| Author | Kanatani, Kenichi| |
|---|---|
| Published Date | 2001-7 |
| Publication Title | Computer Vision |
| Content Type | Journal Article |
| 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 | English |
| File Version | publisher |
| NAID | 120002308447 |
| 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 | English |
| File Version | publisher |
| NAID | 120002308468 |
| 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 | English |
| File Version | publisher |
| NAID | 120002308585 |
| 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 | English |
| File Version | publisher |
| NAID | 120002308410 |
| 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 | English |
| 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 | English |
| File Version | publisher |
| NAID | 120002308664 |
| 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 | English |
| File Version | publisher |
| NAID | 120002308332 |
| 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 | English |
| File Version | publisher |
| NAID | 120002308594 |
| 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 | English |
| File Version | publisher |
| NAID | 120002308366 |
| 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 | English |
| Copyright Holders | Copyright © by the authors |
| File Version | publisher |
| NAID | 120002905952 |
| 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 | English |
| Copyright Holders | Copyright © by the authors |
| File Version | publisher |
| NAID | 80021759249 |
| 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 | English |
| Copyright Holders | Copyright © by the authors |
| File Version | publisher |
| NAID | 80021759250 |
