Using the Gaussian Image to Find the Orientation of Objects

Current three-dimensional vision algorithms can generate depth maps or vector maps from images, but few algorithms extract high-level information from these depth maps. This paper identifies one algorithm that determines an object's orientation by matching object models to depth map data. The object models are constructed by mapping surface orien tation data onto spheres. This process is based on a mathe matical theorem that can be applied only to convex objects, but some extensions for nonconvex objects are presented. The paper shows that a global approach can be used successfully in cases where objects do not touch one another. Another important result illustrates the size of the space of rotations. It shows that even when 6,000 rotations are almost uniformly distributed for matching, errors of 17 degrees are still possible.

[1]  L. A. Li︠u︡sternik.  Convex figures and polyhedra , 1966 .

[2]  William Rowan Hamilton,et al.  Elements of Quaternions , 1969 .

[3]  A. Rosenfeld,et al.  Ordered search techniques in template matching , 1972 .

[4]  Bernard Widrow,et al.  The "Rubber-Mask" Technique I. Pattern Measurement and Analysis , 1973 .

[5]  A. V. Pogorelov.  Extrinsic geometry of convex surfaces , 1973 .

[6]  Berthold K. P. Horn.  Obtaining shape from shading information , 1989 .

[7]  Ann Patricia Fothergill,et al.  Inferring the Positions of Bodies from Specified Spatial Relationships , 1974, Artif. Intell..

[8]  D Marr,et al.  Early processing of visual information. , 1976, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[9]  H. Kenner.  Geodesic Math and How to Use It , 1976 .

[10]  Manfredo P. do Carmo,et al.  Differential geometry of curves and surfaces , 1976 .

[11]  Anthony Pugh,et al.  Polyhedra: A Visual Approach , 1976 .

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

[13]  Ramakant Nevatia,et al.  Description and Recognition of Curved Objects , 1977, Artif. Intell..

[14]  Aristides A. G. Requicha,et al.  Geometric Modeling of Mechanical Parts and Processes , 1977, Computer.

[15]  F. P. Preparata,et al.  Convex hulls of finite sets of points in two and three dimensions , 1977, CACM.

[16]  C. W. Allen,et al.  The Measurement and Use of Registered Reflectance and Range Data in Scene Analysis , 1977 .

[17]  Robert J. Woodham,et al.  Reflectance map techniques for analyzing surface defects in metal castings , 1978 .

[18]  Tomaso Poggio,et al.  A Theory of Human Stereo Vision , 1977 .

[19]  A. E. Brain,et al.  The measurement and use of registered reflectance and range data in scene analysis , 1977, Proceedings of the IEEE.

[20]  Samuel Hunt Drake,et al.  Using compliance in lieu of sensory feedback for automatic assembly. , 1978 .

[21]  Berthold K. P. Horn,et al.  Determining Shape and Reflectance Using Multiple Images , 1978 .

[22]  B K Horn,et al.  Calculating the reflectance map. , 1979, Applied optics.

[23]  T. Poggio,et al.  A computational theory of human stereo vision , 1979, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[24]  Norman I. Badler,et al.  Decomposition of Three-Dimensional Objects into Spheres , 1979, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[25]  Alan L. Mackay.  The packing of three-dimensional spheres on the surface of a four-dimensional hypersphere , 1980 .

[26]  Doctor,et al.  Display Techniques for Octree-Encoded Objects , 1981, IEEE Computer Graphics and Applications.

[27]  Thomas O. Binford,et al.  Inferring Surfaces from Images , 1981, Artif. Intell..

[28]  Robert L. Cook,et al.  A Reflectance Model for Computer Graphics , 1987, TOGS.

[29]  Yoshiaki Shirai.  Image processing for data capture , 1982, Computer.

[30]  T. Okada.  Development of an Optical Distance Sensor for Robots , 1982 .

[31]  Ray A. Jarvis,et al.  A Laser Time-of-Flight Range Scanner for Robotic Vision , 1983, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[32]  Frank J. Pipitone,et al.  A Wide-field Scanning Triangulation Rangefinder for Machine Vision , 1983 .

[33]  James J. Little,et al.  An iterative method for reconstructing convex polyhedra from extended gaussian images , 1983, AAAI 1983.

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

[35]  H. K. Nishihara,et al.  Practical Real-Time Imaging Stereo Matcher , 1984 .

[36]  Jean Ponce,et al.  Object Representation, Identification and Positioning from Range Data , 1984 .

[37]  Tosiyasu L. Kunii,et al.  Octree-Related Data Structures and Algorithms , 1984, IEEE Computer Graphics and Applications.