Analysing images of curved surfaces

摘要

A reflectance map makes the relationship between image intensity and surface orientation explicit. Trade-offs between image intensity and surface orientation emerge which cannot be resolved locally in a single view. Existing methods for determining surface orientation from a single view embody assumptions about surface curvature. The Hessian matrix is introduced to represent surface curvature. Properties of surface curvature are expressed as properties of the Hessian matrix. For several classes of surface, image analysis simplifies. This result has already been established for planar surfaces forming trihedral corners. Similar simplification is demonstrated for developable surfaces and for the subclass of surfaces known as generalized cones. These studies help to delineate shape information that can be determined from geometric measurements at object boundaries and shape information that can be determined from intensity measurements over sections of smoothly curved surface.