Unified Computation of Strict Maximum Likelihood for Geometric Fitting

作者：Kanatani Kenichi^*; Sugaya Yasuyuki

来源：Journal of Mathematical Imaging and Vision, 2010, 38(1): 1-13.

DOI：10.1007/s10851-010-0206-6

• Geometric fitting
• Maximum likelihood
• Ellipse fitting
• Fundamental matrix
• Stereo image triangulation

A new numerical scheme is presented for computing strict maximum likelihood (ML) of geometric fitting problems having an implicit constraint. Our approach is orthogonal projection of observations onto a parameterized surface defined by the constraint. Assuming a linearly separable nonlinear constraint, we show that a theoretically global solution can be obtained by iterative Sampson error minimization. Our approach is illustrated by ellipse fitting and fundamental matrix computation. Our method also encompasses optimal correction, computing, e.g., perpendiculars to an ellipse and triangulating stereo images. A detailed discussion is given to technical and practical issues about our approach.

• 出版日期2010-9