SHAPE FROM FRACTAL GEOMETRY

A novel method for the recovery of a planar surface orientation from its image using fractal measures is presented. A fractal-related feature, the average Holder constant, is defined in the two-dimensional topological space. It is proven that the average Holder constant is scale-sensitive and the distance ratio from any two points on the fractal surface to the viewer can be calculated from their average Holder constants. By incorporating the distance ratio into the surface-vanishing line formula in the geometric model, a method for inferring planar surface shape is derived. The novelty of this method is that the fractal-related feature is used as a direct input in the shape recovery process. Experimental results showing the validity of applying this method to artificially rotated textured images and images of naturally textured surfaces are presented. © 1990.