Abstract

An important part of stereo vision consists of finding and matching points in two images that correspond to the same physical element in the scene. When the two images of the same scene are taken from quite different points of view, matching corresponding elements can be difficult. It is desirable therefore to consider perspective projection invariants, that is, features or image properties that are invariant for arbitrary perspective projections. We prove theorems about the projections of zeros of curvature of curves, namely, that zeros of curvatures of planar curves are perspective invariants and that zeros of curvature of arbitrary curves are almost always perspective invariants. We also show that the projected zeros of curvature of planar curves are only stable for deformations occurring in the plane of the curve.

© 1988 Optical Society of America

Optimized stereo reconstruction of free-form space curves based on a nonuniform rational B-spline model

Yi Jun Xiao and Y. F. Li
J. Opt. Soc. Am. A 22(9) 1746-1762 (2005)

Invariant aberrations. II. p-invariants

H. A. Buchdahl
J. Opt. Soc. Am. A 5(11) 1963-1967 (1988)

Invariant aberrations. III. l-invariants

H. A. Buchdahl
J. Opt. Soc. Am. A 5(11) 1968-1971 (1988)

Perspective projections in the space-frequency plane and fractional Fourier transforms

İ. Şamil Yetik, Haldun M. Ozaktas, Billur Barshan, and Levent Onural
J. Opt. Soc. Am. A 17(12) 2382-2390 (2000)

Invariant aberrations. IV. s-invariants

H. A. Buchdahl
J. Opt. Soc. Am. A 5(11) 1972-1975 (1988)