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 10.18926/48125
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 10.18926/44496
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 10.18926/19959
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 10.18926/19957
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 英語
File Version publisher
NAID 120002309124
Author Kanatani, Kenichi|
Published Date 2001-7
Publication Title Computer Vision
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
Author Kanatani, Kenichi|
Published Date 2004-10
Publication Title Pattern Analysis and Machine Intelligence
Content Type Journal Article
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 10.18926/48126
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 10.18926/47004
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 英語
File Version publisher
NAID 80012855284
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 英語
File Version publisher
NAID 120003497029
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 英語
File Version publisher
NAID 120003497028
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 英語
File Version publisher
NAID 80012855281
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 英語
File Version publisher
NAID 120003457326
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 英語
File Version publisher
NAID 80015664456
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 英語
File Version publisher
NAID 80015664455
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 英語
File Version publisher
NAID 80016889443
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 英語
File Version publisher
NAID 80016889442