By Michael Breuß, Alfred Bruckstein, Petros Maragos

ISBN-10: 3642341411

ISBN-13: 9783642341410

Half I. Discrete form research. Modeling third-dimensional Morse and Morse-Smale Complexes / Lidija Čomić, Leila De Floriani, Federico Iuricich -- Geodesic Regression and Its program to form research / P. Thomas Fletcher -- Segmentation and Skeletonization on Arbitrary Graphs utilizing Multiscale Morphology and energetic Contours / Petros Maragos, Kimon Drakopoulos -- sophisticated Homotopic Thinning Algorithms and caliber Measures for Skeletonisation tools / Pascal Peter, Michael Breuß -- Nested Sphere information of Skeletal versions / Stephen M. Pizer ... [et al.] -- 3D Curve Skeleton Computation and Use for Discrete form research / Gabriella Sanniti di Baja, Luca Serino, Carlo Arcelli -- Orientation and Anisotropy of Multi-component Shapes / Joviša Žunić, Paul L. Rosin -- half II. Partial Differential Equations for form research. strong Semi-local positive aspects for Non-rigid Shapes / Roee Litman, Alexander M. Bronstein, Michael M. Bronstein -- a short Survey on Semi-Lagrangian Schemes for snapshot Processing / Elisabetta Carlini, Maurizio Falcone, Adriano Festa -- form Reconstruction of Symmetric Surfaces utilizing Photometric Stereo / Roberto Mecca, Silvia Tozza -- Remeshing via Curvature pushed Diffusion / Serena Morigi, Marco Rucci -- Group-Valued Regularization for movement Segmentation of Articulated Shapes / man Rosman ... [et al.] -- aspect Cloud Segmentation and Denoising through limited Nonlinear Least Squares basic Estimates / Edward Castillo, Jian Liang, Hongkai Zhao -- Distance photographs and the Enclosure box: functions in Intermediate-Level computing device and organic imaginative and prescient / Steven W. Zucker -- half III. Optimization tools for form research. Non-rigid form Correspondence utilizing Pointwise floor Descriptors and Metric buildings / Anastasia Dubrovina, Dan Raviv, Ron Kimmel -- A evaluate of Geometry restoration from a unmarried photograph targeting Curved item Reconstruction / Martin R. Oswald ... [et al.] -- On Globally optimum neighborhood Modeling: From relocating Least Squares to Over-parametrization / Shachar Shem-Tov ... [et al.] -- Incremental point Set monitoring / Shay Dekel, Nir Sochen, Shai Avidan -- Simultaneous Convex Optimization of areas and sector Parameters in picture Segmentation types / Egil Bae, Jing Yuan, Xue-Cheng Tai -- Fluctuating Distance Fields, components, Three-Partite Skeletons / Sibel Tari -- built-in DEM building and Calibration of Hyperspectral Imagery: A distant Sensing standpoint / Christian Wöhler, Arne Grumpe

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Finally, another difference among the algorithms is given by the entities used in the segmentation process: the algorithms in [11, 19, 21] assign the simplexes of ˙ to cells in the Morse complexes; the algorithm in [26] assigns the vertices of ˙ to cells in the Morse complexes; the algorithms in [27, 31, 38] assign the cells of the cell complex K to cells in the descending Morse complex. The algorithm in [20] computes the segmentation of the 3D simplicial mesh with the correct combinatorial structure described by the quasi-Morse-Smale complex.

4 A Region-Growing Algorithm The algorithm proposed in [26] computes the Morse-Smale complex of a function f defined over the vertices of a simplicial complex ˙ triangulating a manifold M . The ascending cells are computed through region growing, in the order of decreasing cell dimension. Descending cells are computed inside the ascending 3-cells, using the same region-growing approach. The ascending and descending cells of all dimensions are composed of vertices (0-simplexes) of ˙. The computation of the ascending 3-cells consists of two steps.

It computes a Forman gradient vector field V by subdividing the simplexes of ˙ into three lists, denoted as A, B and C , such that lists A and B are of the same length, and for each i -simplex j 2 A, V . i C 1/-simplex in B, and C is the set of critical simplexes. v/. Lists A, B and C are initialized as empty. v/ is empty, then v is a minimum and it is added to C . v/. The lowest critical vertex w is chosen from C 0 and edge Œv; w is added to B. v/ D Œv; w. i C 1/-simplex (cone) v is added to C .

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Innovations for shape analysis by Michael Breuß, Alfred Bruckstein, Petros Maragos

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