α-Decompositionα-Decomposition of polygons

Decomposing a shape into visually meaningful parts comes naturally to humans, but recreating this fundamental operation in computers has been shown to be difficult. Similar challenges have puzzled researchers in shape reconstruction for decades. In this paper, we recognize the strong connection between shape reconstruction and shape decomposition at a fundamental level and propose a method called α-decompositionα-decomposition. The α-decompositionα-decomposition generates a space of decompositions parameterized by αα, the diameter of a circle convolved with the input polygon. As we vary the value of αα, some structural features appear and disappear quickly while others persist. Therefore, by analyzing the persistence of the features, we can determine better decompositions that are more robust to both geometrical and topological noises.

Graphical abstractFigure optionsDownload full-size imageDownload high-quality image (257 K)Download as PowerPoint slideHighlights► Connections between shape reconstruction and shape decomposition are explored. ► Convolution is closely related to bridges and pockets, and concavity. ► Persistence of concavity is analyzed by varying the value of convolution radius. ► Generate decompositions that are robust to geometrical and topological noises.