Forming shape abstractions using optimal solutions

One of the most important problems facing researchers in various fields such as pattern recognition, computer vision, and industrial design is the shape abstraction. A recent shape abstraction method generates an abstracted shape through the correspondences between their features from a given set of shapes. The correspondences are obtained based on the optimal solution of a well known transportation problem. This paper considers the case where multiple optimal solutions exist for one problem and ranks all optimal solutions based on how much they preserve the local neighborhood relations. Afterwards, the abstracted shape is created using the solution with the highest rank. Experimental evaluation of the framework demonstrates that the proposed approach compares favorably with the previous shape abstraction technique.