Recovering LSHGCs and SHGCs from stereo

We examine the problem of computing shape descriptions from stereo, where by shape descriptions we mean 3-D volumetric descriptions of objects rather than a 2 /12-D depth map of the scene. We argue that intermediate 2 /12-D depth measurements may not be always directly available from stereo, especially when there are curved surfaces in the scene, and that 3-D volumetric descriptions of objects may have to be derived directly from stereo correspondences. We then present methods to recover volumetric shape from stereo using LSHGCs and SHGCs as the shape models. Our methods are based on some invariant properties of LSHGCs and SHGCs in their monocular and stereo projections. Experimental results on both synthetic and real images of objects with curved surfaces are given. Our technique allows dense surface descriptions to be recovered even for objects without much texture, and it is not restricted to narrow stereo angles or low resolution images. Our technique can also handle objects in close range where perspective distortion in the images can be significant.