Segmentation and recovery of superquadrics
The models for representing 3D structures can be grouped into local and global models. Methods for local representation try to represent objects as sets of primitives such as surface patches or edges. Global methods, on the other hand, try to represent an object or its parts as an entity in its own coordinate system. When elements of such global models correspond to perceptual equivalents of parts, we speak of part-level models. A part-level shape description is important for several tasks in the digital image processing. The first dedicated part-level models in computer vision were generalized cylinders. The idea of generalized cylinders is due to \textit{I. Biederman} [Human image understanding: Recent research and theory. Comput. Vision, Graphics Image Process. 32, 29-73 (1985)], who suggested using the Cartesian product of qualitative properties such as tapering, cross-section etc., in order to create a qualitative taxonomy of generalized cylinders. Superquadric models appeared in computer vision as an answer to some of the problems with generalized cylinders [\textit{A. P. Petland}, Perceptual organization and the representation of natural form, Artif. Intell. 28, 293-331 (1986)]. Superquadrics are solid models that can, with a fairly simple parameterization, represent a large variety of standard geometric solids, as well as smooth shapes in between. The method of Pentland was extremely slow, Solina and Balcsy developed the first practical method for recovering superquadric parameters [\textit{F. Solina} and \textit{R. Bajcsy}, Range image interpretation of mail pieces with superquadrics. In AAAI-87 Proceedings Sixt National Conference on Artificial Intelligence, Vol. 2., 733-737, Seattle, Washington (1987)]. This method is the standard method for fitting superquadrics. The central theme of the whole book is the method of recovery and segmentation of superquadrics from range images, which was developed by the authors of the book. It is described in details and compared with other methods of superquadric recovery and segmentation. Numerous examples of recovery and segmentation from range images are given. Let us have a look at the structure of the book. Chapter 2 gives the definitions of superquadrics after overviewing a brief history of their development. Chapter 3 is devoted to the extensions of superquadrics. Chapter 4 is an overview of different methods of superquadric recovery. The second part of this chapter is devoted to the least-squares approach to superquadric recovery which is currently one of the most widely used methods. This method was developed by the authors. The third part is an overview of physics-based recovery methods. Chapter 5 is devoted to the segmentation with superquadrics and Chapter 6 presents experimental results of segmentation and recovery of superquadrics from range data.
scientific article; zbMATH DE number 1547329