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 10.18926/49322
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 2013-01
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Volume volume47
Content Type Others
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
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
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 10.18926/48126
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 10.18926/48125
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 10.18926/44495
FullText URL mfe_045_001_014.pdf
Author Akiyoshi, Tatsuro| Imai, Jun| Konishi, Masami|
Abstract This paper presents a method of the controller design for the handling machine by using dsPIC(Digital Signal Processor + Peripheral Interface Controller). Recently, many manufacturing robots are operated in manufacturing facilities, with the aim of labor, cost saving, and improvement of the productivity. Such robots need to have positioning performance of high precision and simultaneously to save cost. In this paper, a digital optimal servo controller is designed, and it is implemented into our barebones controller which involves dsPIC. We have designed and manufactured the controller which is added suitable peripherals to improve the consistency between the mechanical machine operating in continuous time and controller in discrete time. The significance of this research is that digital implementation of the embedded system which has performance-limitation has ensured a comparable result, against the one with PC which has broad utility. When it is used as a controller, it is possible to restrain product prices greatly equivalent PC precision. We demonstrate potential that good control can be achieved even with low cost. Our research has lead to the viability of lower cost and higher performance system for the production process at factories.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2011-01
Volume volume45
Start Page 1
End Page 14
ISSN 1349-6115
language 英語
Copyright Holders Copyright © by the authors
File Version publisher
NAID 120002905951
JaLCDOI 10.18926/44499
FullText URL mfe_045_046_053.pdf
Author Nogami, Yasuyuki| Yanagi, Erika| Izuta, Tetsuya| Morikawa, Yoshitaka|
Abstract Recently, composite order pairing–based cryptographies have received much attention. The composite order needs to be as large as the RSA modulus. Thus, they require a certain pairing–friendly elliptic curve that has such a large composite order. This paper proposes an efficient algorithm for generating an ordinary pairing–friendly elliptic curve of the embedding degree 1 whose order has two large prime factors as the RSA modulus. In addition, the generated pairing–friendly curve has an efficient structure for the Gallant–Lambert–Vanstone (GLV) method.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2011-01
Volume volume45
Start Page 46
End Page 53
ISSN 1349-6115
language 英語
Copyright Holders Copyright © by the authors
File Version publisher
NAID 120002905955
JaLCDOI 10.18926/44500
FullText URL mfe_045_054_059.pdf
Author Nekado, Kenta| Takai, Yusuke| Nogami, Yasuyuki| Morikawa, Yoshitaka|
Abstract Recently, pairing–based cryptographies have attracted much attention. For fast pairing calculation, not only pairing algorithms but also arithmetic operations in extension field should be efficient. Especially for final exponentiation included in pairing calculation, squaring is more important than multiplication. This paper considers squaring algorithms efficient for cubic extension field which is often used for pairing implementaions.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2011-01
Volume volume45
Start Page 54
End Page 59
ISSN 1349-6115
language 英語
Copyright Holders Copyright © by the authors
File Version publisher
NAID 80021759252
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 10.18926/44497
FullText URL mfe_045_027_036.pdf
Author Kanatani, Kenichi| Sugaya, Yasuyuki|
Abstract We describe in detail the algorithm of bundle adjustment for 3-D reconstruction from multiple images based on our latest research results. The main focus of this paper is on the handling of camera rotations and the efficiency of computation and memory usage when the number of variables is very large; an appropriate consideration of this is the core of the implementation of bundle adjustment. Computing the fundamental matrix from two views and reconstructing the 3-D structure from multiple views, we evaluate the performance of our algorithm and discuses technical issues of bundle adjustment implementation.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2011-01
Volume volume45
Start Page 27
End Page 35
ISSN 1349-6115
language 英語
Copyright Holders Copyright © by the authors
File Version publisher
NAID 80021759249
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
JaLCDOI 10.18926/19960
FullText URL Mem_Fac_Eng_OU_44_60.pdf
Author Nogami, Yasuyuki| Morikawa, Yoshitaka|
Abstract This paper proposes a method for generating a certain composite order ordinary pairing–friendly elliptic curve of embedding degree 3. In detail, the order has two large prime factors such as the modulus of RSA cryptography. The method is based on the property that the order of the target pairing–friendly curve is given by a polynomial as r(X) of degree 2 with respect to the integer variable X. When the bit size of the prime factors is about 500 bits, the proposed method averagely takes about 15 minutes on Core 2 Quad (2.66Hz) for generating one.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2010-01
Volume volume44
Start Page 60
End Page 68
ISSN 1349-6115
language 英語
File Version publisher
NAID 120002309063
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 10.18926/19961
FullText URL Mem_Fac_Eng_OU_44_69.pdf
Author Nekado, Kenta| Kato, Hidehiro| Nogami, Yasuyuki| Morikawa, Yoshitaka|
Abstract Recently, pairing–based cryptographies have attracted much attention. For fast pairing calculation, not only pairing algorithms but also arithmetic operations in extension field should be efficient. Especially for final exponentiation included in pairing calculation, squaring is more important than multiplication. This paper proposes an efficient squaring algorithm in extension field for Freeman curve.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2010-01
Volume volume44
Start Page 69
End Page 72
ISSN 1349-6115
language 英語
File Version publisher
NAID 120002309070
JaLCDOI 10.18926/19956
FullText URL Mem_Fac_Eng_OU_44_24.pdf
Author Kanatani, Kenichi| Sugaya Yasuyuki|
Abstract We present an improved version of the MSL method of Sugaya and Kanatani for multibody motion segmentation. We replace their initial segmentation based on heuristic clustering by an analytical computation based on GPCA, fitting two 2-D affine spaces in 3-D by the Taubin method. This initial segmentation alone can segment most of the motions in natural scenes fairly correctly, and the result is successively optimized by the EM algorithm in 3-D, 5-D, and 7-D. Using simulated and real videos, we demonstrate that our method outperforms the previous MSL and other existing methods. We also illustrate its mechanism by our visualization technique.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2010-01
Volume volume44
Start Page 24
End Page 31
ISSN 1349-6115
language 英語
File Version publisher
NAID 120002309159
JaLCDOI 10.18926/19955
FullText URL Mem_Fac_Eng_OU_44_13.pdf
Author Kanatani, Kenichi| Sugaya Yasuyuki|
Abstract 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.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2010-01
Volume volume44
Start Page 13
End Page 23
ISSN 1349-6115
language 英語
File Version publisher
NAID 120002309170