Discrete euclidean skeletons in increased resolution

Orientadores: Roberto de Alencar Lotufo, Michel CouprieTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de ComputaçãoResumo: A extração de esqueletos Euclidianos é uma tema de grande importância na área de processamento de imagens e tem sido discutido pela comunidade científica já há mais de 20 anos. Hoje é consenso que os esqueletos Euclidianos devem ter as seguintes características: ï¬?nos, centrados, homotópicos e reversíveis, i.e., suficientes para a reconstrução do objeto original. Neste trabalho, introduzimos o Eixo Mediano Euclidiano Exato em Resolução Aumentada -HMA, com o objetivo de obter um eixo mediano mais ï¬?no do que o obtido pela definição clássica. Combinando o HMA com um eï¬?ciente algoritmo de afinamento paralelo homotópico, propomos um esqueleto Euclidiano que é centrado, homotópico, reversível e mais ï¬?no que os já existentes na literatura. O esqueleto proposto tem a particularidade adicional de ser único e independente de decisões arbitrárias. São dados algoritmos e provas, assim como exemplos de aplicações dos esqueletos propostos em imagens reais, mostrando as vantagens da proposta. O texto inclui também uma revisão bibliográfica sobre algoritmos de transformada de distância, eixo mediano e esqueletos homotópicosAbstract: The extraction of Euclidean skeletons is a subject of great importance in the domain of image processing and it has been discussed by the scientiï¬?c community since more than 20 years.Today it is a consensus that Euclidean skeletons should present the following characteristics: thin, centered, homotopic and reversible, i.e., sufï¬?cient for the reconstruction of the original object. In this work, we introduce the Exact Euclidean Medial Axis in Higher Resolution -HMA, with the objective of obtaining a medial axis which is thinner than the one obtained by the classical medial axis deï¬?nition. By combining the HMA with an efï¬?cient parallel homotopic thinning algorithm we propose an Euclidean skeleton which is centered, homotopic, reversible and thinner than the existing similars in the literature. The proposed skeleton has the additional particularity of being unique and independent of arbitrary choices. Algorithms and proofs are given, as well as applicative examples of the proposed skeletons in real images, showing the advantages of the proposal. The text also includes an overview on algorithms for the Euclidean distance transform algorithms, the medial axis extraction, as well as homotopic skeletonsDoutoradoEngenharia de ComputaçãoDoutor em Engenharia Elétric

Discrete bisector function and Euclidean skeleton in 2D and 3D

International audienceWe propose a new definition and an exact algorithm for the discrete bisector function, which is an important tool for analyzing and filtering Euclidean skeletons. We also introduce a new thinning algorithm which produces homotopic discrete Euclidean skeletons. These algorithms, which are valid both in 2D and 3D, are integrated in a skeletonization method which is based on exact transformations, allows the filtering of skeletons, and is computationally efficient

Optimal Separable Algorithms to Compute the Reverse Euclidean Distance Transformation and Discrete Medial Axis in Arbitrary Dimension

In binary images, the distance transformation (DT) and the geometrical skeleton extraction are classic tools for shape analysis. In this paper, we present time optimal algorithms to solve the reverse Euclidean distance transformation and the reversible medial axis extraction problems for $d$-dimensional images. We also present a $d$-dimensional medial axis filtering process that allows us to control the quality of the reconstructed shape

Farey Sequences and the Planar Euclidean Medial Axis Test Mask

Abstract. The Euclidean test mask T (r) is the minimum neighbourhood sufficient to detect the Euclidean Medial Axis of any discrete shape whose inner radius does not exceed r. We establish a link between T (r) and the well-known Farey sequences, which allows us to propose two new algorithms. The first one computes T (r) in time O(r 4 ) and space O(r 2 ). The second one computes for any vector − → v the smallest r for which − → v ∈ T (r), in time O(r 3 ) and constant space

Décomposition volumique d'images pour l'étude de la microstructure de la neige

Les avalanches de neige sont des phénomènes naturels complexes dont l'occurrence s'explique principalement par la structure et les propriétés du manteau neigeux. Afin de mieux comprendre les évolutions de ces propriétés au cours du temps, il est important de pouvoir caractériser la microstructure de la neige, notamment en termes de grains et de ponts de glace les reliant. Dans ce contexte, l'objectif de cette thèse est la décomposition d'échantillons de neige en grains individuels à partir d'images 3-D de neige obtenues par microtomographie X. Nous présentons ici deux méthodes de décomposition utilisant des algorithmes de géométrie discrète. Sur la base des résultats de ces segmentations, certains paramètres, comme la surface spécifique et la surface spécifique de contact entre grains sont ensuite estimés sur des échantillons de neiges variées. Ces méthodes de segmentation ouvrent de nouvelles perspectives pour la caractérisation de la microstructure de la neige, de ses propriétés, ainsi que de leur évolution au cours du temps.Snow avalanches are complex natural phenomena whose occurrence is mainly due to the structure and properties of the snowpack. To better understand the evolution of these properties over time, it is important to characterize the microstructure of snow, especially in terms of grains and ice necks that connect them. In this context, the objective of this thesis is the decomposition of snow samples into individual grains from 3-D images of snow obtained by X-ray microtomography. We present two decomposition methods using algorithms of discrete geometry. Based on the results of these segmentations, some parameters such as the specific surface area and the specific contact area between grains are then estimated from samples of several snow types. These segmentation methods offer new outlooks for the characterization of the microstructure of snow, its properties, and its time evolution

Quantification of the pore size distribution of soils:assessment of existing software using tomographic and synthetic 3D images

The pore size distribution (PSD) of the void space is widely used to predict a range of processes in soils. Recent advances in X-ray computed tomography (CT) now afford novel ways to obtain exact data on pore geometry, which has stimulated the development of algorithms to estimate the pore size distribution from 3D data sets. To date there is however no clear consensus on how PSDs should be estimated, and in what form PSDs are best presented. In this article, we first review the theoretical principles shared by the various methods for PSD estimation. Then we select methods that are widely adopted in soil science and geoscience, and we use a robust statistical method to compare their application to synthetic image samples, for which analytical solutions of PSDs are available, and X-ray CT images of soil samples selected from different treatments to obtain wide ranging PSDs. Results indicate that, when applied to the synthetic images, all methods presenting PSDs as pore volume per class size (i.e., Avizo, CTAnalyser, BoneJ, Quantim4, and DTM), perform well. Among them, the methods based on Maximum Inscribed Balls (Bone J, CTAnalyser, Quantim4) also produce similar PSDs for the soil samples, whereas the Delaunay Triangulation Method (DTM) produces larger estimates of the pore volume occupied by small pores, and Avizo yields larger estimates of the pore volume occupied by large pores. By contrast, the methods that calculate PSDs as object population fraction per volume class (Avizo, 3DMA, DFS-FIJI) perform inconsistently on the synthetic images and do not appear well suited to handle the more complex geometries of soils. It is anticipated that the extensive evaluation of method performance carried out in this study, together with the recommendations reached, will be useful to the porous media community to make more informed choices relative to suitable PSD estimation methods, and will help improve current practice, which is often ad hoc and heuristic