ON SEEING SPAGHETTI - SELF-ADJUSTING PIECEWISE TOROIDAL RECOGNITION OF FLEXIBLE EXTRUDED OBJECTS

We present a model for flexible extruded objects, such as wires, tubes , or grommets, and demonstrate a novel, self-adjusting, seven-dimensio nal Hough transform that derives their diameter and three-space curved axes from position and surface normal information. The method is pure ly local and is inexpensive to compute. The model considers such objec ts as piecewise toroidal, and decomposes the seven parameters of a tor us into three nested subspaces, the structures of which counteract the errors implicit in the analysis of objects of great size and/or small curvature. We believe it is the first example of a parameter space st ructure designed to cluster ill-conditioned hypotheses together so tha t they can be easily detected and ignored. This work complements exist ing shape-from-contour approaches for analyzing tori: It uses no edge information, and it does not require the solution of high-degree non-l inear equations by iterative techniques. Most of the results, includin g the conditions for the existence of more than one solution (phantom ''anti-tori''), have been verified using a symbolic mathematical analy sis system. We present, in the environment of the IBM ConVEx system, r obust results on both synthetic CAD-CAM range data (the hasp of a lock ), and actual range data (a knotted piece of coaxial cable), and discu ss several system tuning issues.