires par analyse d'image

National audienceSee http://hal.archives-ouvertes.fr/docs/00/59/27/21/ANNEX/r_9NW7X92J.pd

Lipschitz-Killing curvatures of the Excursion Sets of Skew Student's t Random fields

Best Student PaperInternational audienceIn many real applications related with Geostatistics, medical imaging and material science, the real observations have asymmetric, and heavy-tailed multivariate distributions. These observations are spatially correlated and they could be modelled by the skew random fields. However, certain statistical analysis problems require giving analytical expectations of some integral geometric characteristics of these random fields, such as Lipschitz-Killing curvatures, specifically Euler-Poincaré characteristic. This paper considers a class of skew random fields, namely skew student's t random fields. The goal is to give the analytical expressions of the Lipschitz-Killing curvatures of the skew student's t excursion sets on a compact subset S of R2. The motivation comes from the need to model the roughness of some engineering surfaces, involved in the total hip replacement application, which is characterized by the Euler-Poincaré characteristic function. The analytical and estimated Euler-Poincaré characteristics are fitted in order to test the skew student's t random field with the surface roughness topography

Shape representation and analysis of 2D compact sets by shape diagrams

Shape diagrams are shape representations in the Euclidean plane introduced for studying 3D and 2D compact sets. A compact set is represented by a point within a shape diagram whose coordinates are morphological functionals defined from geometrical functionals and inequalities. Classically, the geometrical functionals for 2D sets are the area, the perimeter, the radii of the inscribed and circumscribed circles, and the minimum and maximum Feret diameters. The purpose of this paper is to present a particular shape diagram for which mathematical properties have been well-defined and to analyse the shape of several families of 2D sets for the discrimination of convex and non convex sets as well as the discrimination of similar sets

Quantitative evaluation of image registration techniques in the case of retinal images

International audienceIn human retina observation (with non mydriatic optical microscopes), an image registration process is often employed to enlarge the field of view. Analyzing all the images takes a lot of time. Numerous techniques have been proposed to perform the registration process. Its good evaluation is a difficult question that is then raising. This article presents the use of two quantitative criterions to evaluate and compare some classical feature-based image registration techniques. The images are first segmented and the resulting binary images are then registered. The good quality of the registration process is evaluated with a normalized criterion based on the ϵ dissimilarity criterion, and the figure of merit criterion (fom), for 25 pairs of images with a manual selection of control points. These criterions are normalized by the results of the affine method (considered as the most simple method). Then, for each pair, the influence of the number of points used to perform the registration is evaluated