JaLCDOI 10.18926/48127
FullText URL mfe_046_021_033.pdf
Author Kanatani, Kenichi| Niitsuma, Hirotaka|
Abstract 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.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2012-01
Volume volume46
Start Page 21
End Page 33
ISSN 1349-6115
language 英語
Copyright Holders Copyright © by the authors
File Version publisher
NAID 80022451622
JaLCDOI 10.18926/48125
FullText URL mfe_046_001_009.pdf
Author Kanatani, Kenichi| Niitsuma, Hirotaka|
Abstract 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.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2012-01
Volume volume46
Start Page 1
End Page 9
ISSN 1349-6115
language 英語
Copyright Holders Copyright © by the authors
File Version publisher
NAID 80022451620
JaLCDOI 10.18926/44498
FullText URL mfe_045_036_045.pdf
Author Kanatani, Kenichi| Niitsuma, Hirotaka|
Abstract 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.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2011-01
Volume volume45
Start Page 36
End Page 45
ISSN 1349-6115
language 英語
Copyright Holders Copyright © by the authors
File Version publisher
NAID 80021759250
JaLCDOI 10.18926/44496
FullText URL mfe_045_015_026.pdf
Author Kanatani, Kenichi| Rangrajan, Prasanna| Sugaya, Yasuyuki| Niitsuma, Hirotaka|
Abstract 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.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2011-01
Volume volume45
Start Page 15
End Page 26
ISSN 1349-6115
language 英語
Copyright Holders Copyright © by the authors
File Version publisher
NAID 120002905952
JaLCDOI 10.18926/19959
FullText URL Mem_Fac_Eng_OU_44_50.pdf
Author Kanatani, Kenichi| Niitsuma Hirotaka| Rangrajan Prasanna|
Abstract 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.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2010-01
Volume volume44
Start Page 50
End Page 59
ISSN 1349-6115
language 英語
File Version publisher
NAID 120002308986
JaLCDOI 10.18926/19957
FullText URL Mem_Fac_Eng_OU_44_32.pdf
Author Kanatani, Kenichi| Niitsuma Hirotaka| Sugaya Yasuyuki|
Abstract 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.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2010-01
Volume volume44
Start Page 32
End Page 41
ISSN 1349-6115
language 英語
File Version publisher
NAID 120002309124