Innovations for Shape Analysis: Models and Algorithms (Mathematics and Visualization)

Part I. Discrete Shape Analysis. Modeling Three-Dimensional Morse and Morse-Smale Complexes / Lidija Čomić, Leila De Floriani, Federico Iuricich -- Geodesic Regression and Its Application to Shape Analysis / P. Thomas Fletcher -- Segmentation and Skeletonization on Arbitrary Graphs Using Multiscale Morphology and Active Contours / Petros Maragos, Kimon Drakopoulos -- Refined Homotopic Thinning Algorithms and Quality Measures for Skeletonisation Methods / Pascal Peter, Michael Breuß -- Nested Sphere Statistics of Skeletal Models / Stephen M. Pizer ... [et al.] -- 3D Curve Skeleton Computation and Use for Discrete Shape Analysis / Gabriella Sanniti di Baja, Luca Serino, Carlo Arcelli -- Orientation and Anisotropy of Multi-component Shapes / Joviša Žunić, Paul L. Rosin -- Part II. Partial Differential Equations for Shape Analysis. Stable Semi-local Features for Non-rigid Shapes / Roee Litman, Alexander M. Bronstein, Michael M. Bronstein -- A Brief Survey on Semi-Lagrangian Schemes for Image Processing / Elisabetta Carlini, Maurizio Falcone, Adriano Festa -- Shape Reconstruction of Symmetric Surfaces Using Photometric Stereo / Roberto Mecca, Silvia Tozza -- Remeshing by Curvature Driven Diffusion / Serena Morigi, Marco Rucci -- Group-Valued Regularization for Motion Segmentation of Articulated Shapes / Guy Rosman ... [et al.] -- Point Cloud Segmentation and Denoising via Constrained Nonlinear Least Squares Normal Estimates / Edward Castillo, Jian Liang, Hongkai Zhao -- Distance Images and the Enclosure Field: Applications in Intermediate-Level Computer and Biological Vision / Steven W. Zucker -- Part III. Optimization Methods for Shape Analysis. Non-rigid Shape Correspondence Using Pointwise Surface Descriptors and Metric Structures / Anastasia Dubrovina, Dan Raviv, Ron Kimmel -- A Review of Geometry Recovery from a Single Image Focusing on Curved Object Reconstruction / Martin R. Oswald ... [et al.] -- On Globally Optimal Local Modeling: From Moving Least Squares to Over-parametrization / Shachar Shem-Tov ... [et al.] -- Incremental Level Set Tracking / Shay Dekel, Nir Sochen, Shai Avidan -- Simultaneous Convex Optimization of Regions and Region Parameters in Image Segmentation Models / Egil Bae, Jing Yuan, Xue-Cheng Tai -- Fluctuating Distance Fields, Parts, Three-Partite Skeletons / Sibel Tari -- Integrated DEM Construction and Calibration of Hyperspectral Imagery: A Remote Sensing Perspective / Christian Wöhler, Arne Grumpe Part I Discrete Shape Analysis: 1 Modeling Three-Dimensional Morse and Morse-Smale Complexes by L. Comic et al.- 2 Geodesic Regression and its Application to Shape Analysis by P.Th.Fletcher.- 3 Segmentation and Skeletonization on Arbitrary Graphs Using Multiscale Morphology and Active Contours by P.Maragos and K.Drakopoulos.- 4 Refined Homotopic Thinning Algorithms and Quality Measures for Skeletonisation Methods by P.Peter and M.Breuss.- 5 Nested Sphere Statistics of Skeletal Models by S.M.Pizer et al.- 6 3D Curve Skeleton Computation and Use for Discrete Shape Analysis by G.Sanniti di Baja and C.Arcelli.- 7 Orientation and Anisotropy of Multi-component Shapes by J. Zunic and P.L.Rosin.- Part II Partial Differential Equations for Shape Analysis: 8 Stable semi-local features for non-rigid shapes by R.Litman et al.- 9 A brief survey on semi-Lagrangian schemes for image processing by E.Carlini et al.- 10 Shape reconstruction of symmetric surfaces using Photometric Stereo by R.Mecca and S.Tozza.- 11 Remeshing by Curvature Driven Diffusion by S.Morigi and M.Rucci.- 12 Group-valued Regularization for Motion Segmentation of Articulated Shapes by G.Rosman et al.- 13 Point Cloud Segmentation and Denoising via Constrained Nonlinear Least Squares Normal Estimates by E.Castillo et al.- 14 Distance Images and the Enclosure Field: Applications in Intermediate-Level Computer and Biological Vision by S.W.Zucker.- Part III Optimization Methods for Shape Analysis: 15 Non-rigid Shape Correspondence Using Pointwise Surface Descriptors and Metric Structures by A.Dubrovina et al.- 16 A Review of Geometry Recovery from a Single Image Focusing on Curved Object Reconstruction by M.R.Oswald et al.- 17 On Globally Optimal Local Modeling: From Moving Least Squares to Over-Parametrization by S. Shem-Tov et al.- 18 Incremental Level Set Tracking by S.Dekel et al.- 19 Simultaneous Convex Optimization of Regions and Region Parameters in Image Segmentation Models by E.Bae et al.- 20 Fluctuating Distance Fields, Parts, Three-Partite Skeletons by S.Tari.- 21 Integrated DEM Construction and Calibration of Hyperspectral Imagery: A Remote Sensing Perspective by Ch.Woehler and A.Grumpe.- Index. Part I Discrete Shape Analysis: 1 Modeling Three-Dimensional Morse and Morse-Smale Complexes by L. Čomić et al 2 Geodesic Regression and its Application to Shape Analysis by P.Th.Fletcher 3 Segmentation and Skeletonization on Arbitrary Graphs Using Multiscale Morphology and Active Contours by P.Maragos and K.Drakopoulos 4 Refined Homotopic Thinning Algorithms and Quality Measures for Skeletonisation Methods by P.Peter and M.Breuß 5 Nested Sphere Statistics of Skeletal Models by S.M.Pizer et al 6 3D Curve Skeleton Computation and Use for Discrete Shape Analysis by G.Sanniti di Baja and C.Arcelli 7 Orientation and Anisotropy of Multi-component Shapes by J. Žunić and P.L.Rosin Part II Partial Differential Equations for Shape Analysis: 8 Stable semi-local features for non-rigid shapes by R.Litman et al 9 A brief survey on semi-Lagrangian schemes for image processing by E.Carlini et al ^ 10 Shape reconstruction of symmetric surfaces using Photometric Stereo by R.Mecca and S.Tozza 11 Remeshing by Curvature Driven Diffusion by S.Morigi and M.Rucci 12 Group-valued Regularization for Motion Segmentation of Articulated Shapes by G.Rosman et al 13 Point Cloud Segmentation and Denoising via Constrained Nonlinear Least Squares Normal Estimates by E.Castillo et al 14 Distance Images and the Enclosure Field: Applications in Intermediate-Level Computer and Biological Vision by S.W.Zucker Part III Optimization Methods for Shape Analysis: 15 Non-rigid Shape Correspondence Using Pointwise Surface Descriptors and Metric Structures by A.Dubrovina et al 16 A Review of Geometry Recovery from a Single Image Focusing on Curved Object Reconstruction by M.R.Oswald et al 17 On Globally Optimal Local Modeling: From Moving Least Squares to Over-Parametrization by S. Shem-Tov et al 18 Incremental Level Set Tracking by S.Dekel et al ^ ^^ 19 Simultaneous Convex Optimization of Regions and Region Parameters in Image Segmentation Models by E.Bae et al 20 Fluctuating Distance Fields, Parts, Three-Partite Skeletons by S.Tari 21 Integrated DEM Construction and Calibration of Hyperspectral Imagery: A Remote Sensing Perspective by Ch.Wöhler and A.Grumpe Index. ^^ The concept of 'shape' is at the heart of image processing and computer vision, yet researchers still have some way to go to replicate the human brain's ability to extrapolate meaning from the most basic of outlines. This volume reflects the advances of the last decade, which have also opened up tough new challenges in image processing. Today's applications require flexible models as well as efficient, mathematically justified algorithms that allow data processing within an acceptable timeframe. Examining important topics in continuous-scale and discrete modeling, as well as in modern algorithms, the book is the product of a key seminar focused on innovations in the field. It is a thorough introduction to the latest technology, especially given the tutorial style of a number of chapters. It also succeeds in identifying promising avenues for future research. The topics covered include mathematical morphology, skeletonization, statistical shape modeling, continuous-scale shape models such as partial differential equations and the theory of discrete shape descriptors. Some authors highlight new areas of enquiry such as partite skeletons, multi-component shapes, deformable shape models, and the use of distance fields. Combining the latest theoretical analysis with cutting-edge applications, this book will attract both academics and engineers.