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E-raamat: Segmentation and Recovery of Superquadrics

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A representation of objects by their parts is the dominant strategy for representing complex 3D objects in many disciplines. In computer vision and robotics, superquadrics are among the most widespread part models. Superquadrics are a family of parametric models that cover a wide variety of smoothly changing 3D symmetric shapes, which are controlled with a small number of parameters and which can be augmented with the addition of global and local deformations. The book covers, in depth, the geometric properties of superquadrics. The main contribution of the book is an original approach to the recovery and segmentation of superquadrics from range images. Several applications of superquadrics in computer vision and robotics are thoroughly discussed and, in particular, the use of superquadrics for range image registration is demonstrated. Audience: The book is intended for readers of all levels who are familiar with and interested in computer vision issues.
List of Figures
ix
List of Tables
xiii
Preface xv
Acknowledgments xvii
Foreword xix
Introduction
1(12)
Part-level models
2(7)
Superquadrics in computer vision
9(1)
Other applications of superquadrics
10(1)
Summary
11(2)
Superquadrics and Their Geometric Properties
13(28)
Superellipse
13(5)
Superellipsoids and superquadrics
18(6)
Superquadrics in general position
24(2)
Some geometric properties of superellipsoids
26(11)
Computation and rendering of superquadrics
37(2)
Summary
39(2)
Extensions of Superquadrics
41(22)
Global deformations
41(8)
Local deformations
49(9)
Hyperquadrics
58(1)
Ratioquadrics
58(2)
Summary
60(3)
Recovery of Individual Superquadrics
63(40)
Overview of superquadric recovery methods
64(8)
Gradient least-squares minimization
72(19)
Physics-based reconstruction
91(5)
Discussion
96(5)
Summary
101(2)
Segmentation with Superquadrics
103(38)
Overview of segmentation methods
105(6)
``Recover-and-select'' segmentation
111(26)
Segmentation with surface models
137(1)
Summary
138(3)
Experimental Results
141(40)
Recover-and-select superquadric segmentation results
142(14)
Analysis of results
156(24)
Summary
180(1)
Applications of Superquadrics
181(36)
A survey of superquadric applications
182(14)
Range image registration
196(19)
Summary
215(2)
Conclusions
217(4)
Appendices 221(16)
A-- Rendering of Superquadrics in Mathematica
221(2)
B-- Superquadric Recovery Code
223(2)
C-- Range Image Acquisition
225(6)
D-- Minimum Description Length and Maximum A Posteriori Probability
231(2)
E-- Object-Oriented Framework for Segmentation (Segmentor)
233(4)
References 237(22)
Author Index 259(4)
Topic Index 263