# Approximate Decomposition

Our goal is to investigate an alternative representation for large geometries, which will allow existing (inefficient) methods and software to perform efficiently for large geometries without designing and implementing new algorithms.

Nearly Convex Decomposition through Convex Ridge Separation (CoRise)papers: In this work, we investigate an approach that decomposes a mesh P based on the identification of Convex Ridges. Intuitively, convex ridges are the protruding parts of the mesh P. Our method, called CoRise, extracts nearly convex components of P by separating each convex ridge from all the other convex ridges. Through the new concept of Residual Concavity, CoRise requires only a single user parameter: concavity tolerance. We show that our method can generate noticeably better segmentation in significant shorter time than the current state-of-art methods. | |

Dual-Space Decomposition of 2D Complex Shapes (DuDe2D) papers: CVPR 2014 We propose a new decomposition method, called Dual-space Decomposition that handles complex 2D shapes by recognizing the importance of holes and classifying holes as either topological noise or structurally important features. Our method creates a nearly convex decomposition of a given shape by segmenting both positive and negative regions of the shape. We compare our results to segmentation produced by non-expert human subjects. | |

Alpha Decomposition of Polygons papers: SMI 2012 Decomposing a shape into visually meaningful parts comes naturally to human vision, but recreating this fundamental operation in computers has been shown to be difficult. In this work, we recognize the strong connections between shape reconstruction and shape decomposition and propose a method called α-decomposition. The α-decomposition can determine better decompositions that are more robust to both geometrical and topological noises. | |

Approximate Convex Decomposition (ACD) papers: SoCG 2004, CGTA 2006 (2D), SPM 2007, CGAD 2008 (3D) While decomposition into convex components results in pieces that are easy to process, such decompositions can be costly to construct and often result in representations with an unmanageable number of components. We propose an alternative partitioning strategy that decomposes a given model (in 2D or 3D) into "approximately convex" pieces. | |

Approximate Star-shaped Decomposition papers: Point-Based Graphics 2007 A* decomposition of a point set : Decomposing a point set into a set of star-shaped subsets. |