CS332: Visual Processing in Computer and Biological Vision Systems

Image Formation and Shape from Shading

Reading:

Woodham, R. J., "Photometric method for determining shape from shading," in: Image Understanding 1984, S. Ullman & W. Richards, eds, Ablex Publishing Co., New Jersey, 1984.

Note: The sections of this chapter that you should read are marked with a dark bar along the left margin.

Outline:

We will explore some of the basic principles of image formation that are used in the study of how physical properties of the environment are recovered from the visual image. In particular, we will cover the following topics:

(1) The physical factors that determine the image intensities. These include the spatial distribution and spectral composition of the light sources in the scene, the structure and material covering the visible surfaces, and the viewing geometry.

(2) The viewing geometry. We will introduce the incident, emergent and phase angles, which define the geometry of the viewer, illumination and reflecting surface. These angles influence the amount of light that is first incident upon the surface and then reflected from the surface toward the viewer.

(3) The reflectance function, ø(i, e, g). This function characterizes the way particular surfaces reflect light from the source to the viewer. We will look at particular examples of the reflectance functions for perfect specular, or mirror-like surfaces, Lambertian or matte surfaces, the maria of the moon, and scanning electron microscope images.

(4) The representation of surface orientation. We will introduce some representations of surface orientation that are used, for example, in computational studies of the recovery of 3-D shape from shading information. One useful representation uses stereographic projection onto a plane of a unit sphere representing all possible surface orientations.

(5) The reflectance map, R(f,g). The reflectance map makes explicit the relationship between brightness and surface shape, for a given combination of light source distribution, viewing geometry, and surface reflectance properties.

(6) The image irradiance equation. This single equation embodies the main physical factors that influence the formation of image irradiance (the light incident upon the eye or camera), and has been useful in studies of visual processes such as the recovery of shape from shading.

(7) The recovery of shape from shading. We will define the shape-from-shading problem and present an algorithm proposed by Ikeuchi and Horn for its solution. We will also discuss perceptual studies that explore the accuracy with which the human visual system can recover 3-D shape from shading.