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
Author Kanatani, Kenichi|
Published Date 2001-7
Publication Title Computer Vision
Content Type Journal Article
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 10.18926/46970
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 10.18926/46971
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 10.18926/46952
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
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
Author Kanatani, Kenichi|
Published Date 2004-10
Publication Title Pattern Analysis and Machine Intelligence
Content Type Journal Article
JaLCDOI 10.18926/14155
FullText URL Mem_Fac_Eng_39_1_63.pdf
Author Kanatani, Kenichi|
Abstract Geometric fitting is one of the most fundamental problems of computer vision. In [8], the author derived a theoretical accuracy bound (KCR lower bound) for geometric fitting in general and proved that maximum likelihood (ML) estimation is statistically optimal. Recently, Chernov and Lesort [3] proved a similar result, using a weaker assumption. In this paper, we compare their formulation with the author’s and describe the background of the problem. We also review recent topics including semiparametric models and discuss remaining issues.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2005-01
Volume volume39
Issue issue1
Start Page 63
End Page 70
ISSN 0475-0071
language 英語
File Version publisher
NAID 120002308366
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
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 10.18926/14124
FullText URL Mem_Fac_Eng_OU_40_1_64.pdf
Author Kanatani, Kenichi|
Abstract 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.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2006-01
Volume volume40
Issue issue1
Start Page 64
End Page 77
ISSN 0475-0071
language 英語
File Version publisher
NAID 120002308332
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 10.18926/14123
FullText URL Mem_Fac_Eng_OU_40_1_53.pdf
Author Kanatani, Kenichi| Sugaya, Yasuyuki| Hanno Ackermann|
Abstract 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.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2006-01
Volume volume40
Issue issue1
Start Page 53
End Page 63
ISSN 0475-0071
language 英語
File Version publisher
NAID 120002308664
JaLCDOI 10.18926/14087
FullText URL Mem_Fac_Eng_OU_41_1_73.pdf
Author Kanatani, Kenichi|
Abstract 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.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2007-01
Volume volume41
Issue issue1
Start Page 73
End Page 92
ISSN 0475-0071
language 英語
File Version publisher
NAID 120002308410
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 10.18926/14056
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