Share Email Print

Proceedings Paper

Affine and projective differential geometric invariants of space curves
Author(s): Alfons H. Salden; Bart M. ter Haar Romeny; Max A. Viergever
Format Member Price Non-Member Price
PDF $14.40 $18.00
cover GOOD NEWS! Your organization subscribes to the SPIE Digital Library. You may be able to download this paper for free. Check Access

Paper Abstract

A space curve, e.g., a parabolic line on a 2-dimensional surface in 3-dimensional Euclidean space, induces a plane curve under projective mapping. But 2-dimensional scalar input images of such an object are, normally, spatio-temporal slices through a luminance field caused by the interaction of an external field and that object. Consequently, the question arises how to obtain from those input images a consistent description of the space curve under projective transformations. By means of classical scale space theory, algebraic invariance theory, and classical differential geometry a new method of shape description for space curves from one or multiple views is proposed in terms of complete and irreducible sets of affine and projective differential geometric invariants. The method is based on defining implicitly connections for the observed curves that are highly correlated to the projected space curves. These projected curves are assumed to reveal themselves as coherent structures in the scale space representation of the differential structure of the input images. Several applications to stereo, optic flow, texture analysis, and image matching are briefly indicated.

Paper Details

Date Published: 23 June 1993
PDF: 11 pages
Proc. SPIE 2031, Geometric Methods in Computer Vision II, (23 June 1993); doi: 10.1117/12.146646
Show Author Affiliations
Alfons H. Salden, Utrecht Univ. Hospital (Netherlands)
Bart M. ter Haar Romeny, Utrecht Univ. Hospital (Netherlands)
Max A. Viergever, Utrecht Univ. Hospital (Netherlands)

Published in SPIE Proceedings Vol. 2031:
Geometric Methods in Computer Vision II
Baba C. Vemuri, Editor(s)

© SPIE. Terms of Use
Back to Top