N-dimension geometry used in the design of a Dynamic neural-network pattern-recognition system

摘要

If the main features, or the skeleton (e.g., the corner points and the boundary lines,) of a 3D moving object can be represented by an ND analog vector, then the whole history of movement (rotation, translation, deformation, etc.) of this object can be described by an ND curve in the ND state space. Each point on the curve corresponds to a snap-shot of the 3D object at a certain time during the course of movement. We can approximate this ND curve by an ND broken line just like the linearization of a 2D curve by a 2D broken line. But the linearization of a branch of an ND curve is just to apply the ND convex operation to the two end points of this branch. Therefore remembering all the end points (or all the extreme points) in the ND curve will allow us to approximately reconstruct the ND curve, or the whole 3D object's moving history, by means of the simple mathematical operation, the ND convex operation. Based on this ND geometry principle, a very simple, yet very robust, and very accurate dynamic neural network system (a computer graphic program) is proposed for recognizing any moving object not only by its static images, but also by the special way this object moves.