| 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 | English |
| File Version | publisher |
| NAID | 120002309170 |
| 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 | English |
| File Version | publisher |
| NAID | 120002309159 |
| JaLCDOI | 10.18926/19957 |
|---|---|
| FullText URL | Mem_Fac_Eng_OU_44_32.pdf |
| Author | Kanatani, Kenichi| Niitsuma Hirotaka| Sugaya Yasuyuki| |
| Abstract | 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. |
| Publication Title | Memoirs of the Faculty of Engineering, Okayama University |
| Published Date | 2010-01 |
| Volume | volume44 |
| Start Page | 32 |
| End Page | 41 |
| ISSN | 1349-6115 |
| language | English |
| File Version | publisher |
| NAID | 120002309124 |
| 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 | English |
| 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 | English |
| File Version | publisher |
| NAID | 120002308986 |
| JaLCDOI | 10.18926/46952 |
|---|---|
| FullText URL | mfe_38_1-2_039_059.pdf |
| Author | Kanatani, Kenichi| |
| Abstract | We investigate the meaning of "statistical methods" for geometric inference based on image feature points. Tracing back the origin of feature uncertainty to image processing operations, we discuss the implications of asymptotic analysis in reference to "geometric fitting" and "geometric model selection", We point out that a correspondence exists between the standard statistical analysis and the geometric inference problem. We also compare the capability of the "geometric AIC" and the "geometric MDL' in detecting degeneracy. Next, we review recent progress in geometric fitting techniques for linear constraints, describing the "FNS method", the "HEIV method", the "renormalization method", and other related techniques. Finally, we discuss the "Neyman-Scott problem" and "semiparametric models" in relation to geometric inference. We conclude that applications of statistical methods requires careful considerations about the nature of the problem in question. |
| Publication Title | Memoirs of the Faculty of Engineering, Okayama University |
| Published Date | 2004-03 |
| Volume | volume38 |
| Issue | issue1-2 |
| Start Page | 39 |
| End Page | 59 |
| ISSN | 0475-0071 |
| language | English |
| File Version | publisher |
| NAID | 80016889442 |
| JaLCDOI | 10.18926/46953 |
|---|---|
| FullText URL | mfe_38_1-2_061_071.pdf |
| Author | Kanatani, Kenichi| Sugaya, Yasuyuki| |
| Abstract | The Tomasi-Kanade factorization for reconstructing the 3-D shape of the feature points tracked through a video stream is widely regarded as based on factorization of a matrix by SVD (singular value decomposition). This paper points out that the core principle is the affine camera approximation to the imaging geometry and that SVD is merely one means of numerical computation. We first describe the geometric structure of the problem and then give a complete programming scheme for 3-D reconstruction. |
| Publication Title | Memoirs of the Faculty of Engineering, Okayama University |
| Published Date | 2004-03 |
| Volume | volume38 |
| Issue | issue1-2 |
| Start Page | 61 |
| End Page | 71 |
| ISSN | 0475-0071 |
| language | English |
| File Version | publisher |
| NAID | 80016889443 |
| JaLCDOI | 10.18926/46969 |
|---|---|
| FullText URL | mfe_37_1_015_023.pdf |
| Author | Kanatani, Kenichi| |
| Abstract | In order to facilitate smooth communications with researchers in other fields including statistics, this paper investigates the meaning of "statistical methods" for geometric inference based on image feature points, We point out that statistical analysis does not make sense unless the underlying "statistical ensemble" is clearly defined. We trace back the origin of feature uncertainty to image processing operations for computer vision in general and discuss the implications of asymptotic analysis for performance evaluation in reference to "geometric fitting", "geometric model selection", the "geometric AIC", and the "geometric MDL". Referring to such statistical concepts as "nuisance parameters", the "Neyman-Scott problem", and "semiparametric models", we point out that simulation experiments for performance evaluation will lose meaning without carefully considering the assumptions involved and intended applications. |
| Publication Title | Memoirs of the Faculty of Engineering, Okayama University |
| Published Date | 2002-11 |
| Volume | volume37 |
| Issue | issue1 |
| Start Page | 15 |
| End Page | 23 |
| ISSN | 0475-0071 |
| language | English |
| File Version | publisher |
| NAID | 80015664455 |
| JaLCDOI | 10.18926/46970 |
|---|---|
| FullText URL | mfe_37_1_025_032.pdf |
| Author | Kanazawa, Yasushi| Kanatani, Kenichi| |
| Abstract | We present a new method for detecting point matches between two images without using any combinatorial search. Our strategy is to impose various local and non-local constraints as "soft" constraints by introducing their "confidence" measures via "mean-field approximations". The computation is a cascade of evaluating the confidence values and sorting according to them. In the end, we impose the "hard" epipolar constraint by RANSAC. We also introduce a model selection procedure to test if the image mapping can be regarded as a homography. We demonstrate the effectiveness of our method by real image examples. |
| Publication Title | Memoirs of the Faculty of Engineering, Okayama University |
| Published Date | 2002-11 |
| Volume | volume37 |
| Issue | issue1 |
| Start Page | 25 |
| End Page | 32 |
| ISSN | 0475-0071 |
| language | English |
| File Version | publisher |
| NAID | 80015664456 |
| JaLCDOI | 10.18926/46971 |
|---|---|
| FullText URL | mfe_37_1_041_049.pdf |
| Author | Sugaya, Yasuyuki| Kanatani, Kenichi| |
| Abstract | We study the problem of segmenting independently moving objects in a video sequence. Several algorithms exist for classifying the trajectories of the feature points into independent motions, but the performance depends on the validity of the underlying camera imaging model. In this paper, we present a scheme for automatically selecting the best model using the geometric AIC before the segmentation stage, Using real video sequences, we confirm that the segmentation accuracy indeed improves if the segmentation is based on the selected model. We also show that the trajectory data can be compressed into low-dimensional vectors using the selected model. This is very effective in reducing the computation time for a long video sequence. |
| Publication Title | Memoirs of the Faculty of Engineering, Okayama University |
| Published Date | 2002-11 |
| Volume | volume37 |
| Issue | issue1 |
| Start Page | 41 |
| End Page | 49 |
| ISSN | 0475-0071 |
| language | English |
| File Version | publisher |
| NAID | 120003457326 |
| JaLCDOI | 10.18926/47001 |
|---|---|
| FullText URL | mfe_36_1_059_077.pdf |
| Author | Kanatani, Kenichi| |
| Abstract | Contrasting "geometric fitting", for which the noise level is taken as the asymptotic variable, with "statistical inference", for which the number of observations is taken as the asymptotic variable, we give a new definition of the "geometric AIC" and the "geometric MDL" as the counterparts of Akaike's AIC and Rissanen's MDL. We discuss various theoretical and practical problems that emerge from our analysis. Finally, we show, doing experiments using synthetic and real images, that the geometric MDL does not necessarily outperform the geometric AIC and that the two criteria have very different characteristics. |
| Publication Title | Memoirs of the Faculty of Engineering, Okayama University |
| Published Date | 2001-12 |
| Volume | volume36 |
| Issue | issue1 |
| Start Page | 59 |
| End Page | 77 |
| ISSN | 0475-0071 |
| language | English |
| File Version | publisher |
| NAID | 80012855281 |
| JaLCDOI | 10.18926/47002 |
|---|---|
| FullText URL | mfe_36_1_079_090.pdf |
| Author | Kanatani, Kenichi| |
| Abstract | We first present an improvement of Kanatani's subspace separation [8] for motion segmentation by newly introducing the affine space constraint. We point out that this improvement does not always fare well due to the effective noise it introduces. In order to judge which solution to adopt if different segmentations are obtained, we present two criteria: one is the standard F test; the other is model selection using the geometric AIC of Kanatani [7] and the geometric MDL of Matsunaga and Kanatani [13]. We test these criteria doing real image experiments. |
| Publication Title | Memoirs of the Faculty of Engineering, Okayama University |
| Published Date | 2001-12 |
| Volume | volume36 |
| Issue | issue1 |
| Start Page | 79 |
| End Page | 90 |
| ISSN | 0475-0071 |
| language | English |
| File Version | publisher |
| NAID | 120003497028 |
| JaLCDOI | 10.18926/47003 |
|---|---|
| FullText URL | mfe_36_1_091_106.pdf |
| Author | Kanatani, Kenichi| Ohta, Naoya| |
| Abstract | We present a theoretically optimal linear algorithm for 3-D reconstruction from point correspondences over two views. We also present a similarly constructed optimal linear algorithm for 3-D reconstruction from optical flow. We then compare the performance of the two algorithms by simulation and real-image experiments using the same data. This is the first impartial comparison ever done in the sense that the two algorithms are both optimal, extracting the information contained in the data to a maximum possible degree. We observe that the finite motion solution is always superior to the optical flow solution and conclude that the finite motion algorithm should be used for 3-D reconstruction. |
| Publication Title | Memoirs of the Faculty of Engineering, Okayama University |
| Published Date | 2001-12 |
| Volume | volume36 |
| Issue | issue1 |
| Start Page | 91 |
| End Page | 106 |
| ISSN | 0475-0071 |
| language | English |
| File Version | publisher |
| NAID | 120003497029 |
| JaLCDOI | 10.18926/47004 |
|---|---|
| FullText URL | mfe_36_1_107_116.pdf |
| Author | Kanatani, Kenichi| Ohta, Naoya| |
| Abstract | We present a new method for automatically detecting circular objects in images: we detect an osculating circle to an elliptic arc using a Hough transform, iteratively deforming it into an ellipse, removing outlier pixels, and searching for a separate edge. The voting space is restricted to one and two dimensions for efficiency, and special weighting schemes are introduced to enhance the accuracy. We demonstrate the effectiveness of our method using real images. Finally, we apply our method to the calibration of a turntable for 3-D object shape reconstruction. |
| Publication Title | Memoirs of the Faculty of Engineering, Okayama University |
| Published Date | 2001-12 |
| Volume | volume36 |
| Issue | issue1 |
| Start Page | 107 |
| End Page | 116 |
| ISSN | 0475-0071 |
| language | English |
| File Version | publisher |
| NAID | 80012855284 |
| Author | Kanatani, Kenichi| |
|---|---|
| Published Date | 2004-10 |
| Publication Title | Pattern Analysis and Machine Intelligence |
| Content Type | Journal Article |
| Author | Kanatani, Kenichi| |
|---|---|
| Published Date | 2005-6 |
| Publication Title | Proceedings of the Fifth International Conference on 3-D Digital Imaging and Modeling |
| Content Type | Conference Paper |
| 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 | English |
| 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 | English |
| 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 | English |
| 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 | English |
| Copyright Holders | Copyright © by the authors |
| File Version | publisher |
| NAID | 120005232372 |
