| JaLCDOI | 10.18926/44497 |
|---|---|
| フルテキストURL | mfe_045_027_036.pdf |
| 著者 | Kanatani, Kenichi| Sugaya, Yasuyuki| |
| 抄録 | 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. |
| 出版物タイトル | Memoirs of the Faculty of Engineering, Okayama University |
| 発行日 | 2011-01 |
| 巻 | 45巻 |
| 開始ページ | 27 |
| 終了ページ | 35 |
| ISSN | 1349-6115 |
| 言語 | 英語 |
| 著作権者 | Copyright © by the authors |
| 論文のバージョン | publisher |
| NAID | 80021759249 |
| 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 |
| 巻 | 45巻 |
| 開始ページ | 36 |
| 終了ページ | 45 |
| ISSN | 1349-6115 |
| 言語 | 英語 |
| 著作権者 | Copyright © by the authors |
| 論文のバージョン | publisher |
| NAID | 80021759250 |
| JaLCDOI | 10.18926/44499 |
|---|---|
| フルテキストURL | mfe_045_046_053.pdf |
| 著者 | Nogami, Yasuyuki| Yanagi, Erika| Izuta, Tetsuya| Morikawa, Yoshitaka| |
| 抄録 | 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. |
| 出版物タイトル | Memoirs of the Faculty of Engineering, Okayama University |
| 発行日 | 2011-01 |
| 巻 | 45巻 |
| 開始ページ | 46 |
| 終了ページ | 53 |
| ISSN | 1349-6115 |
| 言語 | 英語 |
| 著作権者 | Copyright © by the authors |
| 論文のバージョン | publisher |
| NAID | 120002905955 |
| JaLCDOI | 10.18926/44500 |
|---|---|
| フルテキストURL | mfe_045_054_059.pdf |
| 著者 | Nekado, Kenta| Takai, Yusuke| Nogami, Yasuyuki| Morikawa, Yoshitaka| |
| 抄録 | 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. |
| 出版物タイトル | Memoirs of the Faculty of Engineering, Okayama University |
| 発行日 | 2011-01 |
| 巻 | 45巻 |
| 開始ページ | 54 |
| 終了ページ | 59 |
| ISSN | 1349-6115 |
| 言語 | 英語 |
| 著作権者 | Copyright © by the authors |
| 論文のバージョン | publisher |
| NAID | 80021759252 |
| 著者 | Faculty of Engineering, Okayama University| |
|---|---|
| 発行日 | 2012-01 |
| 出版物タイトル | Memoirs of the Faculty of Engineering, Okayama University |
| 巻 | 46巻 |
| 資料タイプ | その他 |
| JaLCDOI | 10.18926/48126 |
|---|---|
| フルテキストURL | mfe_046_010_020.pdf |
| 著者 | Kanatani, Kenichi| |
| 抄録 | 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. |
| 出版物タイトル | Memoirs of the Faculty of Engineering, Okayama University |
| 発行日 | 2012-01 |
| 巻 | 46巻 |
| 開始ページ | 10 |
| 終了ページ | 20 |
| ISSN | 1349-6115 |
| 言語 | 英語 |
| 著作権者 | Copyright © by the authors |
| 論文のバージョン | publisher |
| NAID | 80022451621 |
| 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 |
| 巻 | 46巻 |
| 開始ページ | 21 |
| 終了ページ | 33 |
| ISSN | 1349-6115 |
| 言語 | 英語 |
| 著作権者 | Copyright © by the authors |
| 論文のバージョン | publisher |
| NAID | 80022451622 |
| 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 |
| 巻 | 46巻 |
| 開始ページ | 1 |
| 終了ページ | 9 |
| ISSN | 1349-6115 |
| 言語 | 英語 |
| 著作権者 | Copyright © by the authors |
| 論文のバージョン | publisher |
| NAID | 80022451620 |
| JaLCDOI | 10.18926/49321 |
|---|---|
| フルテキストURL | mfe_047_019_024.pdf |
| 著者 | Nogami, Yasuyuki| Sumo, Taichi| |
| 抄録 | 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. |
| キーワード | pairing–friendly curve torsion point group structure rank |
| 出版物タイトル | Memoirs of the Faculty of Engineering, Okayama University |
| 発行日 | 2013-01 |
| 巻 | 47巻 |
| 開始ページ | 19 |
| 終了ページ | 24 |
| ISSN | 1349-6115 |
| 言語 | 英語 |
| 著作権者 | Copyright © by the authors |
| 論文のバージョン | publisher |
| NAID | 120005232373 |
| JaLCDOI | 10.18926/49320 |
|---|---|
| フルテキストURL | mfe_047_001_018.pdf |
| 著者 | Kanatani, Kenichi| |
| 抄録 | 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. |
| 出版物タイトル | Memoirs of the Faculty of Engineering, Okayama University |
| 発行日 | 2013-01 |
| 巻 | 47巻 |
| 開始ページ | 1 |
| 終了ページ | 18 |
| ISSN | 1349-6115 |
| 言語 | 英語 |
| 著作権者 | Copyright © by the authors |
| 論文のバージョン | publisher |
| NAID | 120005232372 |
| 著者 | Faculty of Engineering, Okayama University| |
|---|---|
| 発行日 | 2013-01 |
| 出版物タイトル | Memoirs of the Faculty of Engineering, Okayama University |
| 巻 | 47巻 |
| 資料タイプ | その他 |
| JaLCDOI | 10.18926/49322 |
|---|---|
| フルテキストURL | mfe_047_025_032.pdf |
| 著者 | Nekado, Kenta| Takai, Yusuke| Nogami, Yasuyuki| |
| 抄録 | 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. |
| 出版物タイトル | Memoirs of the Faculty of Engineering, Okayama University |
| 発行日 | 2013-01 |
| 巻 | 47巻 |
| 開始ページ | 25 |
| 終了ページ | 32 |
| ISSN | 1349-6115 |
| 言語 | 英語 |
| 著作権者 | Copyright © by the authors |
| 論文のバージョン | publisher |
| NAID | 120005232374 |