Integrating Shape-from-Shading & Stereopsis

This thesis is concerned with inferring scene shape by combining two specific techniques: shape-from-shading and stereopsis. Shape-from-shading calculates shape using the lighting equation, which takes surface orientation and lighting information to irradiance. As irradiance and lighting information are provided this is the problem of inverting a many to one function to get surface orientation.
Surface orientation may be integrated to get depth. Stereopsis matches pixels between two images taken from different locations of the same scene - this is the correspondence problem. Depth can then be calculated using camera calibration information, via triangulation. These methods both fail for certain inputs; the advantage of combining them is that where one fails the other may continue to work. Notably, shape-from-shading requires a smoothly shaded surface, without texture, whilst stereopsis requires texture - each works where the other does not.

The first work of this thesis tackles the problem directly.
A novel modular solution is proposed to combine both methods; combining is itself done using Gaussian belief propagation. This modular approach highlights missing and weak modules; the rest of the thesis is then concerned with providing a new module and an improved module. The improved module is given in the second research chapter and consists of a new shape-from-shading algorithm. It again uses belief propagation, but this time with directional statistics to represent surface orientation. Message passing is performed using a novel method; it is analytical, which makes this algorithm particularly fast. In the final research chapter a new module is provided, to estimate the light source direction. Without such a module the user of the system has to provide it; this is tedious and error prone, and impedes automation. It is a probabilistic method that uniquely estimates the light source direction using a stereo pair as input.