Vision models for 3-D surfaces

Different approaches to computational stereo to represent human stereo vision have been developed over the past two decades. The Marr-Poggio theory of human stereo vision is probably the most widely accepted model of the human stereo vision. However, recently developed motion stereo models which use a sequence of images taken by either a moving camera or a moving object provide an alternative method of achieving multi-resolution matching without the use of Laplacian of Gaussian operators. While using image sequences, the baseline between two camera positions for a image pair is changed for the subsequent image pair so as to achieve different resolution for each image pair. Having different baselines also avoids the inherent occlusion problem in stereo vision models. The advantage of using multi-resolution images acquired by camera positioned at different baselines over those acquired by LOG operators is that one does not have to encounter spurious edges often created by zero-crossings in the LOG operated images. Therefore in designing a computer vision system, a motion stereo model is more appropriate than a stereo vision model. However, in some applications where only a stereo pair of images are available, recovery of 3D surfaces of natural scenes are possible in a computationally efficient manner by using cepstrum matching and regularization techniques. Section 2 of this paper describes a motion stereo model using multi-scale cepstrum matching for the detection of disparity between image pairs in a sequence of images and subsequent recovery of 3D surfaces from depth-map obtained by a non convergent triangulation technique. Section 3 presents a 3D surface recovery technique from a stereo pair using cepstrum matching for disparity detection and cubic B-splines for surface smoothing. Section 4 contains the results of 3D surface recovery using both of the techniques mentioned above. Section 5 discusses the merit of 2D cepstrum matching and cubic B-spline interpolation for 3D surface recovery either by motion stereo model or stereo vision model implemented in a machine vision system.