COMPUTER VISION, GRAPHICS, AND IMAGE PROCESSING 51, 217-218 (1990)

Abstracts of Papers Accepted for Publication

PAPERS

Representation and Rewgnition of Sutjkce Shapes in Range Images: A Diffientiul Geometry Approach. PING LIANG. School of Computer Science, Technical University of Nova Scotia, Halifax, Nova Scotia, Canada; JOHN S. TODHUNTER. Department of Electrical Engineering, University of Pitts- burgh, Pittsburgh, Pennsylvania 15260. Received August 5, 1987; revised August 21, 1989.

Theory and matching algorithms are developed for accurate orientation determination and recogni- tion of 3D surface shapes in range images. Two corollaries to the fundamental theorem of surface theory are proved. The first corollary proves the invariance of the fundamental coefficients when lines of curvature are used as the intrinsic parameter curves. The second corollary proves that a diffeomor- phism which preserves the intrinsic distance along the principal directions, in addition to preserving the eigenvectors and eigenvalues of the shape operator (Weingarten map), is necessarily an isometry. Based on these two corollaries, a set of geometric descriptors which satisfy the uniqueness and invariance requirements are theoretically identified for all classes of surfaces, namely, hyperbolic, elliptic, and developable surfaces. The unit normal and shape descriptors list array (UNSDLA) representation and the corresponding matching algorithm are developed. The UNSDLA is a generalization of the extended Gaussian image (EGI). The EGI has a fundamental limitation; that is, it can only uniquely represent convex shapes. The new representation overcomes this limitation of the EGI and extends the scope of unique representation to all classes of surfaces. Moreover, it still has all the advantages of the EGI. This is achieved by preserving the connectivity of the original data. Surface matching can be performed more accurately using the UNSDLA than the EGI. Based on the UNSDLA representations, surfaces can be matched via the Gaussian map by optimization over all possible rotations of a surface shape. The representation and matching algorithm can deal with hyperbolic and elliptic surfaces whose Gaussian maps are not one-to-one. Developable surfaces whose Gaussian maps of lines of curvature with nonzero principal curvature are not one-to-one can also be accommodated. Two theorems on developable surfaces are proved.

A Hiemrchical Appmach fo Line Extmction Based OII the Hough Transfom. JOHN PRINCEN, JOHN

ILLINGWORTH, AND JOSEF LITTLER. Department of Electronic and Electrical Engineering, Univer- sity of Surrey, Guildford, Surrey GU2 5XH, United Kingdom. Received January 24, 1989; accepted September 5, 1989.

An efficient method for finding straight lines in edge maps is described. The algorithm is based on a pyramid structure with each layer in the pyramid splitting the complete image into a number of subimages. At the bottom level of the pyramid short line segments are detected by applying a Hough transform to small subimages. The algorithm proceeds, bottom up, from this low-level description by grouping line segments within local neighborhoods into longer lines. Line segments which have local support propagate up the hierarchy and take part in grouping at higher levels. The length of a line determines approximately the level in the pyramid to which it propagates. Hence we obtain a hierarchical description of the line segments in a scene which can be useful in matching. The algorithm has a number of advantages over previously proposed hierarchical methods for the detection of straight lines. It is quite efficient and has a particularly attractive architecture which is suitable for parallel implementation.

Exploiting Image-Plane Data in the Interpretatbm oj Edge-&ucd B~JWC&U Disparity. TONY P. PRID- MORE, JOHN E W. MAYHEW, AND JOHN P. FRISBY. AI Vision Research Unit, University of Sheffield, Sheffield, United Kingdom. Received December 12, 1988; accepted September 5, 1989.

217 0734-189X/90 $3.00 Copyright B l!Wl by Academic Press, Inc. All rights of reproduction in any form reserved.