Fast Multidimensional Ellipsoid-Specific Fitting by Alternating Direction Method of Multipliers
Many problems in computer vision can be formulated as multidimensional ellipsoid-specific fitting, which is to minimize the residual error such that the underlying quadratic surface is a multidimensional ellipsoid. In this paper, we present a fast and robust algorithm for solving ellipsoid-specific...
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Veröffentlicht in: | IEEE transactions on pattern analysis and machine intelligence 2016-05, Vol.38 (5), p.1021-1026 |
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Sprache: | eng |
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Zusammenfassung: | Many problems in computer vision can be formulated as multidimensional ellipsoid-specific fitting, which is to minimize the residual error such that the underlying quadratic surface is a multidimensional ellipsoid. In this paper, we present a fast and robust algorithm for solving ellipsoid-specific fitting directly. Our method is based on the alternating direction method of multipliers, which does not introduce extra positive semi-definiteness constraints. The computation complexity is thus significantly lower than those of semi-definite programming (SDP) based methods. More specifically, to fit n data points into a p dimensional ellipsoid, our complexity is O(p^6 + np^4)+O(p^3) , where the former O results from preprocessing data once , while that of the state-of-the-art SDP method is O(p^6 + np^4 + n^{\frac{3}{2}}p^2) for each iteration . The storage complexity of our algorithm is about \frac{1}{2}np^2 , which is at most 1/4 of those of SDP methods. Extensive experiments testify to the great speed and accuracy advantages of our method over the state-of-the-art approaches. The implementation of our method is also much simpler than SDP based methods. |
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ISSN: | 0162-8828 1939-3539 2160-9292 |
DOI: | 10.1109/TPAMI.2015.2469283 |