Affine Stereo Calibration for Relative Affine Shape Reconstruction

Abstract

It has been shown that relative projective shape, determined up to an unknown projective transformation, with respect to 5 reference points can be obtained from point-to-point correspondences of a pair of images; Affine shape up to an unknown affine transformation with respect to 4 points can be obtained from parallel projection. We show in this paper that afTine shape with respect to 4 reference points can be obtained from two perspective images provided that the pair of images is affinely calibrated. By affine calibration, it means the establishment of a special plane collineation between two image planes, this collineation is the product of two plane collineations each of which establishes a (1,1) correspondence between an image plane and the plane at infinity. Experimental results are also presented.

Euclidean reconstruction from uncalibrated views

“…On the other hand, Sparr ([18]) gives a method of computing affine structure given a single view, and Koenderink and van Doorn [11] give a method for computing affine structure from pairs of affine views. Quan [16] gives a method of affine construction from two views given affine constraints.…”

Sketching natural terrain from uncalibrated imagery

“…A way to avoid these problems is to perform an affine calibration of the pair of cameras [13,12]. This means that in addition to the fundamental matrix, we need to identify the homography H 1 of the plane at infinity, defined as follows: the projective coordinates of two points m and m 0 , projections in the first and second image of a point at infinity, are related by:…”