Statistics and Analysis of Shapes - Krim, Hamid; Yezzi, Anthony; SpringerLink (Online service) (Boston, MA : Birkhäuser Boston, 2006)
The subject of pattern analysis and recognition pervades many aspects of our daily lives, including user authentication in banking, object retrieval from databases in the consumer sector, and the omnipresent surveillance and security measures around sensitive areas. Shape analysis, a fundamental building block in many approaches to these applications, is also used in statistics, biomedical applications (Magnetic Resonance Imaging), and many other related disciplines. With contributions from some of the leading experts and pioneers in the field, this self-contained, unified volume is the first comprehensive treatment of theory, methods, and algorithms, available in a single resource, without the typical quagmire of vast information scattered over a wide body of literature. Developments are discussed from a rapidly increasing number of research papers in diverse fields, including the mathematical and physical sciences, engineering, and medicine. The initial chapters explore the statistical modeling of landmarks while subsequent chapters address the probabilistic modeling of entire shapes. The latter part of the book, with the exception of the last two chapters, concentrates on case studies as well as implementational and practical challenges in real systems. Extensive illustrations throughout help readers overcome the sometimes terse technical details of the geometric and probabilistic formalism. Knowledge of advanced calculus and basic statistics and probability theory are the only prerequisites for the reader. Statistics and Analysis of Shapes will be an essential learning kit for statistical researchers, engineers, scientists, medical researchers, and students seeking a rapid introduction to the field. It may be used as a textbook for a graduate-level special topics course in statistics and signal/image analysis, or for an intensive short course on shape analysis and modeling. The state-of-the-art techniques presented will also be useful for experienced researchers and practitioners in academia and industry.
Medial Axis Computation and Evolution -- Shape Variation of Medial Axis Representations via Principal Geodesic Analysis on Symmetric Spaces -- 2D Shape Modeling using Skeletal Graphs in a Morse Theoretic Framework -- Matching with Shape Contexts -- Shape Recognition Based on an a Contrario Methodology -- Integral Invariants and Shape Matching -- On the Representation of Shapes Using Implicit Functions -- Computing with Point Cloud Data -- Determining Intrinsic Dimension and Entropy of High-Dimensional Shape Spaces -- Object-Image Metrics for Generalized Weak Perspective Projection -- Wulff Shapes at Zero Temperature for Some Models Used in Image Processing -- Curve Shortening and Interacting Particle Systems -- Riemannian Structures on Shape Spaces: A Framework for Statistical Inferences -- Modeling Planar Shape Variation via Hamiltonian Flows of Curves -- Approximations of Shape Metrics and Application to Shape Warping and Empirical Shape Statistics.
Keywords: MATHEMATICS; OPTICAL PATTERN RECOGNITION; VISUALIZATION; GLOBAL DIFFERENTIAL GEOMETRY; STATISTICS; MATHEMATICS; MATHEMATICAL MODELING AND INDUSTRIAL MATHEMATICS; STATISTICS FOR LIFE SCIENCES, MEDICINE, HEALTH SCIENCES; VISUALIZATION; PATTERN RECOGNITION; SIGNAL, IMAGE AND SPEECH PROCESSING; DIFFERENTIAL GEOMETRY