| 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 | 10.18926/19957 |
|---|---|
| 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 | 10.18926/19956 |
|---|---|
| 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 | 10.18926/19955 |
|---|---|
| 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 | 10.18926/14155 |
|---|---|
| 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 | 10.18926/14153 |
|---|---|
| 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 | 10.18926/14124 |
|---|---|
| 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 | 10.18926/14123 |
|---|---|
| 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 | 10.18926/14122 |
|---|---|
| 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 | 10.18926/14087 |
|---|---|
| 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 | 10.18926/14086 |
|---|---|
| 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 | 10.18926/14056 |
|---|---|
| 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 | 10.18926/14055 |
|---|---|
| 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 |
