Shape Modeling and Shape Analysis Based on Singularities

To analyze given object shapes, it is necessary first to model the shapes and then to analyze the models. This paper proposes a method of modeling and analyzing two-dimensional (2D) and three-dimensional (3D) shapes based on singularities. First, a function is defined on an object. The object is then modeled by the distribution of the singularities of the function. Finally, the extracted singular points are analyzed by a Reeb graph together with wavelets for multiresolution analysis. The applications of the method include analysis of botanical leaf shapes and human facial expressions.

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