Scene Statistics and 3D Surface Perception

The inference of depth information from single images is typically performed by devising models of image formation based on the physics of light interaction and then inverting these models to solve for depth. Once inverted, these models are highly underconstrained, requiring many assumptions such as Lambertian surface reflectance, smoothness of surfaces, uniform albedo, or lack of cast shadows. Little is known about the relative merits of these assumptions in real scenes. A statistical understanding of the joint distribution of real images and their underlying 3D structure would allow us to replace these assumptions and simplifications with probabilistic priors based on real scenes. Furthermore, statistical studies may uncover entirely new sources of information that are not obvious from physical models. Real scenes are affected by many regularities in the environment, such as the natural geometry of objects, the arrangements of objects in space, natural distributions of light, and regularities in the position of the observer. Few current computer vision algorithms for 3D shape inference make use of these trends. Despite the potential usefulness of statistical models and the growing success of statistical methods in vision, few studies have been made into the statistical relationship between images and range (depth) images. Those studies that have examined this relationship in nature have uncovered meaningful and exploitable statistical trends in real scenes which may be useful for designing new algorithms in surface inference, and also for understanding how humans perceive depth in real scenes [?, ?, ?]. In this chapter, we will highlight some results we have obtained in our study on the statistical relationships between 3D scene structures and 2D images, and discuss their implications on understanding human 3D surface perception and its underlying computational principles.