Surface Visibility Probabilities in 3D Cluttered Scenes Michael S. Langer School of Computer Science, McGill University Montreal, H3A2A7, Canada langer@cs.mcgill.ca http://www.cim.mcgill.ca/~langer Abstract. Many methods for 3D reconstruction in computer vision rely on probability models, for example, Bayesian reasoning. Here we intro- duce a probability model of surface visibilities in densely cluttered 3D scenes. The scenes consist of a large number of small surfaces distributed randomly in a 3D view volume. An example is the leaves or branches on a tree. We derive probabilities for surface visibility, instantaneous image velocity under egomotion, and binocular half–occlusions in these scenes. The probabilities depend on parameters such as scene depth, object size, 3D density, observer speed, and binocular baseline. We verify the cor- rectness of our models using computer graphics simulations, and briefly discuss applications of the model to stereo and motion. 1 Introduction The term clutter scene typically refers to a scene that contains many visible objects [2,18,6] distributed randomly over space. In this paper, we consider a particular type of cluttered scene, consisting of a large number of small surfaces distributed over a 3D volume. An example is the leaves or branches of a tree. Reconstructing 3D geometry of a cluttered scene is a very challenging task because so many depth discontinuities and layers are present. Although some computer vision methods allow for many depth discontinuities, such methods typically assume only a small number of layers are present, typically two [28]. The goal of this paper is to better understand the probabilistic constraints of surface visibilities in such scenes. We study how visibility probabilities of surfaces depend on various geometric parameters, namely the area, depth and density of surfaces. We also examine how visibility probabilities depend on observer view- point. Such probability models are fundamental in many methods for computing optical flow [24,29,19] and stereo[1,3]. The hope is that the probability models could be used to improve these methods, for example, in a Bayesian framework by providing a prior on surface visibilities in 3D cluttered scenes. 2 Related Work The probability models that we present are related to several visibility models that have appeared in the literature. We begin with a brief review. D. Forsyth, P. Torr, and A. Zisserman (Eds.): ECCV 2008, Part I, LNCS 5302, pp. 401–412, 2008. c  Springer-Verlag Berlin Heidelberg 2008