Constructive tree recovery using genetic algorithms

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Authors: Fayolle, P.A., Pasko, A., Mirenkov, N., Rosenberger, C. and Toinard, C.

Journal: Proceedings of the 6th IASTED International Conference on Visualization, Imaging, and Image Processing, VIIP 2006

Pages: 349-353

An algorithm is described for recovering a constructive tree representation of a solid from a segmented point-set. The term point-set refers here to a finite set of points on or near the surface of the solid. Constructive geometry refers to the construction of complex solids by recursively applying set operations to simple primitives. It can be implemented on a computer by using a tree data structure with geometric primitives (planes, spheres and others) in the leaves and set-operations in the internal nodes. This tree data structure is called a constructive tree. A constructive tree can be syntactically translated into representations of solids by real-valued functions with the theory of R-functions. The recovered constructive tree is a correct representation of the point-set if the solid defined by the corresponding function matches the solid defined by the point-set. The search for a constructive tree is performed by a genetic algorithm. The formulation of the problem, the genetic algorithm and its parameters are discussed here.

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