Mapping singularities based motion estimation

Existing methods of image-based motion measurement (except point source cases) idealize borders (edges) of objects. Small changes in movement, direction, or projection can introduce errors into movement measurement. We propose a method that applies Differential Mapping Singularities Theory (Catastrophe Theory) in the context of 3-D object projection into a 2-D image plane, and takes advantage of the fact that the edges of an object can be interpreted in mapping singularities (catastrophes). Several theorems show that mapping of an arbitrary smooth surface can create only 14 singularities. Small changes in object position do not change the type of singularity, but simply shift its critical point. A trajectory of moving critical points, extracted from edge and edge vicinity pixels, can be divided into areas that correspond to different singularity types (a so-called phase diagram). Based on a phase diagram, it is possible to select a corresponding Singularity Relationship Graph (SRG). Knowledge of a SRG allows correct prediction of changes during object movement. This approach provides a significant reduction in calculations for motion prediction and permits correction of predicted motion in all sets of predicted frames. In addition, SRG knowledge allows object tracking, even with sudden changes of direction and use of camouflage.