B.D. Lucas. Generalized Image Matching by the Method of Differences. PhD Thesis, Dept. of Computer Science, Carnegie-Mellon University, 1984.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....are three major phases involved in our motion segmentation algorithm. Phase 1: Identification of image flow vectors for the independently moving objects by Hough Transform We identify N image flow vectors (u 1 , v 1 ) u N , v N ) using Hough Transform. Borrowing idea from Lucas and Kanade [20], we smooth image flow constraints at a pixel with a Gaussian filter over a small neighborhood so that the image flow equation (I x u I y v I t = 0 [12] is applicable to a small neighborhood of the image frames in the least squares sense. 2.1) E xx E yx E xy E yy ....

B. D. Lucas, Generalized Image Matching by Method of Differences, Department of Computer Science, Carnegie-Mellon University (1984).

....Foundation grants ASC 9121431, ASC 9217394, and ASC 9404734. 1 of the underlying optical flow field in the neighborhood of an image point. The flow field is typically obtained by solving an overdetermined system of intensity (or other gray level properties) constraint equations [5] 8] [11], 21] 24] The optical flow field and the actual projected 2 D velocity match closely at image points with high intensity gradient values [23] 9] and high gradient points frequently correspond to locations of 3 D motion discontinuities. Thus, it is essential to calculate the optical flow as ....

B.D. Lucas, Generalized image matching by the method of differences, Ph.D. Dissertation, Carnegie-Mellon Univ., 1984.

....expansion approach which combines their strengths and eliminates their weaknesses. One key issue we address is the signal expansion models implied in various approaches. There are mainly two different expansion models. One is based on the spatial Taylor expansion. The gradient approach in [9, 11, 14] is a typical one based on this expansion model. There are also numerous other variants of the gradient approach such as [7, 8, 1, 17] The core of all these approaches is to expand the signal using Taylor expansion such that the disparity variables are separated from the signal. The coefficients ....

B. Lucas. Generalized Image Matching by the Method of Differences. PhD thesis, Department of Computer Science, Carnegie Mellon University, 1984.

.... Flow As noted above, we considered a number of optical flow methods which were found to be accurate and had other interesting features (such as a way of computing confidence measures or certainty factors on the image velocities) We used the local differential method proposed by Lucas and Kanade [24, 23] with modifications proposed by [9] the global differential method proposed by Horn and Schunck [12] the correlation method of Singh [37, 38] and the phased based frequency method of Fleet and Jepson [10, 11] Below, we describe the 4 methods briefly, further details are in the original ....

B. D. Lucas. Generalized image matching by the method of differences. PhD thesis, Carnegie-Mellon Univ., 1984.

....These algorithms have certain properties making them especially suitable for use in biological vision systems: they are fast and direct filter algorithms, and they can calculate disparity with sub pixel precision. In this paper two different direct algorithms are considered, a differential method [14] and a method based on detecting optical flow lines in fourier space [15, 16] The differential method rests on the assumption that for a small patch moving with velocity v, the image intensity I(x; t) is only a function of z = x Gamma vt. From this follows the gradient constraint equation f x ....

....method rests on the assumption that for a small patch moving with velocity v, the image intensity I(x; t) is only a function of z = x Gamma vt. From this follows the gradient constraint equation f x v t gI(x; t) 0 Normally, this equation will be satisfied only approximately. Thus, in [14] an weighted least square fit over an image region selected by a window function W (x) was proposed, minimizing X x2 Omega W (x)f x v t gI(x; t) with respect to the velocity v. The minimization can be formulated as a filtering operation, depicted in figure 3. We will refer to this ....

B. D. Lucas. Generalized Image Matching by the Method of Differences. PhD thesis, Dep. of Computer Science, Carnegie-Mellon University, 1984.

....Jepson, 1990] and regularization [Horn and Schunck, 1981; Hildreth, 1986; Poggio et al. 1985] Nagel [1987] and Anandan [Anandan, 1989] provide comparisons and derive relations between different techniques, while Barron et al. 1994] provide some numerical comparisons. Global motion estimators [Lucas, 1984; Bergen et al. 1992] use a simple flow field model parameterized by a small number of unknown variables. Examples of global motion models include affine and quadratic flow fields. In the taxonomy of Bergen et al. 1992] these fields are called parametric motion models, since they can be used ....

....techniques are often used to speed the search for the optimum displacement field. Another decision that must be made is how to represent the (u; v) fields. Assigning an independent estimate at each pixel (u i ; v i ) is the most commonly made choice, but global motion descriptors are also possible [Lucas, 1984; Bergen et al. 1992] see also Section 5) Constrained motion models which combine a global rigid motion description with a local depth estimate are also used [Horn and Weldon Jr. 1988; Hanna, 1991; Bergen et al. 1992] and we will study these in Section 6. Both local correlation windows (as ....

[Article contains additional citation context not shown here]

B. D. Lucas. Generalized Image Matching by the Method of Differences. PhD thesis, Carnegie Mellon University, July 1984.

....and regularization [Horn and Schunck, 1981; Hildreth, 1986; Poggio et al. 1985] Nagel [1987] Anandan [1989] and Otte and Nagel [1994] provide comparisons and derive relations between different techniques, while Barron et al. 1994] provide some numerical comparisons. Global motion estimators [Lucas, 1984; Bergen et al. 1992] use a simple flow field model parameterized by a small number of unknown variables. Examples of global motion models include affine and quadratic flow fields. In the taxonomy of Bergen et al. 1992] these fields are called parametric motion models, since they can be used ....

....)g are shown as pluses ( The choice of representation for the (u; v) field also strongly influences the performance of the motion estimation algorithm. The most commonly made choice is to assign an independent estimate at each pixel (u i ; v i ) but global motion descriptors are also possible [Lucas, 1984; Bergen et al. 1992; Szeliski and Coughlan, 1994] One can observe, however, that motion estimates at individual pixels are never truly independent. Both local correlation windows (as in SSD) and global smoothness constraints aggregate information from neighboring pixels. The resulting ....

B. D. Lucas. Generalized Image Matching by the Method of Differences. PhD thesis, Carnegie Mellon University, July 1984.

....gradient constraint is superior. This paper reports a comparison of widely cited optical flow methods. We implemented nine techniques including instances of differential methods, region based matching, energy based and phase based techniques, namely those of Horn and Schunck [32] Lucas and Kanade [40, 41], Uras et al. 57] Nagel [44] Anandan [5, 6] Singh [54, 55] Heeger [30] Waxman et al. 61] and Fleet and Jepson [20, 23] Despite their differences, many of these techniques can be viewed conceptually in terms of three stages of processing: 1. prefiltering or smoothing with low pass band pass ....

....deviation of 1.5 pixels in space and 1.5 frames in time (1.5 pixels frames) sampled out to three standard deviations. Results from both the original and our modified method are reported below. Barron, Fleet and Beauchemin IJCV 12:1, pp43 77, 1994 6 Lucas and Kanade Following Lucas and Kanade [41, 40] and others [2, 37, 52, 53] we implemented a weighted least squares (LS) fit of local first order constraints (2.2) to a constant model for v in each small spatial neighbourhood Omega by minimizing X x2 Omega W 2 (x) rI(x; t) Delta v I t (x; t) 2 ; 2.7) where W (x) denotes a window ....

[Article contains additional citation context not shown here]

Lucas B.D. (1984) Generalized Image Matching by the Method of Differences. PhD Dissertation, Dept. of Computer Science, Carnegie-Mellon University

....of correlation called the Sum of Squared Differences (SSD) measure [Anandan, 1989] since it provides us not only with flow estimates but also with uncertainty estimates for each measurement. Alternative approaches to computing optic flow include gradient based techniques [Horn and Schunck, 1981; Lucas, 1984; Nagel, 1987] spatiotemporal filtering [Adelson and Bergen, 1985; Heeger, 1987; Fleet and Jepson, 1989] and direct depth estimation [Heel, 1990] see [Nagel, 1987; Anandan, 1989] for a comparison of several of these techniques) The Sum of Squared Differences method integrates the squared ....

B. D. Lucas. Generalized Image Matching by the Method of Differences. PhD thesis, Carnegie Mellon University, July 1984.

....models listed in Table 1. The complexity of motion estimation largely depends on the model used. A large number of approaches have been proposed to solve this problem [13] 14] 15] The approaches include optical flow (general motion) estimators [16] 17] 18] 19] global parametric motion estimators [20][21] local parametric motion estimators [22] 23] constrained motion estimators [21] stereo and multiframe stereo [24] 25] 26] hierarchical (coarse tofine) methods [21] 27] 29] These approaches are either correlation based or feature based. Correlation based tracking algorithms select a patch ....

B.D. Lucas. Generalized Image Matching by the Method of Differences. Ph.D. thesis, Carnegie Mellon University, July 1984. 28

....i v j e i v k = 2 X i w ij w ik I 2 yi : The entries of A can be computed at the same time as the energy gradients. The 2 Theta 2 sub matrix A j corresponding to the terms a uu jj , a uv jj , and a vv jj encodes the local shape of the sum of squared difference correlation surface [Lucas, 1984; Anandan, 1989] This matrix (for w ij = 1) is identical to the Hessian matrix used in the differential method, i.e. the matrix appearing 6 3 Spline based image registration on the left hand side of (3) The overall A matrix is a sparse multi banded block diagonal matrix, i.e. sub blocks ....

....= Gammaff B Gamma1 g = Gammaffd (11) where B = A I, and A = block diag(A) is the set of 2 Theta 2 block diagonal matrices A j , and d = B Gamma1 g is called the preconditioned residual or direction vector. The update rule is very close to that used in the differential method [Lucas, 1984], with the following differences: 1. the equations for computing the g and A are different (based on spline interpolation) 2. an additional diagonal term is added for stability 4 3. there is a step size ff. The step size ff is necessary because we are ignoring the off block diagonal terms in A, ....

[Article contains additional citation context not shown here]

B. D. Lucas. Generalized Image Matching by the Method of Differences. PhD thesis, Carnegie Mellon University, July 1984.

....fourth term ensures that c varies smoothly. and are simply constants weighing the relative importance of each term in the minimization. 2.1.2 Local Models Local models of velocity assuming single motion patterns are also common. For example, Lucas and Kanade use a local constant model for v [93, 94] which is solved as a weighted least squares solution to (1.3) Velocity estimates are computed by minimizing X x2R W 2 (x) rI(x; t) Delta v I t (x; t) 2 ; 2.9) where W (x) denotes a window function and R is a spatial neighbourhood. Solutions for v are obtained in closed form. ....

.... of basic image motion measurements, such as intensity derivatives or correlation surfaces, significantly increases the accuracy of results [14] For instance, a spatiotemporal Gaussian smoothing of the image sequence results in more accurate derivatives for the methods of Lucas and Kanade [93, 94] and Horn and Schunck [69] Anandan s and Singh s computational schemes [8, 135] also use prefiltering of the images by computing hierarchical Laplacian images. It is believed ACM Computing Surveys, Vol. 27, No. 3, pp. 433 467, 1995 34 that this high pass filtering emphasizes image structures ....

B. D. Lucas. Generalized image matching by the method of differences. PhD thesis, Carnegie-Mellon Univ., 1984.

No context found.

B.D. Lucas. Generalized Image Matching by the Method of Differences. PhD Thesis, Dept. of Computer Science, Carnegie-Mellon University, 1984.

No context found.

B. Lucas. Generalized Image Matching by the Method of Differences, PhD thesis, School of Computer Science, Carnegie-Mellon University, Pittsburgh, PA, 1984.

No context found.

B.D. Lucas. Generalized image matching by the method of differences. PhD Dissertation, Carnegie-Mellon University, 1984.

No context found.

Lucas, B.D., "Generalized Image Matching by the Method of Differences," Carnegie Mellon University, Technical Report CMU-CS-85-160, Ph.D. dissertation, July 1984. 203 203

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC