Amoeba Techniques for Shape and Texture Analysis

Morphological amoebas are image-adaptive structuring elements for morphological and other local image filters introduced by Lerallut et al. Their construction is based on combining spatial distance with contrast information into an image-dependent metric. Amoeba filters show interesting parallels to image filtering methods based on partial differential equations (PDEs), which can be confirmed by asymptotic equivalence results. In computing amoebas, graph structures are generated that hold information about local image texture. This paper reviews and summarises the work of the author and his coauthors on morphological amoebas, particularly their relations to PDE filters and texture analysis. It presents some extensions and points out directions for future investigation on the subject.Comment: 38 pages, 19 figures v2: minor corrections and rephrasing, Section 5 (pre-smoothing) extende

Representations for Morphological Image Operators and Analogies with Linear Operators

1.1 Why a representation theory?...............................

Automatic Detection of Optic Disc Based on PCA and Mathematical Morphology

The algorithm proposed in this paper allows to automatically segment the optic disc from a fundus image. The goal is to facilitate the early detection of certain pathologies and to fully automate the process so as to avoid specialist intervention. The method proposed for the extraction of the optic disc contour is mainly based on mathematical morphology along with principal component analysis (PCA). It makes use of different operations such as generalized distance function (GDF), a variant of the watershed transformation, the stochastic watershed, and geodesic transformations. The input of the segmentation method is obtained through PCA. The purpose of using PCA is to achieve the grey-scale image that better represents the original RGB image. The implemented algorithm has been validated on five public databases obtaining promising results. The average values obtained (a Jaccard s and Dice s coefficients of 0.8200 and 0.8932, respectively, an accuracy of 0.9947, and a true positive and false positive fractions of 0.9275 and 0.0036) demonstrate that this method is a robust tool for the automatic segmentation of the optic disc. Moreover, it is fairly reliable since it works properly on databases with a large degree of variability and improves the results of other state-of-the-art methods.This work was supported in part by the project IMIDTA/2010/47 and in part by projects Consolider-C (SEJ2006-14301/PSIC), "CIBER of Physiopathology of Obesity and Nutrition, an initiative of ISCIII" and Excellence Research Program PROMETEO (Generalitat Valenciana. Conselleria de Educacion, 2008-157).Morales Martínez, S.; Naranjo Ornedo, V.; Angulo Lopez, J.; Alcañiz Raya, ML. (2013). Automatic Detection of Optic Disc Based on PCA and Mathematical Morphology. IEEE Transactions on Medical Imaging. 32(4):786-796. https://doi.org/10.1109/TMI.2013.2238244S78679632

Cell Detection by Functional Inverse Diffusion and Non-negative Group Sparsity−-Part II: Proximal Optimization and Performance Evaluation

In this two-part paper, we present a novel framework and methodology to analyze data from certain image-based biochemical assays, e.g., ELISPOT and Fluorospot assays. In this second part, we focus on our algorithmic contributions. We provide an algorithm for functional inverse diffusion that solves the variational problem we posed in Part I. As part of the derivation of this algorithm, we present the proximal operator for the non-negative group-sparsity regularizer, which is a novel result that is of interest in itself, also in comparison to previous results on the proximal operator of a sum of functions. We then present a discretized approximated implementation of our algorithm and evaluate it both in terms of operational cell-detection metrics and in terms of distributional optimal-transport metrics.Comment: published, 16 page

Information Extraction and Modeling from Remote Sensing Images: Application to the Enhancement of Digital Elevation Models

To deal with high complexity data such as remote sensing images presenting metric resolution over large areas, an innovative, fast and robust image processing system is presented. The modeling of increasing level of information is used to extract, represent and link image features to semantic content. The potential of the proposed techniques is demonstrated with an application to enhance and regularize digital elevation models based on information collected from RS images

Spectral and spatial methods for the classification of urban remote sensing data

Lors de ces travaux, nous nous sommes intéressés au problème de la classification supervisée d'images satellitaires de zones urbaines. Les données traitées sont des images optiques à très hautes résolutions spatiales: données panchromatiques à très haute résolution spatiale (IKONOS, QUICKBIRD, simulations PLEIADES) et des images hyperspectrales (DAIS, ROSIS). Deux stratégies ont été proposées. La première stratégie consiste en une phase d'extraction de caractéristiques spatiales et spectrales suivie d'une phase de classification. Ces caractéristiques sont extraites par filtrages morphologiques : ouvertures et fermetures géodésiques et filtrages surfaciques auto-complémentaires. La classification est réalisée avec les machines à vecteurs supports (SVM) non linéaires. Nous proposons la définition d'un noyau spatio-spectral utilisant de manière conjointe l'information spatiale et l'information spectrale extraites lors de la première phase. La seconde stratégie consiste en une phase de fusion de données pre- ou post-classification. Lors de la fusion postclassification, divers classifieurs sont appliqués, éventuellement sur plusieurs données issues d'une même scène (image panchromat ique, image multi-spectrale). Pour chaque pixel, l'appartenance à chaque classe est estimée à l'aide des classifieurs. Un schéma de fusion adaptatif permettant d'utiliser l'information sur la fiabilité locale de chaque classifieur, mais aussi l'information globale disponible a priori sur les performances de chaque algorithme pour les différentes classes, est proposé. Les différents résultats sont fusionnés à l'aide d'opérateurs flous. Les méthodes ont été validées sur des images réelles. Des améliorations significatives sont obtenues par rapport aux méthodes publiées dans la litterature

Large Deformation Diffeomorphic Metric Mapping Provides New Insights into the Link Between Human Ear Morphology and the Head-Related Transfer Functions

The research findings presented in this thesis is composed of four sections. In the first section of this thesis, it is shown how LDDMM can be applied to deforming head and ear shapes in the context of morphoacoustic study. Further, tools are developed to measure differences in 3D shapes using the framework of currents and also to compare and measure the differences between the acoustic responses obtained from BEM simulations for two ear shapes. Finally this section introduces the multi-scale approach for mapping ear shapes using LDDMM. The second section of the thesis estimates a template ear, head and torso shape from the shapes available in the SYMARE database. This part of the thesis explains a new procedure for developing the template ear shape. The template ear and head shapes were are verified by comparing the features in the template shapes to corresponding features in the CIPIC and SYMARE database population. The third section of the thesis examines the quality of the deformations from the template ear shape to target ears in SYMARE from both an acoustic and morphological standpoint. As a result of this investigation, it was identified that ear shapes can be studied more accurately by the use of two physical scales and that scales at which the ear shapes were studied were dependent on the parameters chosen when mapping ears in the LDDMM framework. Finally, this section concludes by noting how shape distances vary with the acoustic distances using the developed tools. In the final part of this thesis, the variations in the morphology of ears are examined using the Kernel Principle Component Analysis (KPCA) and the changes in the corresponding acoustics are studied using the standard principle component analysis (PCA). These examinations involved identifying the number of kernel principle components that are required in order to model ear shapes with an acceptable level of accuracy, both morphologically and acoustically