Inferring Shape from Motion Fields

TLDR: In this article, a shape from motion (SfM) approach is proposed to derive descriptions of rigidly rotating smooth surfaces from the orthographic projection of the motions of their surface markings.

Abstract: : The human visual system has the ability to utilize motion information to infer the shapes of surfaces. More specifically, we are able to derive descriptions of rigidly rotating smooth surfaces entirely from the orthographic projection of the motions of their surface markings. A computational analysis of this ability is proposed based on a 'shape from motion' proposition. This proposition states that given the first spatial derivatives of the orthographically projected velocity and acceleration fields of a rigidly rotating regular surface, then the angular velocity and the surface normal at each visible point on that surface are uniquely determined up to a reflection. The computational analysis proceeds in three main steps. First it is shown that surface tilt and one component of the angular velocity may be obtained entirely from the first spatial derivatives of the velocity field. Second it is shown that surface slant and the remaining two components of the angular velocity are computable if the first spatial derivatives of the acceleration field are also given. Finally the problem of constructing a velocity field from the temporally changing optic array is briefly discussed. (Author)