A 2D shape structure for decomposition and part similarity

This paper presents a multilevel analysis of 2D shapes and uses it to find similarities between the different parts of a shape. Such an analysis is important for many applications such as shape comparison, editing, and compression. Our robust and stable method decomposes a shape into parts, determines a parts hierarchy, and measures similarity between parts based on a salience measure on the medial axis, the Weighted Extended Distance Function, providing a multi-resolution partition of the shape that is stable across scale and articulation. Comparison with an extensive user study on the MPEG-7 database demonstrates that our geometric results are consistent with user perception.