K. Kanatani, N. Ohta and Y. Kanazawa, Optimal Homography Computation with a Reliability Measure, IEICE Transactions on Information and Systems, Vol. 83-E, No. 7, pp. 1369--1374, June 2000.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... to describe transforms in multi view geometry has become ubiquitous in computer vision (Hartley and Zisserman [3] present a good introduction to the subject) There has been much recent activity in the area of recovering 2D planar homographies, particularly from noisy point correspondences [4]. Treating the projector as a camera enables many results from the field to be applied directly to our problem. One of our algorithms for metric rectification is derived from unstratified rectification [5] The idea of projecting displays onto everyday objects is becoming more popular [6, 8] An ....

....used to find them produce a totally incorrect result. Least squares minimization is very sensitive to outliers, so we require an algorithm to calculate a homography from line correspondences that is robust to such outliers. Homography calculation from noisy point correspondences has been addressed [3, 4], but here we present an algorithm using line correspondences that is based on an algorithm for calculating the fundamental matrix for epipolar geometry [11] Our algorithm takes a set of n line correspondences L j , l # j ) 1 n , and an upper bound # on the fraction of outliers (e.g. ....

K. Kanatani, N. Ohta, and Y. Kanazawa. Optimal homography computation with a reliability measure. IEICE Transactions on Information and Systems, E83-D(7), 2000.

....statistical bias, which can be removed by his renormalization process. Using the optimization method of Kanatani in the computation of H, we can estimate the noise elvel ffl as well as the covariance V [H ] of the homography H . Due to space limit we omit the details that can be found in [9] or [10]. Note also that in practical computations, data re scaling like [4] is important for stable numerical computation. 3.2 Aspect ratio estimation Under the assumption of unknown aspect ratio fl, it is impossible to compute the calibration parameters when the rotation axis is only the x axis or the ....

K. Kanatani. Optimal homography computation with a reliability measure. In Proceedings of MVA'98, IAPR Workshop on Machine Vision Applications, pages 426--429, Nov. 1998.

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K. Kanatani, N. Ohta and Y. Kanazawa, Optimal Homography Computation with a Reliability Measure, IEICE Transactions on Information and Systems, Vol. 83-E, No. 7, pp. 1369--1374, June 2000.

....obtained by the Otsu criterion. by eqs. 3) onto the histograms of correct and incorrect matches, separately. Here, we checked the correctness of the matches as follows. Since two images of a distant scene are related by a homography , we optimally computed the homography by renormalization [4] from a large number of corresponding points selected by hand. For each candidate match (P, Q) we mapped the point P to the second image by the computed homography and judged the match as correct if the point Q is within three pixels from its ideal position HP . The result agrees very well ....

K. Kanatani, N. Ohta, and Y. Kanazawa, Optimal homography computation with a reliability measure, IEICE Trans. Inf. & Syst., E83-D-7 (2000), 1369--1374.

....following n= fo f Throughout this paper, i, j and k denote (1, 0, 0) q , 0, 1,0) q , and (0,0, 1) q , respectively. Eq. 2) de fines an image transformation called homography [3] A statistically optimal algorithm for comput ing it from feature correspondences was presented by Kanatani [4] and its C code is publicly avail able via the Web . Since the unknowns t, R and f have 7 degrees of freedom, we can determine them in theory if four or more points (x, y) are observed. 3. Optimal Computation Let V[ be the covariance matrix of the data vector ; We assume that it is ....

....procedure, which pro duces an exact solution in the absence of noise. First, we compute the homography matrix by least squares as follows: 1 JLS I1 x 11 min. 14) Since Js is a quadratic form in H, the solution is immediately obtained up to scale by the stan dard eigenvalue analysis [4]. Hence, there exits a constant k such that : A ( 5) where we define A = diag(1, 1, Multiplying each side by A k from left and then multiplying each side by its transpose, we obtain H A H : l r r llrll ) 16) Letting 1 1 : 7) and equating (1,1) 2,2) and (1,2) elements ....

K. Kanatani, Optimal homography computation with a reliability measure, Proc. IAPR Workshop on Machine Vision Applications, November 1998, Makuhari, Japan, pp. 426-429.

....this paper, i, j and k denote (1,0,0) q , 0,1,0) and (0,0, 1) respectively. Eq. 2)defines an image transformation called homography [3] A sta tistically optimal algorithm for computing it from feature correspondences by a technique cled renormal ization was presented by Kanatani [5], and its C code is publicly available via the Web . 3. Optimal Computation Let V[x] be the covariance matrix of the data vec tor x. We assume that it is known only up to scale and write (4) We call the unknown magnitude e the noise level md the matrix [x] the normalized covariance matrix. ....

....go back to Step 3. Here, T4(AC) denotes the rotation matrix of angle Ila11 m ound ACL and , e, are e. are thresholds for convergence. The initial guess of 0, r, and R for the above iterations can be obtained by first computing the homography H, say, by the renormalization procedure of Kmmtani [5] and then decomposing it into 0, r, and R in the form of eq. 3) say, by the analytical procedure that we presented in [9] However, this procedure is necessary only for the initial frame: for the subsequent frames, we can use as the initial guess the solution in the preceding frame or az ....

K. Kanatani, Optimal homography computation with a re- liability measure, Proc. IAPR Workshop on Machine Vision Applications, November 1998, Makuhari, Japan, pp. 426 429.

....to match. In such a case, the selected feature points in one image may be mapped to the corresponding points in the other image fairly accurately, but if we extrapolate this mapping to portions apart from the feature points, a large distortion may occur even in the presence of very small noise. In [7], we have observed this instability using real images and presented an algorithm for computing a homography from point correspondences by a technique called renormalization, which not only produces a statistically optimal solution but also evaluates the reliability of the computed solution in ....

....Information Engineering, Toyohashi University of Technology, Toyohashi, Aichi 4418580 Japan, Tel: 0532)44 6888, Fax: 0532)44 6873, E mail: kanazawa tutkie.tut.ac.jp no room for further improvement. Although our algorithm dramatically reduces the instability of the mapping, as demonstrated in [7, 8], it cannot remove the distortion completely. For further improvement, we need to examine the source of the instability. The instability stems from the fact that while homographies constitute an 8 parameter group of transformations, actual transformations are usually in a small subgroup it, e.g. ....

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K. Kanatani, Optimal homography computation with a reliability measure, Proc. IAPR Workshop on Machine Vision Applications, November 1998, Makuhari, Japan, pp. 426--429.

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K. Kanatani. Optimal homography computation with a reliability measure. Proc. IAPR Workshop Machine Vision Applications, Nov. 1998.

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K. Kanatani, N. Ohta, and Y. Kanazawa. Optimal homography computation with a reliability measure. IEICE Transactions on Information and Systems, E83-D(7), 2000.

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K. Kanatani, N. Ohta, and Y. Kanazawa. Optimal homography computation with a reliability measure. IEICE Transactions on Information and Systems, E83-D(7), 2000.

No context found.

K. Kanatani, N. Ohta, and Y. Kanazawa. Optimal homography computation with a reliability measure. IEICE Transactions on Information and Systems, E83-D(7), 2000.

No context found.

K. Kanatani. Optimal homography computation with a reliability measure. Proc. IAPR Workshop Machine Vision Applications, Nov. 1998.

No context found.

K. Kanatani, N. Ohta, and Y. Kanazawa. Optimal homography computation with a reliability measure. IEICE Transactions on Information and Systems, E83-D(7), 2000.

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