Efficient and Robust Segmentations Based on Eikonal and Diffusion PDEs

In this paper, we present efficient and simple image segmentations based on the solution of two separate Eikonal equations, each originating from a different region. Distance functions from the interior and exterior regions are computed, and final segmentation labels are determined by a competition criterion between the distance functions. We also consider applying a diffusion partial differential equation (PDE) based method to propagate information in a manner inspired by the information propagation feature of the Eikonal equation. Experimental results are presented in a particular medical image segmentation application, and demonstrate the proposed methods

Efficient segmentation based on Eikonal and diffusion equations

Segmentation of regions of interest in an image has important applications in medical image analysis, particularly in computer aided diagnosis. Segmentation can enable further quantitative analysis of anatomical structures. We present efficient image segmentation schemes based on the solution of distinct partial differential equations (PDEs). For each known image region, a PDE is solved, the solution of which locally represents the weighted distance from a region known to have a certain segmentation label. To achieve this goal, we propose the use of two separate PDEs, the Eikonal equation and a diffusion equation. In each method, the segmentation labels are obtained by a competition criterion between the solutions to the PDEs corresponding to each region. We discuss how each method applies the concept of information propagation from the labelled image regions to the unknown image regions. Experimental results are presented on magnetic resonance, computed tomography, and ultrasound images and for both two-region and multi-region segmentation problems. These results demonstrate the high level of efficiency as well as the accuracy of the proposed methods

An Efficient Image Segmentation Approach through Enhanced Watershed Algorithm

Image segmentation is a significant task for image analysis which is at the middle layer of image engineering. The purpose of segmentation is to decompose the image into parts that are meaningful with respect to a particular application. The proposed system is to boost the morphological watershed method for degraded images. Proposed algorithm is based on merging morphological watershed result with enhanced edge detection result obtain on pre processing of degraded images. As a post processing step, to each of the segmented regions obtained, color histogram algorithm is applied, enhancing the overall performance of the watershed algorithm. Keywords – Segmentation, watershed, color histogra

Morphological PDE and dilation/erosion semigroups on length spaces

International audienceThis paper gives a survey of recent research on Hamilton-Jacobi partial dierential equations (PDE) on length spaces. This theory provides the background to formulate morphological PDEs for processing data and images supported on a length space, without the need of a Riemmanian structure. We first introduce the most general pair of dilation/erosion semigroups on a length space, whose basic ingredients are the metric distance and a convex shape function. The second objective is to show under which conditions the solution of a morphological PDE in the length space framework is equal to the dilation/erosion semigroups

A comparative study of image segmentation by application of normalized cut on graphs

Orientador: Marco Antonio Garcia de CarvalhoDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de TecnologiaResumo: O particionamento de grafos tem sido amplamente utilizado como meio de segmentação de imagens. Uma das formas de particionar grafos é por meio de uma técnica conhecida como Corte Normalizado, que analisa os autovetores da matriz laplaciana de um grafo e utiliza alguns deles para o corte. Essa dissertação propõe o uso de Corte Normalizado em grafos originados das modelagens por Quadtree e Árvore dos Componentes a fim de realizar segmentação de imagens. Experimentos de segmentação de imagens por Corte Normalizado nestas modelagens são realizados e um benchmark específico compara e classifica os resultados obtidos por outras técnicas propostas na literatura específica. Os resultados obtidos são promissores e nos permitem concluir que o uso de outras modelagens de imagens por grafos no Corte Normalizado pode gerar melhores segmentações. Uma das modelagens pode inclusive trazer outro benefício que é gerar um grafo representativo da imagem com um número menor de nós do que representações mais tradicionaisAbstract: The graph partitioning has been widely used as a mean of image segmentation. One way to partition graphs is through a technique known as Normalized Cut, which analyzes the graph's Laplacian matrix eigenvectors and uses some of them for the cut. This work proposes the use of Normalized Cut in graphs generated by structures based on Quadtree and Component Tree to perform image segmentation. Experiments of image segmentation by Normalized Cut in these models are made and a specific benchmark compares and ranks the results obtained by other techniques proposed in the literature. The results are promising and allow us to conclude that the use of other image graph models in the Normalized Cut can generate better segmentations. One of the structures can also bring another benefit that is generating an image representative graph with fewer graph nodes than the traditional representationsMestradoTecnologia e InovaçãoMestre em Tecnologi

Watersheds on edge or node weighted graphs

The literature on the watershed is separated in two families: the watersheds on node weighted graphs and the watersheds on edge weighted graphs. The simplest node weighted graphs are images, where the nodes are the pixels ; neighboring pixels being linked by unweighted pixels. The edge weights on an edge weighted graph express dissimilarities between the unweighted nodes. Distinct definitions of minima and catchment basins have been given for both types of graphs from which different algorithms have been derived. This paper aims at showing that watersheds on edge or node weighted graphs are strictly equivalent. Moreover, all algorithms developed for edge weighted graphs may be applied on node weighted graphs and vice versa. From any node or edge weighted graph it is possible to derive a flooding graph with node and edge weights. Its regional minima and catchment basins are identical whether one considers the node weights alone or the edge weights alone. A lexicographic order relation permits to compare non ascending paths with the same origin according to their steepness. Overlapping zones between neighboring catchment basins are reduced or even suppressed by pruning edges in the flooding graph through which does not pass a steepest path and reduces, without arbitrary choices the overlapping zones between adjacent catchment basins. We propose several ways to break the remaining ties, the simplest being to assign slightly distinct weights to regional minima with the same weight. Like that each node is linked with only one regional minimum by a path of maximal steepness