Bayesian Assembly of 3D Axially Symmetric Shapes from Fragments
CVPR(2004)
摘要
We present a complete system for the purpose of automat- ically assembling 3D pots given 3D measurements of their fragments commonly called sherds. A Bayesian approach is formulated which, at present, models the data given a set of sherd geometric parameters. Dense sherd measurement data is obtained by scanning the outside surface of each sherd with a laser scanner. Mathematical models, speci- ed by a set of geometric parameters, represent the sherd outer surface and break curves on the outer surface (where two sherds have broken apart). Optimal alignment of as- semblies of sherds, called congur ations, is implemented as maximum likelihood estimation (MLE) of the surface and break curve parameters given the measured sherd data for all sherds in a congur ation. The assembly process starts with a fast clustering scheme which approximates the MLE solution for all sherd pairs, i.e., congur ations of size 2, us- ing a subspace of the geometric parameters, i.e., the sherd break curves. More accurate MLE values based on all pa- rameters, i.e., sherd alignments, are computed when sherd pairs are merged with other sherd congur ations. Merges take place in order of constant probability starting at the most probable congur ation. This method is robust to miss- ing sherds or groups of sherds which contain sherds from more than one pot. The system represents at least three signicant advances over previous 3D puzzle solving ap- proaches : (1) a Bayesian framework which allows for eas- ily combining diverse types of information extracted from each sherd, (2) a search which reduces comparisons on un- likely congur ations, and (3) a robust computationally rea- sonable method for aligning break curves and sherd outer surfaces simultaneously. In addition, a number of insights are given which have not previously been discussed and signicantly reduce computation. Methods proposed for (1),(2), and (3) represent important contributions to the eld of puzzle assembly, 3D geometry learning, and dataset alignment and are critical to making 3D puzzle solutions tractable to compute. Results are presented which include assembling a 13 sherd pot where only an incomplete set of 10 sherds is available. Keywords: automatic 3D puzzle assembly, 3D structure from unorganized 3D data, 3D alignment, geometric learn- ing, perceptual grouping, hierarchical clustering.
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关键词
Bayes methods,computational geometry,image matching,image segmentation,maximum likelihood estimation,pattern clustering,search problems,3D axially symmetric shapes,3D geometry learning,3D pots assembling,3D puzzle solving,Bayesian assembly,break curve parameters,clustering scheme,dataset alignment,dense sherd measurement,fast clustering schemes,geometric parameters,laser scanner,maximum likelihood estimation,optimal alignment,probability,sherd alignments,sherd break curves,sherd configurations,sherd geometric parameters
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