Region-based segmenta-tion on evolving surfaces with application to 3D shape and radiance estimation
Region-based Segmentation on Evolving Surfaces with Application to 3D Reconstruction of Shape and Piecewise Constant Radiance Hailin Jin 1 , Anthony J. Yezzi 2 , and Stefano Soatto 1 Computer Science Department, University of California, Los Angeles, CA 90095, hljin,soatto@cs.ucla.edu School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332, ayezzi@ece.gatech.edu Abstract. We consider the problem of estimating the shape and radi- ance 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 re- construction problem in a variational framework, where the unknowns are the surface, the radiance values and the segmenting curves. We pro- pose 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. Keywords: variational methods, Mumford-Shah functional, image segmen- tation, multi-view stereo, level set methods, curve evolution on manifolds. Fig. 1. (COLOR) A plush model of “nemo.” The object exhibits piecewise constant appearance. From a set of calibrated views, our algorithm can estimate the shape and the piecewise constant radiance. Introduction Inferring three-dimensional shape and appearance of a scene from a collection of images has been a central problem in Computer Vision, known as multi- view stereo. Traditional approaches to this problem ﬁrst match points or small