Relating Properties of Surface Curvature to Image Intensity

Abstract

Reflectance map techniques make explicit the relationship between image intensity and surface orientation. In general, however, trade-offs between image intensity and surface shape emerge which cannot be resolved in a single view. Existing methods for determining shape from a single view embody assumptions about surface curvature. The image Hessian matrix is introduced as a convenient viewer-centered representation of surface curvature. Properties of surface curvature are expressed as properties of the Hessian matrix. For several classes of surfaces, image analysis simplifies. This result has already been established for planar surfaces. Similar simplification is demonstrated for singly curved surfaces and for the subclass of doubly curved surfaces known as generalized cones. These studies help to delineate shape information that can be determined from object boundaries and shape information that can be determined from shading.