3D Visual Shape Processing based on Discrete Differential Geometry

With the increase in the number of 3D scanned shapes, 3D shape processing is becoming popular in the fields of computer vision, computer graphics, computer aided design (CAD), etc. Digital Geometry Processing (DGP) is a new and much needed application area for the next wave of multimedia data: 3D geometry. Thanks to nearly two-decade efforts of many researchers, much of basic theoretical problems in the field of DGP have been solved until about 2010. This book aims to present the techniques and applications of 3D Visual Shape Processing (VSP) based on discrete differential geometry. The book considers the ”perception” of the geometry in the views both of globality (Part I) and locality (Part II). In Part I, we explore some research work on global shape analysis based on manifold harmonics (i.e. the eigenfunctions of the Laplace-Beltrami operators defined on the surface). In Part II, based on local differential operators, we develop new methods for efficient and reliable tools for mesh deformation, correspondence, segmentation and many other types of DGP operations. This provides a complete mesh processing pipeline to allow for easy and efficient manipulation of 3D models.