| 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 |
| 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 | 10.18926/48127 |
|---|---|
| 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 | 10.18926/48126 |
|---|---|
| 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 | 10.18926/44498 |
|---|---|
| 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 | 10.18926/44496 |
|---|---|
| フルテキストURL | mfe_045_015_026.pdf |
| 著者 | Kanatani, Kenichi| Rangrajan, Prasanna| Sugaya, Yasuyuki| Niitsuma, Hirotaka| |
| 抄録 | 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. |
| 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 | 15 |
| 終了ページ | 26 |
| 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 | 120002905952 |
| 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 | 10.18926/19956 |
|---|---|
| フルテキストURL | Mem_Fac_Eng_OU_44_24.pdf |
| 著者 | 金谷 健一| Sugaya Yasuyuki| |
| 抄録 | 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. |
| 出版物タイトル | Memoirs of the Faculty of Engineering, Okayama University |
| 発行日 | 2010-01 |
| 巻 | 44巻 |
| 開始ページ | 24 |
| 終了ページ | 31 |
| ISSN | 1349-6115 |
| 言語 | 英語 |
| 論文のバージョン | publisher |
| NAID | 120002309159 |
| JaLCDOI | 10.18926/19955 |
|---|---|
| フルテキストURL | Mem_Fac_Eng_OU_44_13.pdf |
| 著者 | 金谷 健一| Sugaya Yasuyuki| |
| 抄録 | 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. |
| 出版物タイトル | Memoirs of the Faculty of Engineering, Okayama University |
| 発行日 | 2010-01 |
| 巻 | 44巻 |
| 開始ページ | 13 |
| 終了ページ | 23 |
| ISSN | 1349-6115 |
| 言語 | 英語 |
| 論文のバージョン | publisher |
| NAID | 120002309170 |
| JaLCDOI | 10.18926/19958 |
|---|---|
| フルテキストURL | Mem_Fac_Eng_OU_44_42.pdf |
| 著者 | 金谷 健一| Rangrajan Prasanna| |
| 抄録 | 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. |
| 出版物タイトル | Memoirs of the Faculty of Engineering, Okayama University |
| 発行日 | 2010-01 |
| 巻 | 44巻 |
| 開始ページ | 42 |
| 終了ページ | 49 |
| ISSN | 1349-6115 |
| 言語 | 英語 |
| 論文のバージョン | publisher |
| NAID | 120002309054 |
| JaLCDOI | 10.18926/19959 |
|---|---|
| フルテキストURL | Mem_Fac_Eng_OU_44_50.pdf |
| 著者 | 金谷 健一| Niitsuma Hirotaka| Rangrajan Prasanna| |
| 抄録 | 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. |
| 出版物タイトル | Memoirs of the Faculty of Engineering, Okayama University |
| 発行日 | 2010-01 |
| 巻 | 44巻 |
| 開始ページ | 50 |
| 終了ページ | 59 |
| ISSN | 1349-6115 |
| 言語 | 英語 |
| 論文のバージョン | publisher |
| NAID | 120002308986 |
| JaLCDOI | 10.18926/19957 |
|---|---|
| フルテキストURL | Mem_Fac_Eng_OU_44_32.pdf |
| 著者 | 金谷 健一| Niitsuma Hirotaka| Sugaya Yasuyuki| |
| 抄録 | 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. |
| 出版物タイトル | Memoirs of the Faculty of Engineering, Okayama University |
| 発行日 | 2010-01 |
| 巻 | 44巻 |
| 開始ページ | 32 |
| 終了ページ | 41 |
| ISSN | 1349-6115 |
| 言語 | 英語 |
| 論文のバージョン | publisher |
| NAID | 120002309124 |
| JaLCDOI | 10.18926/14056 |
|---|---|
| フルテキストURL | Mem_Fac_Eng_OU_42_18.pdf |
| 著者 | 金谷 健一| Yasuyuki Sugaya| |
| 抄録 | We classify and review existing algorithms for computing the fundamental matrix from point correspondences and propose new effective schemes: 7-parameter Levenberg-Marquardt (LM) search, EFNS, and EFNS-based bundle adjustment. Doing experimental comparison, we show that EFNS and the 7-parameter LM search exhibit the best performance and that additional bundle adjustment does not increase the accuracy to any noticeable degree. |
| 出版物タイトル | Memoirs of the Faculty of Engineering, Okayama University |
| 発行日 | 2008-01 |
| 巻 | 42巻 |
| 号 | 1号 |
| 開始ページ | 18 |
| 終了ページ | 35 |
| ISSN | 0475-0071 |
| 言語 | 英語 |
| 論文のバージョン | publisher |
| NAID | 120002308468 |
| JaLCDOI | 10.18926/14055 |
|---|---|
| フルテキストURL | Mem_Fac_Eng_OU_42_10.pdf |
| 著者 | 金谷 健一| |
| 抄録 | The author introduced the "geometric AIC" and the "geometric MDL" as model selection criteria for geometric fitting problems. These correspond to Akaike’s "AIC" and Rissanen's "BIC", respectively, well known in the statistical estimation framework. Another criterion well known is Schwarz’ "BIC", but its counterpart for geometric fitting has been unknown. This paper introduces the corresponding criterion, which we call the "geometric BIC", and shows that it is of the same form as the geometric MDL. We present the underlying logical reasoning of Bayesian estimation. |
| 出版物タイトル | Memoirs of the Faculty of Engineering, Okayama University |
| 発行日 | 2008-01 |
| 巻 | 42巻 |
| 号 | 1号 |
| 開始ページ | 10 |
| 終了ページ | 17 |
| ISSN | 0475-0071 |
| 言語 | 英語 |
| 論文のバージョン | publisher |
| NAID | 120002308447 |
| JaLCDOI | 10.18926/14087 |
|---|---|
| フルテキストURL | Mem_Fac_Eng_OU_41_1_73.pdf |
| 著者 | 金谷 健一| |
| 抄録 | A rigorous accuracy analysis is given to various techniques for estimating parameters of geometric models from noisy data for computer vision applications. First, it is pointed out that parameter estimation for vision applications is very different in nature from traditional statistical analysis and hence a different mathematical framework is necessary in such a domain. After general theories on estimation and accuracy are given, typical existing techniques are selected, and their accuracy is evaluated up to higher order terms. This leads to a “hyperaccurate” method that outperforms existing methods. |
| 出版物タイトル | Memoirs of the Faculty of Engineering, Okayama University |
| 発行日 | 2007-01 |
| 巻 | 41巻 |
| 号 | 1号 |
| 開始ページ | 73 |
| 終了ページ | 92 |
| ISSN | 0475-0071 |
| 言語 | 英語 |
| 論文のバージョン | publisher |
| NAID | 120002308410 |
| JaLCDOI | 10.18926/14086 |
|---|---|
| フルテキストURL | Mem_Fac_Eng_OU_41_1_63.pdf |
| 著者 | 金谷 健一| 菅谷 保之| |
| 抄録 | The convergence performance of typical numerical schemes for geometric fitting for computer vision applications is compared. First, the problem and the associated KCR lower bound are stated. Then, three well known fitting algorithms are described: FNS, HEIV, and renormalization. To these, we add a special variant of Gauss-Newton iterations. For initialization of iterations, random choice, least squares, and Taubin’s method are tested. Numerical simulations and real image experiments and conducted for fundamental matrix computation and ellipse fitting, which reveals different characteristics of each method. |
| 出版物タイトル | Memoirs of the Faculty of Engineering, Okayama University |
| 発行日 | 2007-01 |
| 巻 | 41巻 |
| 号 | 1号 |
| 開始ページ | 63 |
| 終了ページ | 72 |
| ISSN | 0475-0071 |
| 言語 | 英語 |
| 論文のバージョン | publisher |
| NAID | 120002308585 |
| JaLCDOI | 10.18926/14123 |
|---|---|
| フルテキストURL | Mem_Fac_Eng_OU_40_1_53.pdf |
| 著者 | 金谷 健一| 菅谷 保之| Hanno Ackermann| |
| 抄録 | In order to reconstruct 3-D Euclidean shape by the Tomasi-Kanade factorization, one needs to specify an affine camera model such as orthographic, weak perspective, and paraperspective. We present a new method that does not require any such specific models. We show that a minimal requirement for an affine camera to mimic perspective projection leads to a unique camera model, which we call a symmetric affine camera, which has two free functions. We determine their values from input images by linear computation and demonstrate by experiments that an appropriate camera model is automatically selected. |
| 出版物タイトル | Memoirs of the Faculty of Engineering, Okayama University |
| 発行日 | 2006-01 |
| 巻 | 40巻 |
| 号 | 1号 |
| 開始ページ | 53 |
| 終了ページ | 63 |
| ISSN | 0475-0071 |
| 言語 | 英語 |
| 論文のバージョン | publisher |
| NAID | 120002308664 |
| JaLCDOI | 10.18926/14124 |
|---|---|
| フルテキストURL | Mem_Fac_Eng_OU_40_1_64.pdf |
| 著者 | 金谷 健一| |
| 抄録 | This article summarizes recent advancements of the theories and techniques for 3-D reconstruction from multiple images. We start with the description of the camera imaging geometry as perspective projection in terms of homogeneous coordinates and the definition of the intrinsic and extrinsic parameters of the camera. Next, we described the epipolar geometry for two, three, and four cameras, introducing such concepts as the fundamental matrix, epipolars, epipoles, the trifocal tensor, and the quadrifocal tensor. Then, we present the self-calibration technique based on the stratified reconstruction approach, using the absolute dual quadric constraint. Finally, we give the definition of the affine camera model and a procedure for 3-D reconstruction based on it. |
| 出版物タイトル | Memoirs of the Faculty of Engineering, Okayama University |
| 発行日 | 2006-01 |
| 巻 | 40巻 |
| 号 | 1号 |
| 開始ページ | 64 |
| 終了ページ | 77 |
| ISSN | 0475-0071 |
| 言語 | 英語 |
| 論文のバージョン | publisher |
| NAID | 120002308332 |
| JaLCDOI | 10.18926/14122 |
|---|---|
| フルテキストURL | Mem_Fac_Eng_OU_40_1_44.pdf |
| 著者 | 菅谷 保之| 金谷 健一| 金沢 靖| |
| 抄録 | Dense point matches are generated over two images by rectifying the two images to align epipolar lines horizontally, and horizontally sliding a template. To overcome inherent limitations of 2-D search, we incorporate the “naturalness of the 3-D shape” implied by the resulting matches. After stating our rectification procedure, we introduce our multi-scale template matching scheme and our outlier removal technique using tentatively reconstructed 3-D shapes. Doing real image experiments, we discuss the performance of our method and remaining issues. |
| 出版物タイトル | Memoirs of the Faculty of Engineering, Okayama University |
| 発行日 | 2006-01 |
| 巻 | 40巻 |
| 号 | 1号 |
| 開始ページ | 44 |
| 終了ページ | 52 |
| ISSN | 0475-0071 |
| 言語 | 英語 |
| 論文のバージョン | publisher |
| NAID | 120002308593 |
| 著者 | Kanatani, Kenichi| |
|---|---|
| 発行日 | 2005-6 |
| 出版物タイトル | Proceedings of the Fifth International Conference on 3-D Digital Imaging and Modeling |
| 資料タイプ | 会議発表論文 |