Variational methods for shape reconstruction in computer vision
Hailin Jin, Stefano Soatto · 2003
This dissertation addresses the problem of inferring the three-dimensional shape and radiance of a scene from a collection of calibrated images taken from different viewpoints. The problem is known as “multi-view stereo” and has been studied extensively in the Computer Vision literature. Most existing multi-view stereo algorithms rely on identification of corresponding points or regions among images. They work effectively only when scenes are Lambertian and have textured radiances, because lack of Lambertianity or absence of texture in the radiance leads to an ill-posed correspondence problem. Targeting scenes with more complex photometric properties, we propose a framework of comparing the images with a model of the scene, which avoids the ill-posed correspondence problem. The model is comprised of a component for shape and a component for radiance. We model the shape as a collection of smooth surfaces and model the radiance based on the underlying reflectance properties. Within this framework, we present two stereo reconstruction algorithms, one for non-Lambertian scenes and the other for Lambertian scenes with smooth radiances. In addressing non-Lambertian scenes, we propose a novel model for the radiance. At the core of the model lies a rank constraint of the radiance tensor field and a discrepancy