Recovery of Parametric Models from Range Images: The Case for Superquadrics with Global Deformations

A method for recovery of compact volumetric models for shape representation of single-part objects in computer vision is introduced. The models are superquadrics with parametric deformations (bending, tapering, and cavity deformation). The input for the model recovery is three-dimensional range points. Model recovery is formulated as a least-squares minimization of a cost function for all range points belonging to a single part. During an iterative gradient descent minimization process, all model parameters are adjusted simultaneously, recovery position, orientation, size, and shape of the model, such that most of the given range points lie close to the model's surface. A specific solution among several acceptable solutions, where are all minima in the parameter space, can be reached by constraining the search to a part of the parameter space. The many shallow local minima in the parameter space are avoided as a solution by using a stochastic technique during minimization. Results using real range data show that the recovered models are stable and that the recovery procedure is fast. >

[1]  E. Gombrich.  Art and Illusion , 1962 .

[2]  Azriel Rosenfeld,et al.  Digital Picture Processing , 1976 .

[3]  D. Brandt,et al.  Multi-level adaptive solutions to boundary-value problems math comptr , 1977 .

[4]  Eleanor Rosch,et al.  Principles of Categorization , 1978 .

[5]  Barr,et al.  Superquadrics and Angle-Preserving Transformations , 1981, IEEE Computer Graphics and Applications.

[6]  Dana H. Ballard,et al.  Computer Vision , 1982 .

[7]  J. Fodor.  The Modularity of mind. An essay on faculty psychology , 1986 .

[8]  Robert C. Bolles,et al.  3DPO: A Three- Dimensional Part Orientation System , 1986, IJCAI.

[9]  A. Witkin,et al.  On the Role of Structure in Vision , 1983 .

[10]  Michael R. Lowry,et al.  Learning Physical Descriptions From Functional Definitions, Examples, and Precedents , 1983, AAAI.

[11]  Rodney A. Brooks,et al.  Model-Based Three-Dimensional Interpretations of Two-Dimensional Images , 1981, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[12]  B. Tversky,et al.  Objects, parts, and categories. , 1984 .

[13]  Alan H. Barr,et al.  Global and local deformations of solid primitives , 1984, SIGGRAPH.

[14]  W. Grimson,et al.  Model-Based Recognition and Localization from Sparse Range or Tactile Data , 1984 .

[15]  Irving Biederman,et al.  Human image understanding: Recent research and a theory , 1985, Comput. Vis. Graph. Image Process..

[16]  L. E. Scales,et al.  Introduction to Non-Linear Optimization , 1985 .

[17]  Berthold K. P. Horn.  Robot vision , 1986, MIT electrical engineering and computer science series.

[18]  Alex Pentland,et al.  Perceptual Organization and the Representation of Natural Form , 1986, Artif. Intell..

[19]  S. Harnad.  Category Induction and Representation , 1987 .

[20]  John R. Kender,et al.  What is a 'Degenerate' View? , 1987, IJCAI.

[21]  Andrew P. Witkin,et al.  Energy constraints on parameterized models , 1987, SIGGRAPH.

[22]  A. Pentland.  Recognition by Parts , 1987 .

[23]  Terrance E. Boult,et al.  Recovery of superquadrics from depth information , 1987 .

[24]  Ruzena Bajcsy,et al.  Range Image Interpretation of Mail Pieces with Superquadrics , 1987, AAAI.

[25]  Ruzena Bajcsy,et al.  Segmentation of three-dimensional scenes using multi-modal interaction between machine vision and programmable, mechanical scene manipulation , 1987 .

[26]  Michael Leyton,et al.  Nested structures of control: An intuitive view , 1987, Comput. Vis. Graph. Image Process..

[27]  John C. Platt,et al.  Elastically deformable models , 1987, SIGGRAPH.

[28]  B. Tversky,et al.  Cognitive constraints on ordering operations: the case of geometric analogies. , 1987, Journal of experimental psychology. General.

[29]  Ruzena Bajcsy,et al.  Multiresolution elastic matching , 1989, Comput. Vis. Graph. Image Process..

[30]  Alex Pentland,et al.  Part Segmentation for Object Recognition , 1989, Neural Computation.

[31]  William H. Press,et al.  Numerical recipes , 1990 .