THE USE OF THE FACET MODEL AND THE TOPOGRAPHIC PRIMAL SKETCH IN IMAGE ANALYSIS
LINDA G. SHAPIRO
ROBERT M. HARALICK
University of Washington
University of Minnesota
The facet model states that all processing of digital-image data has its final authoritative interpretation relative to what the processing does to the underlying gray-tone intensity surface. The digital image's pixel values are noisy sampled observations of the underlying surface. Thus, in order to do any processing, we must estimate this underlying surface at each pixel position. This requires a model that describes what the general form of the surface would be in the neighborhood of any pixel if there were no noise. To estimate the surface from the neighborhood around a pixel, then, amounts to estimating the free parameters of the general form. The processing that takes place is then defined in terms of the estimated parameters.
The topographic primal sketch ( Haralick, Watson, & Laffey, 1983) is one possible way of representing the fundamental structure of a digital image in a rich and robust way. The basis of the topographic primal sketch is the classification and grouping of the underlying image-intensity surface patches according to the categories defined by monotonic, gray-tone invariant functions of directional derivatives. Examples of such categories are peak, pit, ridge, ravine, saddle, flat, and hillside. From this initial classification, categories can be grouped to obtain a rich, hierarchical, and structurally complete representation of the fundamental image structure. By contrast, representations of the fundamental image structure only involving edges or the primal sketch as described by Marr ( 1976) are impoverished in the sense that they are insufficient for unambiguous matching. They also do not have the required invariance with respect to monotonically increasing gray-tone transformations.