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Viscosity solutions of a level-set method for anisotropic geometric diffusion in image processing

JOURNAL OF MAthEMATICAL IMAGING AND VISION 2007年第2-3期29卷 205-217页

作者： Preusser, Tobias Univ Bremen Ctr Comp Syst & Visualizat CeVis D-28359 Bremen Germany

We discuss the existence of viscosity solutions for a class of anisotropic level-set methods which can be seen as an extension of the mean-curvature motion with a nonlinear anisotropic diffusion tensor. In an earlier work (Mikula et al. in Comput. Vis. Sci. 6(4):197-209, [2004];Preusser and Rumpf in SIAM J. Appl. Math. 62(5):1772-1793, [2002]) we have applied such methods for the denoising and enhancement of static images and image sequences. the models are characterized by the fact that-unlike the mean-curvature motion-they are capable of retaining important geometric structures like edges and corners of the level-sets. the article reviews the definition of the model and discusses its geometric behavior. the proof of the existence of viscosity solutions for these models is based on a fixed point argument which utilizes a compactness property of the diffusion tensor. For the application to image processing suitable regularizations of the diffusion tensor are presented for which the compactness assumptions of the existence proof hold. Finally, we consider the half relaxed limits of the solutions of auxiliary problems to show the compactness of the solution operator and thus the existence of a solution to the original problem.

关键词： image processing anisotropic diffusion level set method viscosity solution half relaxed limits

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XIX brazilian symposium on computer graphics and image processing - Table of contents

XIX Brazilian Symposium on Computer Graphics and Image Proce...

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brazilian symposium on computer graphics and image processing (sibgrapi)

Presents the table of contents of the proceedings.

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Differential representations for mesh processing

Differential representations for mesh processing

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18th brazilian symposium on computer graphics and image processing (sibgrapi 2005)

作者： Sorkine, Olga Tel Aviv Univ Sch Comp Sci IL-69978 Tel Aviv Israel

Surface representation and processing is one of the key topics in computer graphics and geometric modeling, since it greatly affects the range of possible applications. In this paper we will present recent advances in geometry processing that are related to the Laplacian processing framework and differential representations. this framework is based on linear operators defined oil polygonal meshes, and furnishes a variety of processing applications, such as shape approximation and compact representation, mesh editing, watermarking and morphing. the core of the framework is the definition of differential coordinates and new bases for efficient mesh geometry representation, based on the mesh Laplacian operator.

关键词： discrete Laplacian surface representation detail preservation geometry compression mesh editing

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XIX brazilian symposium on computer graphics and image processing - Title

XIX Brazilian Symposium on Computer Graphics and Image Proce...

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brazilian symposium on computer graphics and image processing (sibgrapi)

the following topics are dealt with: computer graphics; image processing; photography; segmentation; animation and collision detection; interactive computer graphics; tracking; meshes and compression; statistical imag...

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Determining the branchings of 3D structures from respective 2D projections

Determining the branchings of 3D structures from respective ...

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sibgrapi 2006: 19th brazilian symposium on computer graphics and image processing

作者： Leandro, Jorge J. G. Cesar Jr., Roberto M. Da Fontoura Costa, Luciano Institute of Mathematics and Statistics USP Department of Computer Science Rua do Matão 1010 São Paulo SP 05508-090 Brazil Instituto de Física de São Carlos USP Department of Physics and Informatics Av. Trabalhador Saocarlense 400 São Carlos SP 13560-970 Brazil

ISBN: (纸本)0769526861

this work describes a new framework for automatic extraction of 2D branching structures images obtained from 3D shapes, such as neurons and retinopathy images. the majority of methods for neuronal cell shape analysis that are based on the 2D contours of cells fall short of properly characterizing such cells because crossings among neuronal processes constrain the access of contour following algorithms to the innermost regions of the cell. the framework presented in this article addresses, possibly for the first time, the problem of determining the continuity along crossings, therefore granting to the contour following algorithm full access to all processes of the neuronal cell under analysis. First, the raw image is preprocessed so as to obtain an 8-connected, one-pixel wide skeleton as well as a set of seed pixels for each subtree and all the branching/crossing regions. then, for each seed pixel, the algorithm labels all valid neighbors, until a branching/crossing region is reached, when a decision about the proper continuation is taken based on the tangent continuity. the algorithm has shown robustness for images with parallel segments and low densities of branching/crossing densities. the problem of too high densities of branching/crossing regions can be addressed by using a suitable data structure. Successful experimental results using real data (neural cell images) are presented. © 2006 IEEE.

关键词： three dimensional computer graphics

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Multiple testing correction in medical image analysis

Multiple testing correction in medical image analysis

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19th brazilian symposium on computer graphics and image processing (sibgrapi 2006)

作者： Machado, Alexei Manso Correa Pontifical Catholic Univ Minas Gerias BR-30535610 Belo Horizonte MG Brazil

We present a novel method for correcting the significance level of hypothesis testing that requires multiple comparisons. It is based on the spectral graph theory, in which the variables are seen as the vertices of a complete undirected graph and the correlation matrix as the adjacency matrix that weights its edges. the method increases the statistical power of the analysis by refuting the assumption of independence among variables, while keeping the probability of false positives low. By computing the eigenvalues of the correlation matrix, it is possible to obtain valuable information about the dependence levels among the variables of the problem, so that the effective number of independent variables can be estimated. the method is compared to other available models and its effectiveness illustrated in case studies involving high-dimensional sets of variables.

关键词： hypothesis testing Bonferroni correction spectral graph theory

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Automatic image segmentation by tree pruning

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JOURNAL OF MAthEMATICAL IMAGING AND VISION 2007年第2-3期29卷 141-162页

作者： Bergo, Felipe P. G. Falcao, Alexandre X. Miranda, Paulo A. V. Rocha, Leonardo M. Univ Estadual Campinas LIV Inst Comp BR-13083970 Campinas SP Brazil Univ Estadual Campinas DECOM FEEC BR-13083970 Campinas SP Brazil

the image Foresting Transform (IFT) is a tool for the design of image processing operators based on connectivity, which reduces image processing problems into an optimum-path forest problem in a graph derived from the image. A new image operator is presented, which solves segmentation by pruning trees of the forest. An IFT is applied to create an optimum-path forest whose roots are seed pixels, selected inside a desired object. In this forest, object and background are connected by optimum paths (leaking paths), which cross the object's boundary through its "most weakly connected" parts (leaking pixels). these leaking pixels are automatically identified and their subtrees are eliminated, such that the remaining forest defines the object. Tree pruning runs in linear time, is extensible to multidimensional images, is free of ad hoc parameters, and requires only internal seeds, with little interference from the heterogeneity of the background. these aspects favor solutions for automatic segmentation. We present a formal definition of the obtained objects, algorithms, sufficient conditions for tree pruning, and two applications involving automatic segmentation: 3D MR-image segmentation of the human brain and image segmentation of license plates. Given that its most competitive approach is the watershed transform by markers, we also include a comparative analysis between them.

关键词： image segmentation graph-search algorithms image foresting transform image processing watershed transform

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Generalized rigid and generalized affine image registration and interpolation by geometric multigrid

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JOURNAL OF MAthEMATICAL IMAGING AND VISION 2007年第2-3期29卷 163-183页

作者： Keeling, Stephen L. Karl Franzens Univ Graz Inst Math & Wissenschaftliches Rechmen A-8010 Graz Austria

Generalized rigid and generalized affine registration and interpolation obtained by finite displacements and by optical flow are here developed variationally and numerically as well as with respect to a geometric multigrid solution process. For high order optimality systems under natural boundary conditions, it is shown that the convergence criteria of Hackbusch (Iterative Solution of Large Sparse Systems of Equations. Springer, Berlin, 1993) are met. Specifically, the Galerkin formalism is used together with a multi-colored ordering of unknowns to permit vectorization of a symmetric successive over-relaxation on image processing systems. the geometric multigrid procedure is situated as an inner iteration within an outer Newton or lagged diffusivity iteration, which in turn is embedded within a pyramidal scheme that initializes each outer iteration from predictions obtained on coarser levels. Differences between results obtainable by finite displacements and by optical flows are elucidated. Specifically, independence of image order can be shown for optical flow but in general not for finite displacements. Also, while autonomous optical flows are used in practice, it is shown explicitly that finite displacements generate a broader class of registrations. this work is motivated by applications in histological reconstruction and in dynamic medical imaging, and results are shown for such realistic examples.

关键词： generalized rigid generalized affine image registration image interpolation geometric multigrid

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Viscosity solutions of a level-set method for anisotropic geometric diffusion in image processing

Viscosity solutions of a level-set method for anisotropic ge...

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19th brazilian symposium on computer graphics and image processing (sibgrapi 2006)

作者： Preusser, Tobias Univ Bremen Ctr Comp Syst & Visualizat CeVis D-28359 Bremen Germany

关键词： image processing anisotropic diffusion level set method viscosity solution half relaxed limits

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Reconstruction of 3D object meshes from silhouette images

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JOURNAL OF MAthEMATICAL IMAGING AND VISION 2007年第2-3期29卷 119-130页

作者： Montenegro, Anselmo Antunes Velho, Luiz Carvalho, Paulo C. P. Sossai, Jonas, Jr. Univ Fed Fluminense Dept Ciencia Comp BR-24210240 Niteroi RJ Brazil Inst Nacl Matemat Pura & Aplicada Rio De Janeiro Brazil

In this work we propose a method for computing mesh representations of 3D objects reconstructed from a set of silhouette images. Our method is based on the polygonization of volumetric reconstructions by using a modified version of the dual contouring method. In order to apply dual contouring on volumetric reconstruction from silhouettes we devised a method that is able to determine the discrete topology of the surface in relation to the octree cells. We also developed a new scheme for computing hermitian data representing the intersections of conic volumes with the octree cells and their corresponding normals with subpixel accuracy. Due to the discrete and extremely noisy nature of the data used in the reconstruction we had to devise a different criterion for mesh simplification that applies topological consistency tests only when the geometric error measure is beyond a given tolerance. We present results of the application of the proposed method in the extraction of a mesh corresponding to the surface of objects of a real scene.

关键词： polygonization of volumetric reconstructions mesh reconstruction from silhouettes dual contouring octree polygonization Visual hulls image-based modeling mesh simplification

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