Structure from Motion on Textures: Theory and Application to Calibration

Abstract

This dissertation introduces new mathematical constraints that enable us, for the first time, to investigate the correspondence problem using texture rather than point and lines. These three multilinear constraints are formulated on parallel equidistant lines embedded in a plane. We choose these sets of parallel lines as proxies for fourier harmonics embedded on a plane as a sort of ``texture atom''. From these texture atoms we can build up arbitrarily textured surfaces in the world. If we decompose these textures in a Fourier sense rather than as points and lines, we use these new constraints rather than the standard multifocal constraints such as the epipolar or trifocal. We propose some mechanisms for a possible feedback solution to the correspondence problem. As the major application of these constraints, we describe a multicamera calibration system written in C and MATLAB which will be made available to the public. We describe the operation of the program and give some preliminary results.