19 January 2009 Unified computation of strict maximum likelihood for geometric fitting
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Abstract
A new numerical scheme is presented for strictly computing maximum likelihood (ML) of geometric fitting problems. Intensively studied in the past are those methods that first transform the data into a computationally convenient form and then assume Gaussian noise in the transformed space. In contrast, our method assumes Gaussian noise in the original data space. It is shown that the strict ML solution can be computed by iteratively using existing methods. Then, our method is applied to ellipse fitting and fundamental matrix computation. Our method is also shown to encompasses optimal correction, computing, e.g., perpendiculars to an ellipse and triangulating stereo images. While such applications have been studied individually, our method generalizes them into an application independent form from a unified point of view.
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Kenichi Kanatani, "Unified computation of strict maximum likelihood for geometric fitting", Proc. SPIE 7239, Three-Dimensional Imaging Metrology, 72390Q (19 January 2009); doi: 10.1117/12.805692; https://doi.org/10.1117/12.805692
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