On identification of singular points using photometric invariants for global shape from shading problem

The paper is concerned with the problem of identifying types of image singular points as either maxima, minima, or saddle points, especially for the case of unknown lighting direction. Singular points are defined as maximally bright points in the image whose corresponding surface normals coincide with the lighting direction. The identification of their type is the key to the global shape from shading problem, and it can be viewed as rough estimation of the object shape in itself. Using photometric invariants (e.g., extrema of the image grey level profile always lie on the parabolic curves of the object surface), it is shown that the two singular points which are connected by two steepest ascent curves starting from an image saddle point usually have different signs with each other. This constrains the possible combination of the types of the singular points in the global shape from shading problem