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Medial Spheres for Shape Approximation
June 2012 (vol. 34 no. 6)
pp. 1234-1240
P. Kry, Sch. of Comput. Sci., McGill Univ., Montreal, QC, Canada
S. Stolpner, Sch. of Comput. Sci., McGill Univ., Montreal, QC, Canada
K. Siddiqi, Sch. of Comput. Sci., McGill Univ., Montreal, QC, Canada
We study the problem of approximating a 3D solid with a union of overlapping spheres. In comparison with a state-of-the-art approach, our method offers more than an order of magnitude speedup and achieves a tighter approximation in terms of volume difference with the original solid while using fewer spheres. The spheres generated by our method are internal and tangent to the solid's boundary, which permits an exact error analysis, fast updates under local feature size preserving deformation, and conservative dilation. We show that our dilated spheres offer superior time and error performance in approximate separation distance tests than the state-of-the-art method for sphere set approximation for the class of (σ, θ)-fat solids. We envision that our sphere-based approximation will also prove useful for a range of other applications, including shape matching and shape segmentation.

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Index Terms:
solid modelling,error analysis,image matching,image segmentation,shape recognition,shape segmentation,medial spheres,shape approximation,3D solid approximation,overlapping sphere union,volume difference,solid boundary tangent,error analysis,local feature size preserving deformation,conservative dilation,dilated spheres,time performance,error performance,approximate separation distance test,fat solid,sphere-based set approximation,shape matching,Approximation methods,Solids,Shape,Three dimensional displays,Volume measurement,Measurement uncertainty,Upper bound,sphere-based representations.,Medial axis,shape approximation
Citation:
P. Kry, S. Stolpner, K. Siddiqi, "Medial Spheres for Shape Approximation," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 34, no. 6, pp. 1234-1240, June 2012, doi:10.1109/TPAMI.2011.254
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