出版者

Faculty of Engineering, Okayama University

雑誌

Memoirs of the Faculty of Engineering, Okayama University (ISSN:04750071)

巻号頁・発行日

vol.38, no.1, pp.39-59, 2004-03

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We investigate the meaning of "statistical methods" for geometric inference based on image feature points. Tracing back the origin of feature uncertainty to image processing operations, we discuss the implications of asymptotic analysis in reference to "geometric fitting" and "geometric model selection", We point out that a correspondence exists between the standard statistical analysis and the geometric inference problem. We also compare the capability of the "geometric AIC" and the "geometric MDL' in detecting degeneracy. Next, we review recent progress in geometric fitting techniques for linear constraints, describing the "FNS method", the "HEIV method", the "renormalization method", and other related techniques. Finally, we discuss the "Neyman-Scott problem" and "semiparametric models" in relation to geometric inference. We conclude that applications of statistical methods requires careful considerations about the nature of the problem in question.

出版者

Faculty of Engineering, Okayama University

雑誌

Memoirs of the Faculty of Engineering, Okayama University (ISSN:13496115)

巻号頁・発行日

vol.45, pp.36-45, 2011-01

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We present a new method for optimally computing the 3-D rotation from two sets of 3-D data.Unlike 2-D data, the noise in 3-D data is inherently inhomogeneous and anisotropic, reflecting the characteristics of the 3-D sensing used. To cope with this, Ohta and Kanatani introduced a technique called "renormalization". Following them, we represent a 3-D rotation in terms of a quaternion and compute an exact maximum likelihood solution using the FNS of Chojnacki etal. As an example, we consider 3-D data obtained by stereo vision and optimally compute the 3-D rotation by analyzing the noise characteristics of stereo reconstruction. We show that the widely used method is not suitable for 3-D data. We confirm that the renormalization of Ohta andKanatani indeed computes almost an optimal solution and that, although the difference is small, the proposed method can compute an even better solution.