M. J. Black. Robust Incremental Optical Flow. PhD thesis, Yale Univ., New Haven, CT, 1992. ResearchRep.YALEU/DCS/RR-923.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....given by the ground truth. To analyze the behavior of the estimate we take the approach described in [12] and [25] based on influence function. The influence function characterizes the bias that a particular measurement has on the solution and is proportional to the derivative, of the estimate [4]: z) j dae(z) dz (2) In case the noise is Gaussian distributed: P robfn i g exp( Gamman i ) 3) then ae(z) z (z) z (4) If the errors are distributed as a double or two sided exponential, namely P robfn i g exp( Gammajn i j) 5) then, by contrast, ae(z) jzj (z) sgn(z) ....

M. J. Black. Robust Incremental Optical Flow. PhD thesis, Yale University, September 1992.

....of argmin p s Ap f t 2 kpk 2 ; 2.8) for some regularizing scalar . The purpose of the regularization term in (2.8) is to encourage well behaved solutions. With = 0, we recover the least squares solution. Other regularization approaches, e.g. robust estimation framework [13], have also been proposed. Di erentiating with respect to p and setting to 0, we get s Ap A f s f t p = 0: 2.9) Hence, p = s A I f s f t : 2.10) Operator Horizontal Vertical Roberts Smoothed 1 0 1 5 2 0 0 0 5 Sobel 2 0 2 5 2 0 0 0 5 ....

M. Black. Robust Incremental Optical Flow. PhD thesis, Yale University, Sep. 1992.

....the implicit constraint of block matching. Without this initialization their models converge slowly through the stochastic process. Our approach involves the implicit constraint on the beginning of the optimization process. Gradually it shifts to the explicit constraint of MRF model. Black [9] also mentions that we can enforce an implicit or explicit smoothness constraint on the motion of neighboring points in the image plane. In other words, the implicit smoothness is referring to the intensity structure of a small region (in this case blocks) in one image that remains constant over ....

M.J. Black, Robust Incremental Optical Flow, Ph.D. Thesis, YALEU/CSD/RR#923, Sept., 1992.

....a robust cylindrical model based method to recover full motion of the head under perspective projection. Three main techniques contribute to the robustness of the approach. First, to deal with non rigid motion and occlusion, we use the iteratively re weighted least squares (IRLS) technique [14]. The unintended side effect of IRLS, however, is to discount some useful information, such as edges. We compensate for this effect with use of image gradients. Second, we update the templates dynamically in order to deal with gradual changes in lighting and self occlusion. This enables recovery ....

....and occlusion, some pixels in the template may disappear or may have been changed in the processed image. Those pixels should contribute less to motion estimation than others. To take this factor into account, we apply a robust technique, called iteratively re weighted least squares (IRLS) [14]. Recall at each iteration of using (4) we warp the template by the incremental transformation and use the warped template to compute the new incremental parameters. The warped template is also used for computing the weights. For a pixel u in the template, its IRLS weight w I is : ....

M. BLACK. Robust incremental optical flow. PhD thesis, Yale University, 1992.

....bank. The scales of the DOG Gaussian lters are 1 = 4:9 and 2 = 0:3. Recursive Gabor and Gaussian lters [12] are used to speed up the algorithm. The maximum estimated velocity is bounded by the rst order approximation (1) This bound can be thrown out by using a multiresolution strategy [2]. This technique allows a coarse and large motion estimation at the highest level of a Gaussian low pass pyramidal image decomposition. This coarse motion is then transmitted to a ne level where a new estimation is performed. This process is repeated until the nest level is reached. 2 4 ....

M.J. Black. Robust Incremental Optical Flow. PhD thesis, Yale University, Department of Computer Science, 1992.

....are designed to model neuronal and perceptual behavior [11] 18] 25] 28] usually using psychophysical stimuli, e.g. plaids and random dot images, and have not been tested using real motion scenes. Unlike neural network methods, image processing algorithms can deal with real scenes [3] [5], 7] 8] 16] 26] 29] 33] 34] However, they also fail to consider all of the three challenges simultaneously. One class of algorithms employs motion energy filters for motion detection [2] 21] 26] 33] These algorithms can represent motion transparency. However, they are ....

....they are fundamentally limited to translational motion and provide limited spatial localization. Starting from the pioneering study by Horn and Schunck [15] another class utilizes the brightness constraint equation wherein local motion components are related to temporal and spatial derivatives [5], 7] 8] 15] 16] These algorithms can represent translational, 1045 9227 00 10.00 2000 IEEE 936 IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 11, NO. 4, JULY 2000 affine, and planar motions. When translational motion is assumed, cross correlation methods, such as the one proposed by Anandan ....

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M. J. Black, "Robust incremental optical flow," Ph.D. dissertation, Dept. Comput. Sci., Yale Univ., New Heaven, CT, 1992.

....in the feature vectors. To analyze the behavior of the estimate we take the approach described in [6] and [8] based on an influence function. The influence function characterizes the bias that a particular measurement has on the solution and is proportional to the derivative, of the estimate [2]. n) j dae(n) dz (7) In case the noise is Gaussian distributed: P robfx i Gamma y i g exp( Gamma[x i Gamma y i ] 2 ) 8) then ae(n) n 2 (n) n (9) If the errors are distributed as a double or two sided exponential, namely P robfx i Gamma y i g exp( Gammajx i Gamma y i j) 10) ....

M.J. Black. Robust Incremental Optical Flow. PhD thesis, Yale University, September 1992.

....region is therefore of great importance, given that we want to deal with complex situations or to get rid of a preliminary segmentation step, which is usually a computationnally heavy and difficult task. The class of robust estimators [Hub81, Rou84] which has become popular in image processing [MMR91, Bla92, JMB91] offers an appealing direction of investigation. Such an approach has already been used in [DP91] for motion estimation, but only for a 3D translation with constant depth ; i.e. a second order 2D motion model with three parameters at a single resolution has been considered. However, a robust ....

M. J. Black. Robust incremental optical flow. PhD thesis, Yale University, Computer Science Dept, September 1992.

....towards dynamic environments. As is noted by Black, the goal is incrementally to integrate motion information from new images with previous optical flow estimates to obtain more accurate information about the motion in the scene over time. A detailed description of this method can be found in [6]. Ideally optical flow is computed continuously # as the animat navigates in its world, but to reduce computational cost # Reasonably small areas suffice, since objects in the ## # ## peripheral image are typically small at peripheral resolution. Methods for estimating appropriate areas for ....

M.J. Black. Robust incremental optical flow. Technical Report YALEU/DCS/RR-923, Yale University, Dept. of Computer Science, 1992.

.... coloring 1 of the graph associated to the neighborhood system defined on the image grid (this partition of the image sites is often called a codage [4] Most implementations of non linear relaxation schemes on 2D simd arrays make use of this paradigm (see for instance [26, 36] on the dap 510 or [2, 5, 27, 40, 45] on the cm2) Implementations on linear simd arrays, based on the same principle [13, 34, 33] have also been described, in order to design specialized architectures. Alternate approaches involve the development of highly specialized linear or non linear (electrical) analog networks [25, 32, 41] ....

M. J. BLACK. -- Robust incremental optical flow. -- PhD thesis, Yale university, Sept. 1992.

.... influence function characterizes the bias herringbone (D15) wool (D19) calf (D24) sand (D29) waves (D38) wood (D68) raffia (D84) pigskin (D92) plastic (D112) Figure 1: Brodatz textures that a particular measurement has on the solution and is proportional to the derivative, of the estimate [1]: n) j dae(n) dn (5) In case the noise is Gaussian distributed: P robfng exp( Gamma[n] 2 ) 6) then ae(n) n 2 (n) n (7) If the errors are distributed as a double or two sized exponential, namely P robfng exp( Gammajnj) 8) then, by contrast, ae(n) jnj (n) sgn(n) 9) In ....

M.J. Black. Robust Incremental Optical Flow. PhD thesis, Yale University, September 1992.

....where the ofce is not valid at all. Considering energy function (4) which consists of a data model part (sum of site wise data model deviation) and a smoothing part (sum of local smoothness measures) it seems natural to embed robust M estimators within both terms, as proposed by Black et al. [5, 7]. Namely, at each resolution level k, we consider the following energy function of dw k given w k and f k : H k (dw k ; f k ; w k ) 4 = H k 1 (dw k ; f k ; w k ) ffH k 2 (dw k ; w k ) 8) 4 The grid S k is 4 k times smaller than S. INRIA 9 with: H k 1 ....

M. BLACK and P. ANANDAN. Robust incremental optical flow. In Proc. Conf. Comp. Vision Pattern Rec., 1992.

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M. J. Black. Robust Incremental Optical Flow. PhD thesis, Yale Univ., New Haven, CT, 1992. ResearchRep.YALEU/DCS/RR-923.

....approximations of the phenomena being modeled. In particular, the field addresses how to handle outliers, or gross errors, that do not conform to the statistical assumptions. Robust estimators, like line processes, have been used to account for spatial discontinuities in early vision problems [2, 12]. But, while line process formulations typically are concerned with violations of the spatial smoothness assumption, measurements (of depth, optical flow, etc. may also contain outliers. Black and Anandan [3] use robust estimation to account for both spatial discontinuities and measurement errors ....

....sparse and line processes. Eliminating the line processes by minimizing over them [4] or integrating them out [5] produces an objective function with an energy functional which is similar to the redescending estimators [10] used in robust statistics. A number of authors have noted this similarity [2, 3, 6, 7, 8]. The connection becomes clearer when we consider analog line processes with general penalty functions. Geman and Reynolds [8] show that minimizing over the analog processes produces particular estimators and they also specify conditions on an estimator that must be satisfied if it is to have an ....

[Article contains additional citation context not shown here]

M. J. Black. Robust Incremental Optical Flow. PhD thesis, Yale University, New Haven, CT, 1992. Research Report YALEU/DCS/RR-923.

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M.J. Black. Robust Incremental Optical Flow. PhD thesis, Yale Univeristy, New Haven, CT, 1992. Research Report YALEU/DCS/RR-923.

....about the scene, the motion, and the imaging process. These assumptions are often violated in real scenes and the measurements made by the constraints can be viewed in a statistical context as outliers. To reduce the effect of these outlying measurements we adopt the robust estimation framework of [3, 5] in which the standard constraints are formulated in terms of robust estimation [8] We choose the ae to be robust estimators; in this case the Lorentzian estimator: ae(x; oe) log 1 1 2 i x oe j 2 ; x; oe) 2x 2oe 2 x 2 : 7) The function is the derivative of the ....

....outliers. In the case of the Lorentzian, the influence of outliers tends to zero. This robust estimation formulation results in a computationally expensive non convex minimization problem. 3. 1 Global Optimization Local minimization of E is performed using Simultaneous Over Relaxation (SOR) see [3] for details of the approach) We focus here on the problem of finding a globally optimal solution when the function is non convex. The general idea is to take the non convex objective function and construct a convex approximation. In the case of the Lorentzian estimator, this can be achieved by ....

[Article contains additional citation context not shown here]

M. J. Black. Robust Incremental Optical Flow. PhD thesis, Yale Univ., New Haven, CT, 1992. Research Rep. YALEU/DCS/RR-923.

....by a grants from the National Aeronautics and Space Administration (NGT 50749) and the Office of Naval Research (N00014 91 J 1577) estimating optical flow and allows assumption violations to be detected. We have applied the approach to three standard techniques for recovering optical flow [1]: area based regression, correlation, and regularization techniques. Previous work in optical flow estimation has focused on the violation of spatial smoothness at motion boundaries while ignoring violations of the brightness constancy assumption. Within the robust estimation framework, ....

....the influence of outliers goes to zero beyond the threshold. For the remainder of the paper we will consider the Lorentzian estimator (Figure 1, bottom) but the treatment here could equally be applied to a wide variety of the other estimators. A discussion of various estimators can be found in [1]. 3.1 Robust Estimation Framework We make the simple observation that may common approaches to recovering optical flow are formulated as least squares estimation (including: correlation, regularization, and area base techniques) Because each approach involves pooling information over a spatial ....

[Article contains additional citation context not shown here]

M. J. Black. Robust Incremental Optical Flow. PhD thesis, Yale Univeristy, New Haven, CT, 1992. Research Report YALEU/DCS/RR-923.

....approximations of the phenomena being modeled. In particular, the field addresses how to handle outliers, or gross errors, that do not conform to the statistical assumptions. Robust estimators, like line processes, have been used to account for spatial discontinuities in early vision problems [2, 12]. But, while line process formulations typically are concerned with violations of the spatial smoothness assumption, measurements (of depth, optical flow, etc. may also contain outliers. Black and Anandan [3] use robust estimation to account for both spatial discontinuities and measurement errors ....

....sparse and line processes. Eliminating the line processes by minimizing over them [4] or integrating them out [5] produces an objective function with an energy functional which is similar to the redescending estimators [10] used in robust statistics. A number of authors have noted this similarity [2, 3, 6, 7, 8]. The connection becomes clearer when we consider analog line processes with general penalty functions. Geman and Reynolds [8] show that minimizing over the analog processes produces particular estimators and they also specify conditions on an estimator that must be satisfied if it is to have an ....

[Article contains additional citation context not shown here]

M. J. Black. Robust Incremental Optical Flow. PhD thesis, Yale University, New Haven, CT, 1992. Research Report YALEU/DCS/RR-923.

No context found.

M.J. Black. Robust Incremental Optical Flow. PhD thesis, Yale University, Department of Computer Science, 1992.

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M.J. Black. Robust Incremental Optical Flow. PhD thesis, Yale University, Department of Computer Science, 1992.

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M. Black. Robust incremental optical flow. PhD thesis, Yale University, 1992.

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M.J. Black. Robust Incremental Optical Flow. PhD thesis, Yale University, September 1992.

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M. Black and P. Anandan. Robust incremental optical flow. In Proceedings of the International Conference on Computer Vision and Pattern Recognition, Urbana Champaign, IL, June 1992. IEEE.

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M. J. Black. Robust Incremental Optical Flow. PhD thesis, Yale University, September 1992.

No context found.

M. Black and P. Anandan. Robust incremental optical flow. In Proceedings of the International Conference on Computer Vision and Pattern Recognition, Urbana Champaign, IL, June 1992. IEEE.

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