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 10.18926/47004
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 10.18926/44497
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 10.18926/48126
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 10.18926/47003
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 10.18926/14086
FullText URL Mem_Fac_Eng_OU_41_1_63.pdf
Author Kanatani, Kenichi| Sugaya, Yasuyuki|
Abstract 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.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2007-01
Volume volume41
Issue issue1
Start Page 63
End Page 72
ISSN 0475-0071
language 英語
File Version publisher
NAID 120002308585
JaLCDOI 10.18926/14153
FullText URL Mem_Fac_Eng_39_1_56.pdf
Author Sugaya, Yasuyuki| Kanatani, Kenichi|
Abstract We present a new method for extracting objects moving independently of the background from a video sequence taken by a moving camera. We first extract and track feature points through the sequence and select the trajectories of background points by exploiting geometric constraints based on the affine camera model. Then, we generate a panoramic image of the background and compare it with the individual frames. We describe our image processing and thresholding techniques.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2005-01
Volume volume39
Issue issue1
Start Page 56
End Page 62
ISSN 0475-0071
language 英語
File Version publisher
NAID 120002308594
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 10.18926/46969
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 10.18926/14056
FullText URL Mem_Fac_Eng_OU_42_18.pdf
Author Kanatani, Kenichi| Yasuyuki Sugaya|
Abstract 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.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2008-01
Volume volume42
Issue issue1
Start Page 18
End Page 35
ISSN 0475-0071
language 英語
File Version publisher
NAID 120002308468
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 10.18926/14122
FullText URL Mem_Fac_Eng_OU_40_1_44.pdf
Author Sugaya, Yasuyuki| Kanatani, Kenichi| Kanazawa, Yasushi|
Abstract 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.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2006-01
Volume volume40
Issue issue1
Start Page 44
End Page 52
ISSN 0475-0071
language 英語
File Version publisher
NAID 120002308593
JaLCDOI 10.18926/14055
FullText URL Mem_Fac_Eng_OU_42_10.pdf
Author Kanatani, Kenichi|
Abstract 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.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2008-01
Volume volume42
Issue issue1
Start Page 10
End Page 17
ISSN 0475-0071
language 英語
File Version publisher
NAID 120002308447
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 10.18926/44496
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 10.18926/19958
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 10.18926/19956
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 英語
File Version publisher
NAID 120002309159
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
Author Kanatani, Kenichi|
Published Date 2001-7
Publication Title Computer Vision
Content Type Journal Article