JaLCDOI 10.18926/19957
フルテキストURL Mem_Fac_Eng_OU_44_32.pdf
著者 金谷 健一| Niitsuma Hirotaka| Sugaya Yasuyuki|
抄録 We present an alternative approach to what we call the “standard optimization”, which minimizes a cost function by searching a parameter space. Instead, the input is “orthogonally projected” in the joint input space onto the manifold defined by the “consistency constraint”, which demands that any minimal subset of observations produce the same result. This approach avoids many difficulties encountered in the standard optimization. As typical examples, we apply it to line fitting and multiview triangulation. The latter produces a new algorithm far more efficient than existing methods. We also discuss optimality of our approach.
出版物タイトル Memoirs of the Faculty of Engineering, Okayama University
発行日 2010-01
44巻
開始ページ 32
終了ページ 41
ISSN 1349-6115
言語 English
論文のバージョン publisher
NAID 120002309124
JaLCDOI 10.18926/19959
フルテキストURL Mem_Fac_Eng_OU_44_50.pdf
著者 金谷 健一| Niitsuma Hirotaka| Rangrajan Prasanna|
抄録 We present highly accurate least-squares (LS) alternatives to the theoretically optimal maximum likelihood (ML) estimator for homographies between two images. Unlike ML, our estimators are non-iterative and yield solutions even in the presence of large noise. By rigorous error analysis, we derive a “hyperaccurate” estimator which is unbiased up to second order noise terms. Then, we introduce a computational simplification, which we call “Taubin approximation”, without incurring a loss in accuracy. We experimentally demonstrate that our estimators have accuracy surpassing the traditional LS estimator and comparable to the ML estimator.
出版物タイトル Memoirs of the Faculty of Engineering, Okayama University
発行日 2010-01
44巻
開始ページ 50
終了ページ 59
ISSN 1349-6115
言語 English
論文のバージョン publisher
NAID 120002308986
JaLCDOI 10.18926/44496
フルテキストURL mfe_045_015_026.pdf
著者 Kanatani, Kenichi| Rangrajan, Prasanna| Sugaya, Yasuyuki| Niitsuma, Hirotaka|
抄録 We present a new least squares (LS) estimator, called “HyperLS”, specifically designed for parameter estimation in computer vision applications. It minimizes the algebraic distance under a special scale normalization, which is derived by rigorous error analysis in such a way that statistical bias is removed up to second order noise terms. Numerical experiments suggest that our HyperLS is far superior to the standard LS and comparable in accuracy to maximum likelihood (ML), which is known to produce highly accurate results in image applications but may fail to converge if poorly initialized. Our HyperLS is a perfect candidate for ML initialization. In addition, we discuss how image-based inference problems have different characteristics form conventional statistical applications, with a view to serving as a bridge between mathematicians and computer engineers.
出版物タイトル Memoirs of the Faculty of Engineering, Okayama University
発行日 2011-01
45巻
開始ページ 15
終了ページ 26
ISSN 1349-6115
言語 English
著作権者 Copyright © by the authors
論文のバージョン publisher
NAID 120002905952
JaLCDOI 10.18926/44498
フルテキストURL mfe_045_036_045.pdf
著者 Kanatani, Kenichi| Niitsuma, Hirotaka|
抄録 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 et al. 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 and Kanatani indeed computes almost an optimal solution and that, although the difference is small, the proposed method can compute an even better solution.
出版物タイトル Memoirs of the Faculty of Engineering, Okayama University
発行日 2011-01
45巻
開始ページ 36
終了ページ 45
ISSN 1349-6115
言語 English
著作権者 Copyright © by the authors
論文のバージョン publisher
NAID 80021759250
JaLCDOI 10.18926/48125
フルテキストURL mfe_046_001_009.pdf
著者 Kanatani, Kenichi| Niitsuma, Hirotaka|
抄録 We optimally estimate the similarity (rotation, translation, and scale change) between two sets of 3-D data in the presence of inhomogeneous and anisotropic noise. Adopting the Lie algebra representation of the 3-D rotational change, we derive the Levenberg-Marquardt procedure for simultaneously optimizing the rotation, the translation, and the scale change. We test the performance of our method using simulated stereo data and real GPS geodetic sensing data. We conclude that the conventional method assuming homogeneous and isotropic noise is insufficient and that our simultaneous optimization scheme can produce an accurate solution.
出版物タイトル Memoirs of the Faculty of Engineering, Okayama University
発行日 2012-01
46巻
開始ページ 1
終了ページ 9
ISSN 1349-6115
言語 English
著作権者 Copyright © by the authors
論文のバージョン publisher
NAID 80022451620
JaLCDOI 10.18926/48127
フルテキストURL mfe_046_021_033.pdf
著者 Kanatani, Kenichi| Niitsuma, Hirotaka|
抄録 Because 3-D data are acquired using 3-D sensing such as stereo vision and laser range finders, they have inhomogeneous and anisotropic noise. This paper studies optimal computation of the similarity (rotation, translation, and scale change) of such 3-D data. We first point out that the Gauss-Newton and the Gauss-Helmert methods, regarded as different techniques, have similar structures. We then combine them to define what we call the modified Gauss-Helmert method and do stereo vision simulation to show that it is superior to either of the two in convergence performance. Finally, we show an application to real GPS geodetic data and point out that the widely used homogeneous and isotropic noise model is insufficient and that GPS geodetic data are prone to numerical problems.
出版物タイトル Memoirs of the Faculty of Engineering, Okayama University
発行日 2012-01
46巻
開始ページ 21
終了ページ 33
ISSN 1349-6115
言語 English
著作権者 Copyright © by the authors
論文のバージョン publisher
NAID 80022451622