CO~IP~TER VISION, GRAPHICS, AND IMAGE PllGCxSSING x,394-396 (1986)

Abstracts of Papers Accepted for Publication

PAPERS

SymmCtry-Cm Dndty. MICKQ.L LEYTON. Harvard University, Cambridge, Massachusetts 02138 and Department of Computer Science, State University of New York, Buffalo, New York 14260. Received December 12,1985; revised June 21,1986.

Several studies have shown the importance of two very different descriptors for shape: symmetry structure and curvature extrema. The main theorem proved by this paper, i.e., the symmetry-curvature

duo& theorem, states that there is an important relationship between symmetry and curvature extrema: If we say that curvature extrema are of two opposite types, either maxima or minima Then the theorem states: Any segment of a smooth planar curve, bounded by two consecutive curvature extrema of the same type, has a unique symmetry axis, and the axis terminates at the curvature extremum of the opposite type. The theorem is initially proved using Brady’s SLS as the symmetry analysis. However, the theorem is then generalized for any differential symmetry analysis. In order to prove the theorem, a number of results are established concerning the symmetry structure of Hoffman and Richards’ codons. All results are obtained by first observing that any codon is a string of two, three, or four spirals, and then by reducing the theory of codons to that of spirals. We show that the SLS of a codon is either (1) an SAT, which is a more restricted symmetry analysis that was introduced by Blum, or (2) an ESAT, which is a symmetry analysis that is introduced in the present paper and is dual to Blum’s SAT.

Estimation of u Circu& Arc Center and Its R&us. U. M. LANDAU. Rafael, Haifa, Israel. Received February 18,1986; revised June 23,1986.

A simple algorithm for estimating the location of the center of a circular arc and its radius is suggested. Some of its features are explored.

Fast Edge-only Matching Techniqaes for Robot Pat&n Recognition. TIZRRY CAELLI AND SHYAMALA

NAGENDRAN. Alberta Centre for Machine Intelligence and Robotics and Department of Psychology, The University of Alberta, Edmonton, Alberta, Canada T6G 2E9. Received September 17, 1985; accepted July 22,1986.

A technique for detecting arbitrary two-dimensional signals by cross-correlating edge-only information is developed from fast pipe-line pixel processor logical and convolution operations. The procedures are incorporated into a robot visual system capable of locating, moving towards, and pointing to a target signal, independent of its orientation and size.

Smcctwc ami Morton front Q&al Flow under Perspectitz Projection. KEN-ICHI KANATANI. Center for Automation Research, University of Maryland, College Park, Maryland 20742. Received January 7, 1986; accepted July 23,1986.

The 3D structure and motion of an object are determined from its optical flow under perspective projection. The solution is given in explicit analytical form in terms of the parameters characterizing the flow of planar motion. The solution is not unique, but the spurious solution disappears if two or more planar parts of the same object are observed, and the adjacency condition of optical flows is explicitly obtained. Unique interpretation also becomes possible by considering the transition to the “pseudo- orthographic approximation,” since no spurious solution arises in this approximation. The choice of the coordinate system and parameterization of rigid motion are discussed in relation to robustness of computation.

394 0734189X/86 $3.00 Copyright (D 1986 by Academic Pr.%, Inc. Au rights of reprodIwion in my form -ed.