Region-Based Segmentation on Evolving Surfaces with Application to 3D Reconstruction of Shape and Piecewise Constant Radiance

We consider the problem of estimating the shape and radiance of a scene from a calibrated set of images under the assumption that the scene is Lambertian and its radiance is piecewise constant. We model the radiance segmentation explicitly using smooth curves on the surface that bound regions of constant radiance. We pose the scene reconstruction problem in a variational framework, where the unknowns are the surface, the radiance values and the segmenting curves. We propose an iterative procedure to minimize a global cost functional that combines geometric priors on both the surface and the curves with a data fitness score. We carry out the numerical implementation in the level set framework.