2,621 research outputs found

    Discrete euclidean skeletons in increased resolution

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    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

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

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    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 dd-dimensional images. We also present a dd-dimensional medial axis filtering process that allows us to control the quality of the reconstructed shape

    Medial Axis Approximation and Regularization

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    Medial axis is a classical shape descriptor. Among many good properties, medial axis is thin, centered in the shape, and topology preserving. Therefore, it is constantly sought after by researchers and practitioners in their respective domains. However, two barriers remain that hinder wide adoption of medial axis. First, exact computation of medial axis is very difficult. Hence, in practice medial axis is approximated discretely. Though abundant approximation methods exist, they are either limited in scalability, insufficient in theoretical soundness, or susceptible to numerical issues. Second, medial axis is easily disturbed by small noises on its defining shape. A majority of current works define a significance measure to prune noises on medial axis. Among them, local measures are widely available due to their efficiency, but can be either too aggressive or conservative. While global measures outperform local ones in differentiating noises from features, they are rarely well-defined or efficient to compute. In this dissertation, we attempt to address these issues with sound, robust and efficient solutions. In Chapter 2, we propose a novel medial axis approximation called voxel core. We show voxel core is topologically and geometrically convergent to the true medial axis. We then describe a straightforward implementation as a result of our simple definition. In a variety of experiments, our method is shown to be efficient and robust in delivering topological promises on a wide range of shapes. In Chapter 3, we present Erosion Thickness (ET) to regularize instability. ET is the first global measure in 3D that is well-defined and efficient to compute. To demonstrate its usefulness, we utilize ET to generate a family of shape revealing and topology preserving skeletons. Finally, we point out future directions, and potential applications of our works in real world problems

    Fast and robust curve skeletonization for real-world elongated objects

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    We consider the problem of extracting curve skeletons of three-dimensional, elongated objects given a noisy surface, which has applications in agricultural contexts such as extracting the branching structure of plants. We describe an efficient and robust method based on breadth-first search that can determine curve skeletons in these contexts. Our approach is capable of automatically detecting junction points as well as spurious segments and loops. All of that is accomplished with only one user-adjustable parameter. The run time of our method ranges from hundreds of milliseconds to less than four seconds on large, challenging datasets, which makes it appropriate for situations where real-time decision making is needed. Experiments on synthetic models as well as on data from real world objects, some of which were collected in challenging field conditions, show that our approach compares favorably to classical thinning algorithms as well as to recent contributions to the field.Comment: 47 pages; IEEE WACV 2018, main paper and supplementary materia

    An Unified Multiscale Framework for Planar, Surface, and Curve Skeletonization

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    Computing skeletons of 2D shapes, and medial surface and curve skeletons of 3D shapes, is a challenging task. In particular, there is no unified framework that detects all types of skeletons using a single model, and also produces a multiscale representation which allows to progressively simplify, or regularize, all skeleton types. In this paper, we present such a framework. We model skeleton detection and regularization by a conservative mass transport process from a shape's boundary to its surface skeleton, next to its curve skeleton, and finally to the shape center. The resulting density field can be thresholded to obtain a multiscale representation of progressively simplified surface, or curve, skeletons. We detail a numerical implementation of our framework which is demonstrably stable and has high computational efficiency. We demonstrate our framework on several complex 2D and 3D shapes
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