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 10.18926/48126
FullText URL mfe_046_010_020.pdf
Author Kanatani, Kenichi|
Abstract We present a new technique for calibrating ultra-wide fisheye lens cameras by imposing the constraint that collinear points be rectified to be collinear, parallel lines to be parallel, and orthogonal lines to be orthogonal. Exploiting the fact that line fitting reduces to an eigenvalue problem, we do a rigorous perturbation analysis to obtain a Levenberg-Marquardt procedure for the optimization. Doing experiments, we point out that spurious solutions exist if collinearity and parallelism alone are imposed. Our technique has many desirable properties. For example, no metric information is required about the reference pattern or the camera position, and separate stripe patterns can be displayed on a video screen to generate a virtual grid, eliminating the grid point extraction processing.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2012-01
Volume volume46
Start Page 10
End Page 20
ISSN 1349-6115
language 英語
Copyright Holders Copyright © by the authors
File Version publisher
NAID 80022451621
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 10.18926/49320
FullText URL mfe_047_001_018.pdf
Author Kanatani, Kenichi|
Abstract We summarize techniques for optimal geometric estimation from noisy observations for computer vision applications. We first discuss the interpretation of optimality and point out that geometric estimation is different from the standard statistical estimation. We also describe our noise modeling and a theoretical accuracy limit called the KCR lower bound. Then, we formulate estimation techniques based on minimization of a given cost function: least squares (LS), maximum likelihood (ML), which includes reprojection error minimization as a special case, and Sampson error minimization. We describe bundle adjustment and the FNS scheme for numerically solving them and the hyperaccurate correction that improves the accuracy of ML. Next, we formulate estimation techniques not based on minimization of any cost function: iterative reweight, renormalization, and hyper-renormalization. Finally, we show numerical examples to demonstrate that hyper-renormalization has higher accuracy than ML, which has widely been regarded as the most accurate method of all. We conclude that hyper-renormalization is robust to noise and currently is the best method.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2013-01
Volume volume47
Start Page 1
End Page 18
ISSN 1349-6115
language 英語
Copyright Holders Copyright © by the authors
File Version publisher
NAID 120005232372
JaLCDOI 10.18926/49321
FullText URL mfe_047_019_024.pdf
Author Nogami, Yasuyuki| Sumo, Taichi|
Abstract Recent efficient pairings such as Ate pairing use two efficient rational point subgroups such that π(P) = P and π(Q) = [p]Q, where π, p, P, and Q are the Frobenius map for rational point, the characteristic of definition field, and torsion points for pairing, respectively. This relation accelerates not only pairing but also pairing–related operations such as scalar multiplications. It holds in the case that the embedding degree k divides r − 1, where r is the order of torsion rational points. Thus, such a case has been well studied. Alternatively, this paper focuses on the case that the degree divides r + 1 but does not divide r − 1. Then, this paper shows a multiplicative representation for r–torsion points based on the fact that the characteristic polynomial f(π) becomes irreducible over Fr for which π also plays a role of variable.
Keywords pairing–friendly curve torsion point group structure rank
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2013-01
Volume volume47
Start Page 19
End Page 24
ISSN 1349-6115
language 英語
Copyright Holders Copyright © by the authors
File Version publisher
NAID 120005232373
JaLCDOI 10.18926/49322
FullText URL mfe_047_025_032.pdf
Author Nekado, Kenta| Takai, Yusuke| Nogami, Yasuyuki|
Abstract Pairing–based cryptosystems are well implemented with Ate–type pairing over Barreto–Naehrig (BN) curve. Then, for instance, their securities depend on the difficulty of Discrete Logarithm Problem (DLP) on the so–denoted G3 over BN curve. This paper, in order to faster solve the DLP, first proposes to utilize Gauss period Normal Basis (GNB) for Pollard’s rho method, and then considers to accelerate the solving by an adoption of lazy random walk, namely tag tracing technique proposed by Cheon et al.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2013-01
Volume volume47
Start Page 25
End Page 32
ISSN 1349-6115
language 英語
Copyright Holders Copyright © by the authors
File Version publisher
NAID 120005232374
Author Faculty of Engineering, Okayama University|
Published Date 2011-01
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Volume volume45
Content Type Others
Author Faculty of Engineering, Okayama University|
Published Date 2004-03
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Volume volume38
Issue issue1-2
Content Type Others
Author Faculty of Engineering, Okayama University|
Published Date 2004-03
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Volume volume38
Issue issue1-2
Content Type Others
Author Faculty of Engineering, Okayama University|
Published Date 2002-11
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Volume volume37
Issue issue1
Content Type Others
Author Faculty of Engineering, Okayama University|
Published Date 2002-11
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Volume volume37
Issue issue1
Content Type Others
Author Faculty of Engineering, Okayama University|
Published Date 2003-03
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Volume volume37
Issue issue2
Content Type Others
Author Faculty of Engineering, Okayama University|
Published Date 2003-03
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Volume volume37
Issue issue2
Content Type Others
Author Faculty of Engineering, Okayama University|
Published Date 2001-12
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Volume volume36
Issue issue1
Content Type Others
Author Faculty of Engineering, Okayama University|
Published Date 2001-12
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Volume volume36
Issue issue1
Content Type Others
Author Faculty of Engineering, Okayama University|
Published Date 2002-03
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Volume volume36
Issue issue2
Content Type Others
Author Faculty of Engineering, Okayama University|
Published Date 2002-03
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Volume volume36
Issue issue2
Content Type Others
Author Faculty of Engineering, Okayama University|
Published Date 2012-01
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Volume volume46
Content Type Others
Author Faculty of Engineering, Okayama University|
Published Date 2013-01
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Volume volume47
Content Type Others
JaLCDOI 10.18926/14125
FullText URL Mem_Fac_Eng_OU_40_1_78.pdf
Author Funabiki, Nobuo| Isogai, Megumi| Higashino, Teruo| Oda Masashi|
Abstract A variety of studies on face components such as eyes, lips, noses, and teeth have been proceeding in medicine, psychology, biometrics authentication, and other areas. In this paper, we present an algorithm of extracting eye contours from a face image using the deformable template matching method. Our template for an eye contour is composed of three quadratic functions for the perimeter and one circle for the pupil. In our algorithm, a digital color face image is rst converted to a binary image of representing eyes, after the region around eyes is identied on the face image by using hues and values of the color image. Then, parameters in the template are optimized by a local search method with a tabu period and a hill-climbing, so as to t the template to the eye contour in the binary image. The accuracy of our algorithm is evaluated through sample face images of students. In addition, the application of our proposal to eye shape indices is investigated in a face image database "HOIP", where recognizable dierence exists in index distributions between males and females.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2006-01
Volume volume40
Issue issue1
Start Page 78
End Page 82
ISSN 0475-0071
language 英語
File Version publisher
NAID 120002308500