Some New Results on Non-rigid Correspondence and Classification of Curves

We present two new algorithms for correspondence and classification of planar curves in a non-rigid sense. In the first algorithm we define deforming energy based on aligning curves using certain of their properties, namely Multi-Step-Size Local Similarity (MSSLS) and the difference between the angle changes of beginning and ending tangent lines of two corresponding curve segments, as well as local scale of stretching. MSSLS overcomes the noise of local shape information of curves to be aligned. In the second algorithm, we improve the computation of shape context so that it catches the local information of ordered sets representing planar curves better. The optimal correspondence is found by a modified dynamic-programming method. Based on deforming energy, we can do pattern recognition among curves, which is very important in many areas such as recognition of hand-written characters and cardiac curves where rigid transformations and scaling do not work well. Finally, the effect of correspondence and classification is shown in application to hand-written characters and cardiac curves.