Extracting salient points and parts of shapes using modified kd-trees

This paper explores the use of tree-based data structures in shape analysis. We consider a structure which combines several properties of traditional tree models and obtain an efficiently compressed yet faithful representation of shapes. Constructed in a top-down fashion, the resulting trees are unbalanced but resolution adaptive. While the interior of a shape is represented by just a few nodes, the structure automatically accounts for more details at wiggly parts of a shape's boundary. Since its construction only involves simple operations, the structure provides an easy access to salient features such as concave cusps or maxima of curvature. Moreover, tree serialization leads to a representation of shapes by means of sequences of salient points. Experiments with a standard shape database reveal that correspondingly trained HMMs allow for robust classification. Finally, using spectral clustering, tree-based models also enable the extraction of larger, semantically meaningful, salient parts of shapes.