| 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 |
| 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 | 2013-01 |
| Publication Title | Memoirs of the Faculty of Engineering, Okayama University |
| Volume | volume47 |
| Content Type | Others |
| 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 | 10.18926/48125 |
|---|---|
| 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 |
| 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 |
| 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 | 10.18926/44495 |
|---|---|
| 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 | 10.18926/44498 |
|---|---|
| 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 | 10.18926/44500 |
|---|---|
| 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 | 10.18926/44497 |
|---|---|
| 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 |
| 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 | 10.18926/44496 |
|---|---|
| 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 | 10.18926/19953 |
|---|---|
| FullText URL | Mem_Fac_Eng_OU_44_1.pdf |
| Author | Nagai Shinji| Umeda Ryosuke| Tsuruta, Kenji| |
| Abstract | In this paper, we investigate a light-confinement phenomenon in the structure which has triangular latice composed of Double NeGative Metamaterial (DNGM). In geometrical optics consideration, this structure is expected to confine lights completely by sequential refractions in the structure. We demonstrate it by using the two dimensional finite-difference time-domain simulations. We introduce Drude-Lorentz model for dielectric and magnetic dispersion of the material at optical frequencies. We analyze quantitatively the effects of energy loss in the DNGM on the light-confinement efficiency. |
| Publication Title | Memoirs of the Faculty of Engineering, Okayama University |
| Published Date | 2010-01 |
| Volume | volume44 |
| Start Page | 1 |
| End Page | 6 |
| ISSN | 1349-6115 |
| language | 英語 |
| File Version | publisher |
| NAID | 120002309117 |
| JaLCDOI | 10.18926/19962 |
|---|---|
| FullText URL | Mem_Fac_Eng_OU_44_73.pdf |
| Author | Imanaka, Hiroyuki| Tanaka, Soukichi| Feng, Bin| Imamura, Koreyoshi| Nakanishi, Kazuhiro| |
| Abstract | We used modified Czapek-Dox (mCD) or dextrin-peptone-yeast extract (DPY) media to cultivate a filamentous fungus, Aspergillus oryzae IAM 2706 by three different cultivation methods, i.e., shaking-flask culture (SFC), agar-plate culture (APC), and membrane-surface liquid culture (MSLC), to identify the differences in cultivation behaviors and gene transcriptional profiles. The fungi cultivated by APC or MSLC secreted a greater number of different proteins/enzymes in larger quantities compared with fungi cultivated by SFC, particularly when DPY medium was used. In particular, the amounts of protease secreted by fungi cultivated via MSLC or APC were much greater compared with SFC. When mCD medium was used, α-amylase activity was barely detectable in all cultures while the activity was detected in MSLC and APC in a quantity that was several times higher than that in SFC using DPY medium. SDS-PAGE analysis and N-terminal amino acid sequences confirmed 6 proteins in the culture supernatants when DPY medium was used. Among these proteins oryzin (an alkaline protease) and α-amylase were detected at much higher levels in APC and MSLC compared with SFC, which was consistent with the measured activity of the secreted enzymes. However, when mCD medium was used, only oryzin was detected in significant amounts in MSLC and APC. Microarray analyses of the fungi cultivated by SFC, APC or MSLC using either mCD or DPY media indicated that the gene transcriptional profile of the MSLC sample was similar to that of the APC sample but different from that of the SFC sample. When mCD medium was used, most of the genes that were up-regulated 10-folds or greater in the MSLC sample relative to the SFC sample were unknown or predicted proteins. Transcription of the oryzin gene was only slightly up-regulated in the MSLC sample while transcription of the α-amylase gene was slightly down-regulated. On the other hand, when DPY medium was used, many known genes including the oryzin gene were up-regulated in the MSLC sample versus the SFC sample. |
| Publication Title | Memoirs of the Faculty of Engineering, Okayama University |
| Published Date | 2010-01 |
| Volume | volume44 |
| Start Page | 73 |
| End Page | 83 |
| ISSN | 1349-6115 |
| language | 英語 |
| File Version | publisher |
| NAID | 120002309053 |
| 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 |
| JaLCDOI | 10.18926/19958 |
|---|---|
| FullText URL | Mem_Fac_Eng_OU_44_42.pdf |
| Author | Kanatani, Kenichi| Rangrajan Prasanna| |
| Abstract | This paper presents a new method for fitting an ellipse to a point sequence extracted from images. It is widely known that the best fit is obtained by maximum likelihood. However, it requires iterations, which may not converge in the presence of large noise. Our approach is algebraic distance minimization; no iterations are required. Exploiting the fact that the solution depends on the way the scale is normalized, we analyze the accuracy to high order error terms with the scale normalization weight unspecified and determine it so that the bias is zero up to the second order. We demonstrate by experiments that our method is superior to the Taubin method, also algebraic and known to be highly accurate. |
| Publication Title | Memoirs of the Faculty of Engineering, Okayama University |
| Published Date | 2010-01 |
| Volume | volume44 |
| Start Page | 42 |
| End Page | 49 |
| ISSN | 1349-6115 |
| language | 英語 |
| File Version | publisher |
| NAID | 120002309054 |
| 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 |
