Partially Similar Object Matching Based On Differential Geometry

Partially similar object matching is a universal approach to object recognition. During the past decade, the problem of finding a partial match between three-dimensional surfaces attracted considerable attention. In this paper, the research of partially similar object matching is combined with fundamental differential geometry definitions, some matching algorithms are proposed and experimentations indicate encouraged results. The research fields include the two-dimensional partially similar object matching, three-dimensional partially similar object matching and three-dimensional deformed isometric surface matching. In addition, some prospects are proposed in the end of the paper.An efficient coding approach is firstly proposed for two-dimensional partially similar object matching. Considering the invariance of curvature, a new coding approach based on the abstraction of contour curvature is presented, and then the discrete approximation storage and reconstruction solutions are demonstrated. The curve-matching algorithm based on improving KMP (D. E. Knuth, V. R. Pratt and J. H. Morris) algorithm is proposed. Experiments indicate a simpler matching algorithm, reduced storage and greater convenience for pattern recognition when the differential geometry approaches is utilized to describe the contour.Secondly, considering the matching accuracy of the differential geometry coding, an improved approach based on similar skeleton is proposed for two-dimensional partially similar object matching. According to differential geometry, considering the invariance of curvature when rigid transformation is applied to plane curve, a new model utilizing curvature to illustrate the inherent characteristic of object contours is proposed; Point-pair set is constructed by means of filtrating points with similar inherent characteristic in object contours; possible transformation is located by similar straight line segments pair; finally, optimum transformation is computed and optimum matching is determined by score function. Simulation experiments indicate an encouraging matching efficiency and low run time complexity of the algorithm for partially similar object matching, especially for complex shape.Thirdly, the idea of similar skeleton is extended to the case of three-dimensional partially similar object matching. Curvature and torsion are employed to represent the inherent characteristic of three-dimensional curves; Gauss curvature and mean curvature are used to represent the inherent characteristic of three-dimensional surfaces. After the construction of Point-pair set, possible transformation is located by similar asymmetry triangle pair; finally, optimum transformation and optimum matching are determined by score function.In addition, a novel recognition approach for deformed isometric surfaces is presented in this paper. Firstly, some signatures of isometric surfaces are demonstrated based on geodesic distance, and then the Signature Matrix(SM) is constructed by computing the geodesic distance of every point pair using Fast Marching Method on Triangulate Domains (FMTD). Secondly, a normalization procedure is utilized to eliminate the difference of the Signature Matrices for the same object. A new series of moment invariants is proposed based on the Normalized Signature Matrix (NSM). In comparison with some recent methods, experiments indicate a lower computation complexity to the recognition for deformed isometric surfaces without reducing the recognition rate. Finally, extensions of this approach are introduced to the recognition for occluded and arbitrarily topologically deformed surfaces.