Sparsity Model for Robust Optical Flow Estimation at Motion Discontinuities
|
|
- Winifred Bryant
- 5 years ago
- Views:
Transcription
1 Sparsity Model for Robust Optical Flow Estimation at Motion Discontinuities Xiaohui Shen and Ying Wu Northwestern University Sheridan Road, Evanston, IL Abstract This paper introduces a new sparsity prior to the estimation of dense flow fields. Based on this new prior, a complex flow field with motion discontinuities can be accurately estimated by finding the sparsest representation of the flow field in certain domains. In addition, a stronger additional sparsity constraint on the flow gradients is incorporated into the model to cope with the measurement noises. Robust estimation techniques are also employed to identify the outliers and to refine the results. This new sparsity model can accurately and reliably estimate the entire dense flow field from a small portion of measurements when other measurements are corrupted by noise. Experiments show that our method significantly outperforms traditional methods that are based on global or piecewise smoothness priors. model, the flow field and the separation of multiple motions can be done jointly by motion layer models[, ]. In addition, the motion discontinuity can be modeled in an inhomogeneous MRF so that the flow field can be inferred while preserving the discontinuity[]. Motion segmentation is also adopted to differentiate multiple motions[, 7]. Another interesting idea is to learn the statistics of the flow field and use it as the prior for inference[, 3]. Despite these efforts, finding a simple and effective solution to handle motion discontinuities is still very attractive. 1. Introduction Computing optical flow is a fundamental problem in computer vision. Most contemporary methods more or less originate from or are related to the two classical methods, i.e., Lucas & Kanade s method[1] based on the assumption that the set of pixels in a local region share the same motion, and Horn & Schunck s method[13] based on global smoothness regularization through variational methods. These methods generally perform well when their assumptions hold. Unfortunately, in practice, these assumptions are largely violated at motion boundaries. When there are multiple motions in an image patch, motion boundaries and motion discontinuities exist, and thus the flow field is neither smooth nor reflecting a single motion. Because the motion boundaries are unknown, computing the optical flow over motion boundaries remains a very difficult problem. To overcome this difficulty, many approaches have been investigated to modify these priors to fit the flow field better. Based on robust statistics, robust functions can be introduced to the least squares estimation[], so that the dominant motion can be estimated and other motions treated as outliers can be identified. Based on a piecewise smoothness (a) (b) (c) (d) Figure 1. Sparsity model for optical flow. (a) The flow field, (b) the component of flow u and v, (c) -D Haar Wavelet decomposition, (d) the flow gradient field is also sparse. The values are mapped to color for display. Different from any previous methods originated from Horn & Schunck or Lucas & Kanade, this paper introduces a new prior to the flow field, and presents a simple and elegant method to handle the complexity incurred by multiple motions and motion discontinuities. Instead of explicitly modeling the discontinuities and learning all sorts of priors, we only impose a simple assumption, i.e., the flow field has a sparse representation in other domains. This assumption is looser than the single motion assumption and the smooth flow field assumption, because it covers the case where the flow field exhibits multiple motions. This sparsity assumption is generally held in reality, because the flow field is much more structured than random Brownian motion and much simpler than natural images. See Fig.1(c) for example, most coefficients are zero after performing -D Wavelet decomposition to the flow field. Therefore the flow can be sparsely represented in the Wavelet domain. Based on this
2 assumption, we formulate flow computation in an underdetermined linear system, and its minimum L 1 norm solution leads to a very accurate estimate of the flow field. The proposed new approach is very simple and accurate. The novelty of this work lies in three aspects: a) we validate that the flow field is sparse in other domain such as Wavelet and DCT, and such sparsity can well capture multiple motions and motion discontinuities in the flow field. Moreover, the sparsest fitting of the model can be obtained by the L 1 -norm minimization, and yields very accurate flow estimation. b) A stronger additional gradient sparsity constraint is incorporated into the sparsity model, as shown in Fig.1(d), which distinguishes motion boundaries from measurement noises. c) Robust estimation techniques are performed to remove the outliers and reliably estimate the flow from a small portion of measurements.. Related Work Ever since Horn & Schunck s and Lucas & Kanade s solutions, many approaches have been proposed to improve these methods to estimate high quality flow fields. Early work includes robust statistics[] and MRF models for preserving motion discontinuities[]. In [], robust functions were introduced to the least squares estimation to identify the outliers, while in [] multiple gradient-based and edgebased constraints were added and fused in an MRF to preserve motion discontinuities. All these methods are based on energy function optimization. Following this trend, more accurate energy functions (MRF models) as well as new optimization approaches were introduced recently[, 1, ]. [] used rotation invariant convex regularizers to find the connection between the intensity constancy and smoothness regularization. Such a connection was further explored by [9], which introduced the complementarity of these two terms. [1] proposed a more accurate MRF energy as well as a discrete and continuous combined optimization method. [] also proposed a new energy function based on discrete optimization. Besides the MRF models, another natural way to depict piecewise smoothness and motion discontinuities is to segment the motion. In [] a motion segmentation model was first generated by energy function optimization, and then used to introduce another mixture of local smoothness and region-wise parameterizations. In [7], the images were partitioned to segments in which the flow was constrained by an affine motion. The final results were obtained by minimizing the error in segmentation. More recently, along with the establishment of Middlebury Dataset[3], more flow data with ground truth were available and accordingly were used to learn the statistics of flow field[, 3]. In [17], 3D structure sensors was used to construct a parametric model for optical flow. Despite such great efforts, most of them are still based on global or piecewise smoothness constraints. On the other hand, the initial application of sparsity to the image domain can be traced back to Olshausen s image sparse coding[1]. The direct way to seek sparsity is L - norm minimization, which is a NP-hard problem. Therefore no global optimum is guaranteed, which limited its application. Since the theory of compressive sensing[11, ] was proposed, which proved the equivalence of L -norm minimization and L 1 -norm minimization for sparsity under certain conditions, such limitation has been relieved. Immediately after the emergence of compressive sensing, it has been applied to many vision related areas. In face recognition[], a face image is considered as a linear combination of the training images of the same person with some measurement noises, and thus can be sparsely represented by the image training dataset. [] also proposed a method to handle the noise problem when the noises are sparse. Similarly, in the application of target tracking[19], each object can also be sparsely represented by templates with sparse noises caused by lighting change or occlusion. [] designed an overcomplete codebook by randomly choosing small image patches, and used it to sparsely represent other image patches for image super-resolution. In [9], a compressive sensing method was described to directly recover background subtracted images. When the objects of interest(foreground) occupy a small portion of the camera view, the background images can be sparsely represented in spatial domain. A low dimensional sparse representation of the background is then learned and adapted. To the best of our knowledge, this paper is a first attempt in exploring the sparsity for optical flow estimation. By imposing sparsity, smoothness in local regions and motion discontinuities can be encoded at the same time. Therefore we don t need other constraints before accurately recovering the flow field. In addition, dense noise problem in sparse representation is still an open problem in general. The method in [] can work when only some portion of the measurements have noises. In this paper we address this problem in optical flow by adding gradient sparsity constraint and performing robust estimation. In Section 3 we will validate that optical flow field can be sparsely represented. Accurately estimated flow based on sparsity will also be shown. Section introduces our robust flow estimation method against noise in detail. Experiments are shown in Section, and Section draws the conclusions. 3. Formulation 3.1. Sparsity model for the flow field A basic assumption for most differential methods in optical flow estimation is that the intensities across the images remain constant over time. When the displacements are small, we can perform a first-order Taylor expansion
3 and obtain the optical flow constraint: I x u + I y v + I t = (1) where I x, I y and I t are the first-order partial derivatives of the image intensities I(x, t), while (u, v) are the components of motion in the horizontal and vertical direction respectively. By stacking the constraints of all pixels in the image together, we have the following representation: I t = [ I x I y ] [ u v where I t, u and v are all vectors of length n, the number of pixels in image. I x and I y are n-dimensional diagonal matrix. Since it is a highly underdetermined system, various additional constraints or priors are imposed to regularize the problem, such as the global smoothness[13] and local velocity constancy[1]. However, they fail at some local regions in the flow field, especially those at motion discontinuities. In this paper, we consider the optical flow problem from a distinct perspective. If we divide the whole images into small blocks (e.g. 1 1, or 3 3), the flow field in each block, although discontinuities and large variations may still be present, always has some simple structures and exhibits homogeneity in each structure. Thus we can find a basis to represent the flow field such that it is sparse in another domain. Actually if we look at u and v respectively, each can be considered as a simple image. Therefore commonly used bases for sparse representation of natural images can be adopted here, such as Wavelet, DCT or Curvelet. Fig. gives us an illustration. Although the flow field in Fig.(a) seems complex, most Haar Wavelet coefficients of u and v are nearly zero, which means the flow in the Haar Wavelet domain is sparse. 3 3 (a) (b) (c) Figure. Sparse representation of the flow field. (a) The flow field, (b) the color map of u and v respectively, and (c) the Wavelet coefficients of u and v, most of which are small values near zero. Consider W as the bases, then the flow can be sparsely represented as u = Ws u and v = Ws v, where s are the sparsity coefficients. Accordingly, () can be rewritten as I t = [ I x I y ] [ W W ] ][ su s v ] () (3) The optical flow estimation problem therefore can be formulated as sparse signal recovery based on highly shorted measurements. 3.. Computing optical flow using the sparsity model The theory in compressive sensing has already validated that when the signal is sparse, it can be accurately recovered from much fewer measurements with high probability, by minimizing its L 1 -norm[, 11]. Let y = I t, A = [ [ ] ] W I x I y, B =, and s =[ s W u s v ] T. The problem can be casted as s =argmin s 1 s.t. y = ABs () and the estimated flow can be computed by f = [ u v ] T = Bs This is a convex optimization problem that can be conveniently converted to a linear program like basis pursuit[11]. Such a sparsity model is quite simple, but powerful. Consider a noise-free case in Fig.3, in a 1 1 flow block, assuming the measurements y have no noise and the constraints in (1) strictly hold, and the Haar Wavelet is used for sparse representation. The estimated flow by this basic sparsity model is almost perfect, preserving crisp motion boundaries and notably outperforming the results from traditional methods based on smoothness priors[13, ]. Notice that when solving (), we solely maximized the sparsity of s under the intensity constancy constraints without any other assumed priors. This is the most different point for our method from others, and is also the main reason that the method performs well at discontinuities in Fig.3. Meanwhile, as a non-parametric method, it can accurately estimate the motion generated by various parametric models, such as affine transformation and rotation(fig.). Moreover, even if the measurements are not fully sampled, our method can still work effectively. In Fig., the partial derivatives are calculated on a limited number of pixels. We can accurately estimate the whole dense flow field, even if only % of the partial derivatives are known. That means, by our sparse model, we can estimate n flow signals from no more than.n observed measurements. Up to now we assume that the constraint in (1) strictly holds. However, it is a first-order approximation of intensity constancy. In addition, there inevitably exist noises when calculating the derivatives I x, I y and I t, which violate the constraints and impair the performance of our method. In the next section, we will thoroughly discuss our robust flow estimation when the constraint in (1) is not satisfied at some pixels. ()
4 (a) Ground Truth (b) Sparsity Model (AAE =.). Robust Optical Flow.1. The noise problem The noises may come from 1) the residuals after firstorder approximation, ) the measurement noises in the calculation of I t, which are reflected by y in (), and 3) the noises in computing of I x and I y, which is contained in A. The constraint y = ABs hence can be modified as 1 1 (c) Horn & Schunck (AAE =.3) 1 1 (d) Black & Anandan (AAE =.3) Figure 3. Computing optical flow without measurement noise. The flow field is 1 1. AAE = Average Angular Error. No pyramid is used in all methods (a) AAE =.79 (b) AAE = 1. (c)aae = 3.3 Figure. Estimating different parametric flow using nonparametric sparsity model. First row: ground truth, second row: estimated results. AAE = Average Angular Error (a) Ground Truth 1 1 (c) Measurement Number =.7*N (AAE = 1.) (b) Measurement Number =.*N (AAE =.3) 1 1 (d) Measurement Number =.*N (AAE = 1.93) Figure. Optical flow estimation from small portion of measurement. N =. y = (A + N A )Bs + e y = ABs + e A + e y = ABs + e Accordingly, our sparsity model in () can be reformulated as () s =argmin y ABs + λ s 1 (7) where λ is the Lagrangian multiplier. (7) relaxes the constraint y = ABs, which is more reasonable than () when measurement noises need to be considered. Unlike the noises in other applications of compressive sensing to the computer vision problems (e.g. face recognition[] and human tracking[19]), the noise e here is always dense with large variations. We looked into that property by comparing the differences between the estimated noise-free measurements and the ground truth. Fig.(a) shows the statistical distribution of the noise values. The noise distribution can be considered as a zeromean Gaussian. We tested the performance of (7) by manually adding dense zero-mean Gaussian noises with different variations. The relationship of the the reconstructed errors and the measurement noises is shown in Fig.(b) y-y* (a) (b) Figure. The property of noise in optical flow. In Fig.(b) the x-axis is the L -norm of measurement noise e, and the y-axis is the L -norm of reconstructed error e s = s s. We can see that the reconstructed errors increase linearly with respect to the measurement noises. This linear relationship is also stated and proved theoretically in [7]. Moreover, when the noises are large, the solution by L 1 -norm minimization may not converge to the ground truth. Look at a simple -D space illustration in Fig.7. In Fig.7(a), S is the constraint, x has the minimum L 1 norm among all points falling onto S, and therefore is the optimal solution. Due to the existence of noises, the x-x* 3 3
5 original constraint becomes S in Fig.7(b), and the optimal solution becomes x, which is far away from x. g = Df (9) where g = [ ] T g u g v, f =[ u v ] T. Combining with the original sparsity model (7), we propose a new sparsity model: (a) Figure 7. The influence of noise on L 1-norm minimization. Therefore, traditional way to solve () or (7) is not good enough to handle noises. Meanwhile, the error correction method for sparse noises would also fail when the noises are dense. To this end, we propose a new way to handle the noise problem: add a new sparsity constraint, and use robust estimation techniques to reject the outliers... Additional sparsity constraint In Section 3.1 we stated that the flow field is sparse in the Wavelet domain. Now we argue that not only the flow field is sparse, but the gradient field of the flow is also sparse. It is straightforward to understand. As we stated in 3.1, the flow field usually has some structures. In each structure the motion tends to change smoothly, the gradients of the flow are also small; while at the discontinuities between structures, the gradients are large. Therefore only a small number of gradients should have large values, and the flow gradient field has to be sparse in the image domain. Here we want to emphasize on two points: 1. This is a strong complement to our original sparsity constraint, as a sparse flow field does not necessarily have sparsity on its gradient field.. This constraint is clearly different from other first order constraints like global smoothness. It allows large values on some derivatives, and imposes no constraints on their spatial relationships. Similarly, we want to minimize f 1. Normally it is difficult to compute f 1 accurately. However, if we calculate the horizontal and vertical components respectively, and use simple kernel [1, 1] and [1, 1] T to convolute u and v, each component can be linearly approximated as g u = [ ] T D x D y u g v = [ ] T () D x D y v where g u and g v have length n, D x and D y denote linearized first order derivative operators. Hereby we can represent the flow gradient field as a linear combination of the flow field: (b) (s, g ) = argmin y ABs + λ 1 s 1 +μ( y AD + g + λ g 1 ) f = argmin f Bs + μ f D + g () where μ is the parameter to balance these two constraints. D + is the pseudo-inverse of D. We can modify the derivative operators on the boundaries of the flow field to make D x and D y full rank respectively without influencing the whole sparse representation. By adding this additional sparsity constraint, the performance can be significantly improved, as shown in Fig.. We crop an image region of size 3 3 from the Dimetrodon sequence in the Middlebury Dataset[3]. The first frame is shown in Fig.(a), and the ground truth is shown in Fig.(b). Fig.(c) is the result by solving (7), and the result by solving () is shown in Fig.(d). Obviously combing two constraints achieved better performance, the average angular error decreased from. to.3. 3 (a) The first frame 3 (c) Original Sparsity Model (d) Additional constraint (AAE =.) (AAE =.3) Figure. The improvement by performing the additional sparsity constraint on the flow gradient field..3. Robust estimation 3 3 (b) Ground truth 3 3 In Section 3. we already showed that our sparsity model can recover the flow field from a small portion of measurements, while in Section.1 we analyzed that the measurement noises in flow estimation obey quasi-gaussian distribution. Most measurements contain small errors while
6 Grove AAE =.1 AAE = 3.93 AAE =.7 Venus AAE =.17 AAE =.1 AAE =.73 (a) (b) (c) (d) (e) Figure 9. The improvement by additional sparsity constraint and robust estimation. (a) Ground truth, (b) results by Wavelet sparsity, (c) combing derivative sparsity, (d) robust estimation, (e) color map for flow. some may be completely corrupted and become outliers. Therefore, if we can reject those outliers and use the remaining samples to estimate the entire flow, the results shall be improved. Thus we can use robust estimation techniques to remove the outliers and refine the estimated flow. Among those techniques, RANSAC is the most commonly used one. The algorithm of robust optical flow estimation using RANSAC can be described in three steps: a) Initialization. Let n be the number of all measurements, thus the number of variables in flow field is n. Inthe beginning of each iteration, randomly select βn( < β<1) samples as the measurements y. Estimate the entire flow field by solving (). b) Model fitting. For the remaining (1 β)n samples, each sample has its estimated flow u i and v i from Step 1. Compute SSD as its matching score: S = (I (x, y) I 1 (x + u i,y+ v i )) (x,y) N (i) (11) where N (i) are the neighbors of sample i. Normally the neighborhood is 3 3 or. If S is small, it means that u i and v i are accurately estimated. Therefore if S < T, we consider sample i fits the model, otherwise not. T here is a pre-defined threshold. c) Refining. If more than εn(β <ε<1) samples are fitted, the model is considered good. We then use all the fitted samples to estimate the flow again. Compare the average SSD of all flows estimated by this model with the initial model in Step 1, and choose the one of a smaller SSD. If less than εn samples are fitted, the model is considered bad and is discarded. Repeat the above three steps until we find a model with a sufficiently good matching score. The model with the best score then gives us the final result. In our experiments we set β =. and ε =.. T is initially set to be a small value. If after many iterations we still cannot find a model with enough fitted samples, T can be increased sequentially. We use this robust estimation algorithm to refine the result in Fig., the average angular error is reduced from.3 to.. It is a distinctive property for the sparsity model that it can reconstruct the whole signal from a small portion of the measurements, which allows us to estimate the flow field using robust estimators such as RANSAC. The robust estimation for the sparsity model is not confined in optical flow, but can be generalized to most applications of sparse representation and compressive sensing.. Experiments We performed our algorithm to estimate dense optical flow of two-frame gray images on the Middlebury Dataset[3](Dimetrodon, Venus, Hydrangea, Grove and Grove3). As we assume the first-order approximation of intensity constancy (1) holds, which requires small u and v, we downsampled all the images to 1/ of their original heights and widths. The images are then divided by overlapping blocks of size 1 1. The sparsity model is used for each image block to generate the final results. The Haar Wavelet is used as the codebook for sparse representation. In L 1 -norm minimization, we used the method introduced in [1] and the code in []. As for the regularization parameters, there are no guidelines to select them at this moment. Instead, we tried different parameters and used the one with the best performance. In particular, we set λ 1 = λ =., and μ =in (). We observed that the results only have insignificant differences in a range around these parameters. The Horn & Schunck s method and Black & Anandan s method is based on the implementation of [1]. Since the images are already downsampled, the pyramid level in
7 these two methods is set to be 1. Fig.9 gives us two examples that the additional sparse constraint and robust estimation helped improve the performance of sparsity model. We display the flow field according to the color map in Fig.9(e). Fig.9(b) are the results by solely seeking the sparsity in the Wavelet domain. As we can see there are many noises in the estimated flow. The flow field of the Grove sequence looks pale. It is because the colors are mapped from the relative values of the flow. There are some large noises which make other flow values relatively small. In the Venus sequence, the flows in the middle region as well as the upper right corner are fully corrupted. By performing additional gradient sparsity constraint, the influence of measurement noises is attenuated, and the flows present stronger homogeneity in local regions, as shown in Fig.9(c). Large noises are removed in Grove, and the upper right corner of the flow field in Venus is recovered well. However, the middle part is still very noisy. After robust estimation, the outliers in the measurements are removed, and accordingly the performance is significantly improved, especially in those noisy regions. Notice that the flows in a small region of the middle part of Venus are still not very accurate. It is in part because that the image derivatives in this region are very small and most measurements are severely corrupted by noise. As for now we only estimate the flows block by block based on their own information, if too many measurements in a block have large noise, robust estimation would also fail. A possible way to handle this problem is to enlarge the block size and adjust the flows in each block according to the results in the surrounding blocks. We also compared the results with Horn & Schunck s method[13], and Black & Anandan s method[]. The reason we choose these two methods to compare is that we aim to investigate the effectiveness of different assumptions in optical flow under the same condition, i.e., the sparsity assumption vs. global and piecewise smoothness assumption. Therefore we didn t choose other multiple layer methods with coarse-to-fine strategies. Meanwhile, the reported performance of these two methods in the Middlebury benchmark is comparable with others. The average angular error and endpoint error on each sequence have been listed in Table1. The errors of our method are much lower than that of the other two methods on every sequence. The estimated flow of the remaining sequences other than Grove and Venus (which have already been shown in Fig.9) are shown in Fig.. We can see from Fig. that our results are more crisp at the motion discontinuities and meanwhile also smooth in homogeneous regions. It validated that our method is powerful to handle motion discontinuities without any other priors or using methods like model selection. Currently we have not submitted our results to the Mid- Sequences H&S B&A Sparsity Dimetrodon AAE Endpoint..9.1 Venus AAE Endpoint Hydrangea AAE Endpoint Grove AAE Endpoint Grove3 AAE Endpoint Table 1. Average angular error and endpoint error of three methods on sequences.sparsity model achieved better performance. dlebury Benchmark for evaluation, as we performed our model in downsampled images with small motion. However, our results can be refined by any coarse-to-fine methods such as warping[] and motion segmentation. Actually simply interpolating our results to higher resolution level can still provide comparable performance. Since this is not the focus of this paper, and it is hard to clarify whether the final high resolution results benefit from our approach or the coarse-to-fine techniques, we choose to present the performance in the initial coarse level. And the comparison results under the same condition has already proved its effectiveness.. Conclusion This paper introduced a new sparsity prior in optical flow estimation. Unlike traditional smoothness constraints, sparsity can handle motion homogeneities and motion discontinuities at the same time, which leads to accurate estimation of the flow field. A stronger sparsity constraint on flow gradient field and robust estimation techniques are also introduced to guarantee the robustness of the sparsity model in handling the measurement noises. We believe that this sparsity model is a new fundamental assumption in optical flow, and can be well combined with other existing methods in flow estimation. It worths more research efforts to further explore the sparsity in optical flow estimation. Acknowledgements This work was supported in part by National Science Foundation grant IIS-3777, IIS-917, and US Army Research Laboratory and the US Army Research Office under grant ARO W911NF--1-. References [1] dqsun/research/software.html. [] boyd/l1 ls/.
8 Dimetrodon Grove3 Hydrangea (a) Ground truth (b) H & S (c) B & A (d) Sparsity model Figure. Comparison Results. (a) Ground truth, (b) Horn & Schunck s method, (c) Black & Anandan s method, (d) Sparsity model. [3] S. Baker, D. Scharstein, J. Lewis, S. Roth, M. J. Black, and R. Szeliski. A database and evaluation methodology for optical flow. In ICCV, 7. [] M. J. Black and P. Anandan. The robust estimation of multiple motions: Parametric and piecewise-smooth flow fields. CVIU, 3(1):7, 199. [] T. Brox, A. Bruhn, N. Papenberg, and J. Weickert. High accuracy optical flow estimation based on a theory for warping. ECCV,. [] E. J. Candès, J. Romberg, and T. Tao. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inform. Theory, ():9 9,. [7] E.J.Candès, J. Romberg, and T. Tao. Stable signal recovery from incomplete and inaccurate measurements. Comm. Pure Appl. Math, 9():7 3,. [] E. J. Candès and M. B. Wakin. An introduction to compressive sampling. IEEE Signal Processing Magazine, ():1 3,. [9] V. Cevher, D. Reddy, M. Duarte, A. Sankaranarayanan, R. Chellappa, and R. Baraniuk. Compressive sensing for background subtraction. In ECCV,. [] T. Darrell and A. Pentland. Robust estimation of a multilayered motion representation. In CVPR, pages 9 3, [11] D. L. Donoho. Compressed sensing. IEEE Trans. Inform. Theory, :9 13,. [] F. Heitz and P. Bouthemy. Multimodal estimation of discontinuous optical flow using markov random fields. PAMI, :17 3, [13] B. Horn and B. Schunck. Determining optical flow. Artificial Intelligence, 17: 3, 191. [1] S. J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky. A method for large-scale l 1-regularized least squares. IEEE Selected Topics in Signal Processing, 1, 7. [] C. Lei and Y. H. Yang. Optical flow estimation on coarse-tofine region-trees using discrete optimization. In ICCV, 9. [1] V. Lempitsky, S. Roth, and C. Rother. Discrete-continuous optimization for optical flow estimation. In CVPR,. [17] H. Liu, R. Chellappa, and A. Rosenfeld. Accurate dense optical flow estimation using adaptive structure tensors and a parametric model. TIP, :117 11, 3. [1] B. Lucas and T. Kanade. An iterative image registration technique with an application to stereo vision. In IJCAI, pages 7 79, 191. [19] X. Mei and H. Ling. Robust visual tracking using l1 minimization. In ICCV, 9. [] E.Mémin and P. Pérez. Hierarchical estimation and segmentation of dense motion fields. IJCV, :9,. [1] B. A. Olshausen and D. J. Field. Emergence of simple-cell receptive field properties by learning a sparse code for natural images. Nature, 31:7 9, 199. [] S. Roth and M. J. Black. On the spatial statistics of optical flow. In ICCV,. [3] D. Sun, S. Roth, J. Lewis, and M. Black. Learning optical flow. In ECCV,. [] J. Wang and E. Adelson. Representing moving images with layers. TIP, 3: 3, 199. [] J. Weickert and C. Schnörr. A theoretical framework for convex regularizers in pde-based computation of image motion. IJCV, :, 1. [] J. Wright, A. Yang, A. Ganesh, S. Sastry, and Y. Ma. Robust face recognition via sparse representation. PAMI, 31(), 9. [7] L. Xu, J. Chen, and J. Jia. Segmentation based variational model for accurate optical flow estimation. In ECCV,. [] J. Yang, J. Wright, T. Huang, and Y. Ma. Image superresolution as sparse representation of raw image patches. In CVPR,. [9] H. Zimmer, A. Bruhn, J. Weickert, L. Valgaerts, A. Salgado, B. Rosenhahn, and H. Seidel. Complementary optic flow. EMMCVPR, 9.
EE795: Computer Vision and Intelligent Systems
EE795: Computer Vision and Intelligent Systems Spring 2012 TTh 17:30-18:45 FDH 204 Lecture 14 130307 http://www.ee.unlv.edu/~b1morris/ecg795/ 2 Outline Review Stereo Dense Motion Estimation Translational
Enhancing Gradient Sparsity for Parametrized Motion Estimation
HAN et al.: ENHANCING GRADIENT SPARSITY FOR MOTION ESTIMATION 1 Enhancing Gradient Sparsity for Parametrized Motion Estimation Junyu Han pengjie.han@gmail.com Fei Qi fred.qi@ieee.org Guangming Shi gmshi@xidian.edu.cn
Notes 9: Optical Flow
Course 049064: Variational Methods in Image Processing Notes 9: Optical Flow Guy Gilboa 1 Basic Model 1.1 Background Optical flow is a fundamental problem in computer vision. The general goal is to find
CS6670: Computer Vision
CS6670: Computer Vision Noah Snavely Lecture 19: Optical flow http://en.wikipedia.org/wiki/barberpole_illusion Readings Szeliski, Chapter 8.4-8.5 Announcements Project 2b due Tuesday, Nov 2 Please sign
Motion Estimation. There are three main types (or applications) of motion estimation:
Members: D91922016 朱威達 R93922010 林聖凱 R93922044 謝俊瑋 Motion Estimation There are three main types (or applications) of motion estimation: Parametric motion (image alignment) The main idea of parametric motion
EE795: Computer Vision and Intelligent Systems
EE795: Computer Vision and Intelligent Systems Spring 2012 TTh 17:30-18:45 FDH 204 Lecture 11 140311 http://www.ee.unlv.edu/~b1morris/ecg795/ 2 Outline Motion Analysis Motivation Differential Motion Optical
ADAPTIVE LOW RANK AND SPARSE DECOMPOSITION OF VIDEO USING COMPRESSIVE SENSING
ADAPTIVE LOW RANK AND SPARSE DECOMPOSITION OF VIDEO USING COMPRESSIVE SENSING Fei Yang 1 Hong Jiang 2 Zuowei Shen 3 Wei Deng 4 Dimitris Metaxas 1 1 Rutgers University 2 Bell Labs 3 National University
Part II: Modeling Aspects
Yosemite test sequence Illumination changes Motion discontinuities Variational Optical Flow Estimation Part II: Modeling Aspects Discontinuity Di ti it preserving i smoothness th tterms Robust data terms
Motion Estimation (II) Ce Liu Microsoft Research New England
Motion Estimation (II) Ce Liu celiu@microsoft.com Microsoft Research New England Last time Motion perception Motion representation Parametric motion: Lucas-Kanade T I x du dv = I x I T x I y I x T I y
Deconvolution with curvelet-domain sparsity Vishal Kumar, EOS-UBC and Felix J. Herrmann, EOS-UBC
Deconvolution with curvelet-domain sparsity Vishal Kumar, EOS-UBC and Felix J. Herrmann, EOS-UBC SUMMARY We use the recently introduced multiscale and multidirectional curvelet transform to exploit the
Comparison of stereo inspired optical flow estimation techniques
Comparison of stereo inspired optical flow estimation techniques ABSTRACT The similarity of the correspondence problems in optical flow estimation and disparity estimation techniques enables methods to
COMPUTER VISION > OPTICAL FLOW UTRECHT UNIVERSITY RONALD POPPE
COMPUTER VISION 2017-2018 > OPTICAL FLOW UTRECHT UNIVERSITY RONALD POPPE OUTLINE Optical flow Lucas-Kanade Horn-Schunck Applications of optical flow Optical flow tracking Histograms of oriented flow Assignment
Perceptual Grouping from Motion Cues Using Tensor Voting
Perceptual Grouping from Motion Cues Using Tensor Voting 1. Research Team Project Leader: Graduate Students: Prof. Gérard Medioni, Computer Science Mircea Nicolescu, Changki Min 2. Statement of Project
Motion Estimation with Adaptive Regularization and Neighborhood Dependent Constraint
0 Digital Image Computing: Techniques and Applications Motion Estimation with Adaptive Regularization and Neighborhood Dependent Constraint Muhammad Wasim Nawaz, Abdesselam Bouzerdoum, Son Lam Phung ICT
SURVEY OF LOCAL AND GLOBAL OPTICAL FLOW WITH COARSE TO FINE METHOD
SURVEY OF LOCAL AND GLOBAL OPTICAL FLOW WITH COARSE TO FINE METHOD M.E-II, Department of Computer Engineering, PICT, Pune ABSTRACT: Optical flow as an image processing technique finds its applications
Feature Tracking and Optical Flow
Feature Tracking and Optical Flow Prof. D. Stricker Doz. G. Bleser Many slides adapted from James Hays, Derek Hoeim, Lana Lazebnik, Silvio Saverse, who 1 in turn adapted slides from Steve Seitz, Rick Szeliski,
The Lucas & Kanade Algorithm
The Lucas & Kanade Algorithm Instructor - Simon Lucey 16-423 - Designing Computer Vision Apps Today Registration, Registration, Registration. Linearizing Registration. Lucas & Kanade Algorithm. 3 Biggest
CS 565 Computer Vision. Nazar Khan PUCIT Lectures 15 and 16: Optic Flow
CS 565 Computer Vision Nazar Khan PUCIT Lectures 15 and 16: Optic Flow Introduction Basic Problem given: image sequence f(x, y, z), where (x, y) specifies the location and z denotes time wanted: displacement
Detecting Burnscar from Hyperspectral Imagery via Sparse Representation with Low-Rank Interference
Detecting Burnscar from Hyperspectral Imagery via Sparse Representation with Low-Rank Interference Minh Dao 1, Xiang Xiang 1, Bulent Ayhan 2, Chiman Kwan 2, Trac D. Tran 1 Johns Hopkins Univeristy, 3400
Dense Image-based Motion Estimation Algorithms & Optical Flow
Dense mage-based Motion Estimation Algorithms & Optical Flow Video A video is a sequence of frames captured at different times The video data is a function of v time (t) v space (x,y) ntroduction to motion
Matching. Compare region of image to region of image. Today, simplest kind of matching. Intensities similar.
Matching Compare region of image to region of image. We talked about this for stereo. Important for motion. Epipolar constraint unknown. But motion small. Recognition Find object in image. Recognize object.
Peripheral drift illusion
Peripheral drift illusion Does it work on other animals? Computer Vision Motion and Optical Flow Many slides adapted from J. Hays, S. Seitz, R. Szeliski, M. Pollefeys, K. Grauman and others Video A video
Optical Flow Estimation with CUDA. Mikhail Smirnov
Optical Flow Estimation with CUDA Mikhail Smirnov msmirnov@nvidia.com Document Change History Version Date Responsible Reason for Change Mikhail Smirnov Initial release Abstract Optical flow is the apparent
Robust Principal Component Analysis (RPCA)
Robust Principal Component Analysis (RPCA) & Matrix decomposition: into low-rank and sparse components Zhenfang Hu 2010.4.1 reference [1] Chandrasekharan, V., Sanghavi, S., Parillo, P., Wilsky, A.: Ranksparsity
Incoherent noise suppression with curvelet-domain sparsity Vishal Kumar, EOS-UBC and Felix J. Herrmann, EOS-UBC
Incoherent noise suppression with curvelet-domain sparsity Vishal Kumar, EOS-UBC and Felix J. Herrmann, EOS-UBC SUMMARY The separation of signal and noise is a key issue in seismic data processing. By
Visual Tracking (1) Tracking of Feature Points and Planar Rigid Objects
Intelligent Control Systems Visual Tracking (1) Tracking of Feature Points and Planar Rigid Objects Shingo Kagami Graduate School of Information Sciences, Tohoku University swk(at)ic.is.tohoku.ac.jp http://www.ic.is.tohoku.ac.jp/ja/swk/
Feature Tracking and Optical Flow
Feature Tracking and Optical Flow Prof. D. Stricker Doz. G. Bleser Many slides adapted from James Hays, Derek Hoeim, Lana Lazebnik, Silvio Saverse, who in turn adapted slides from Steve Seitz, Rick Szeliski,
Multi-stable Perception. Necker Cube
Multi-stable Perception Necker Cube Spinning dancer illusion, Nobuyuki Kayahara Multiple view geometry Stereo vision Epipolar geometry Lowe Hartley and Zisserman Depth map extraction Essential matrix
CS 4495 Computer Vision Motion and Optic Flow
CS 4495 Computer Vision Aaron Bobick School of Interactive Computing Administrivia PS4 is out, due Sunday Oct 27 th. All relevant lectures posted Details about Problem Set: You may *not* use built in Harris
Face Recognition via Sparse Representation
Face Recognition via Sparse Representation John Wright, Allen Y. Yang, Arvind, S. Shankar Sastry and Yi Ma IEEE Trans. PAMI, March 2008 Research About Face Face Detection Face Alignment Face Recognition
Capturing, Modeling, Rendering 3D Structures
Computer Vision Approach Capturing, Modeling, Rendering 3D Structures Calculate pixel correspondences and extract geometry Not robust Difficult to acquire illumination effects, e.g. specular highlights
Learning and Inferring Depth from Monocular Images. Jiyan Pan April 1, 2009
Learning and Inferring Depth from Monocular Images Jiyan Pan April 1, 2009 Traditional ways of inferring depth Binocular disparity Structure from motion Defocus Given a single monocular image, how to infer
Motion and Optical Flow. Slides from Ce Liu, Steve Seitz, Larry Zitnick, Ali Farhadi
Motion and Optical Flow Slides from Ce Liu, Steve Seitz, Larry Zitnick, Ali Farhadi We live in a moving world Perceiving, understanding and predicting motion is an important part of our daily lives Motion
Using Subspace Constraints to Improve Feature Tracking Presented by Bryan Poling. Based on work by Bryan Poling, Gilad Lerman, and Arthur Szlam
Presented by Based on work by, Gilad Lerman, and Arthur Szlam What is Tracking? Broad Definition Tracking, or Object tracking, is a general term for following some thing through multiple frames of a video
Robust Model-Free Tracking of Non-Rigid Shape. Abstract
Robust Model-Free Tracking of Non-Rigid Shape Lorenzo Torresani Stanford University ltorresa@cs.stanford.edu Christoph Bregler New York University chris.bregler@nyu.edu New York University CS TR2003-840
Segmentation and Tracking of Partial Planar Templates
Segmentation and Tracking of Partial Planar Templates Abdelsalam Masoud William Hoff Colorado School of Mines Colorado School of Mines Golden, CO 800 Golden, CO 800 amasoud@mines.edu whoff@mines.edu Abstract
Robust Face Recognition via Sparse Representation
Robust Face Recognition via Sparse Representation Panqu Wang Department of Electrical and Computer Engineering University of California, San Diego La Jolla, CA 92092 pawang@ucsd.edu Can Xu Department of
SIFT: SCALE INVARIANT FEATURE TRANSFORM SURF: SPEEDED UP ROBUST FEATURES BASHAR ALSADIK EOS DEPT. TOPMAP M13 3D GEOINFORMATION FROM IMAGES 2014
SIFT: SCALE INVARIANT FEATURE TRANSFORM SURF: SPEEDED UP ROBUST FEATURES BASHAR ALSADIK EOS DEPT. TOPMAP M13 3D GEOINFORMATION FROM IMAGES 2014 SIFT SIFT: Scale Invariant Feature Transform; transform image
P257 Transform-domain Sparsity Regularization in Reconstruction of Channelized Facies
P257 Transform-domain Sparsity Regularization in Reconstruction of Channelized Facies. azemi* (University of Alberta) & H.R. Siahkoohi (University of Tehran) SUMMARY Petrophysical reservoir properties,
Hierarchical Belief Propagation To Reduce Search Space Using CUDA for Stereo and Motion Estimation
Hierarchical Belief Propagation To Reduce Search Space Using CUDA for Stereo and Motion Estimation Scott Grauer-Gray and Chandra Kambhamettu University of Delaware Newark, DE 19716 {grauerg, chandra}@cis.udel.edu
Computational Optical Imaging - Optique Numerique. -- Single and Multiple View Geometry, Stereo matching --
Computational Optical Imaging - Optique Numerique -- Single and Multiple View Geometry, Stereo matching -- Autumn 2015 Ivo Ihrke with slides by Thorsten Thormaehlen Reminder: Feature Detection and Matching
Optical Flow-Based Motion Estimation. Thanks to Steve Seitz, Simon Baker, Takeo Kanade, and anyone else who helped develop these slides.
Optical Flow-Based Motion Estimation Thanks to Steve Seitz, Simon Baker, Takeo Kanade, and anyone else who helped develop these slides. 1 Why estimate motion? We live in a 4-D world Wide applications Object
Motion Estimation for Video Coding Standards
Motion Estimation for Video Coding Standards Prof. Ja-Ling Wu Department of Computer Science and Information Engineering National Taiwan University Introduction of Motion Estimation The goal of video compression
Leow Wee Kheng CS4243 Computer Vision and Pattern Recognition. Motion Tracking. CS4243 Motion Tracking 1
Leow Wee Kheng CS4243 Computer Vision and Pattern Recognition Motion Tracking CS4243 Motion Tracking 1 Changes are everywhere! CS4243 Motion Tracking 2 Illumination change CS4243 Motion Tracking 3 Shape
Improving Motion Estimation Using Image-Driven Functions and Hybrid Scheme
Improving Motion Estimation Using Image-Driven Functions and Hybrid Scheme Duc Dung Nguyen and Jae Wook Jeon Department of Electrical and Computer Engineering, Sungkyunkwan University, Korea nddunga3@skku.edu,
Module 7 VIDEO CODING AND MOTION ESTIMATION
Module 7 VIDEO CODING AND MOTION ESTIMATION Lesson 20 Basic Building Blocks & Temporal Redundancy Instructional Objectives At the end of this lesson, the students should be able to: 1. Name at least five
Motion Estimation using Block Overlap Minimization
Motion Estimation using Block Overlap Minimization Michael Santoro, Ghassan AlRegib, Yucel Altunbasak School of Electrical and Computer Engineering, Georgia Institute of Technology Atlanta, GA 30332 USA
Particle Tracking. For Bulk Material Handling Systems Using DEM Models. By: Jordan Pease
Particle Tracking For Bulk Material Handling Systems Using DEM Models By: Jordan Pease Introduction Motivation for project Particle Tracking Application to DEM models Experimental Results Future Work References
Motion. 1 Introduction. 2 Optical Flow. Sohaib A Khan. 2.1 Brightness Constancy Equation
Motion Sohaib A Khan 1 Introduction So far, we have dealing with single images of a static scene taken by a fixed camera. Here we will deal with sequence of images taken at different time intervals. Motion
Modified Iterative Method for Recovery of Sparse Multiple Measurement Problems
Journal of Electrical Engineering 6 (2018) 124-128 doi: 10.17265/2328-2223/2018.02.009 D DAVID PUBLISHING Modified Iterative Method for Recovery of Sparse Multiple Measurement Problems Sina Mortazavi and
Colour Segmentation-based Computation of Dense Optical Flow with Application to Video Object Segmentation
ÖGAI Journal 24/1 11 Colour Segmentation-based Computation of Dense Optical Flow with Application to Video Object Segmentation Michael Bleyer, Margrit Gelautz, Christoph Rhemann Vienna University of Technology
Technion - Computer Science Department - Tehnical Report CIS
Over-Parameterized Variational Optical Flow Tal Nir Alfred M. Bruckstein Ron Kimmel {taln, freddy, ron}@cs.technion.ac.il Department of Computer Science Technion Israel Institute of Technology Technion
Computer Vision Lecture 20
Computer Perceptual Vision and Sensory WS 16/17 Augmented Computing Computer Perceptual Vision and Sensory WS 16/17 Augmented Computing Computer Perceptual Vision and Sensory WS 16/17 Augmented Computing
Mixture Models and EM
Mixture Models and EM Goal: Introduction to probabilistic mixture models and the expectationmaximization (EM) algorithm. Motivation: simultaneous fitting of multiple model instances unsupervised clustering
Computer Vision Lecture 20
Computer Perceptual Vision and Sensory WS 16/76 Augmented Computing Many slides adapted from K. Grauman, S. Seitz, R. Szeliski, M. Pollefeys, S. Lazebnik Computer Vision Lecture 20 Motion and Optical Flow
Optical flow and tracking
EECS 442 Computer vision Optical flow and tracking Intro Optical flow and feature tracking Lucas-Kanade algorithm Motion segmentation Segments of this lectures are courtesy of Profs S. Lazebnik S. Seitz,
CS 664 Structure and Motion. Daniel Huttenlocher
CS 664 Structure and Motion Daniel Huttenlocher Determining 3D Structure Consider set of 3D points X j seen by set of cameras with projection matrices P i Given only image coordinates x ij of each point
Comparison between Motion Analysis and Stereo
MOTION ESTIMATION The slides are from several sources through James Hays (Brown); Silvio Savarese (U. of Michigan); Octavia Camps (Northeastern); including their own slides. Comparison between Motion Analysis
Learning based face hallucination techniques: A survey
Vol. 3 (2014-15) pp. 37-45. : A survey Premitha Premnath K Department of Computer Science & Engineering Vidya Academy of Science & Technology Thrissur - 680501, Kerala, India (email: premithakpnath@gmail.com)
CHAPTER 9 INPAINTING USING SPARSE REPRESENTATION AND INVERSE DCT
CHAPTER 9 INPAINTING USING SPARSE REPRESENTATION AND INVERSE DCT 9.1 Introduction In the previous chapters the inpainting was considered as an iterative algorithm. PDE based method uses iterations to converge
Compressive Sensing: Opportunities and Perils for Computer Vision
Compressive Sensing: Opportunities and Perils for Computer Vision Rama Chellappa And Volkan Cevher (Rice) Joint work with Aswin C. Sankaranarayanan Dikpal Reddy Dr. Ashok Veeraraghavan (MERL) Prof. Rich
Optical Flow Estimation on Coarse-to-Fine Region-Trees using Discrete Optimization
Optical Flow Estimation on Coarse-to-Fine Region-Trees using Discrete Optimization Cheng Lei and Yee-Hong Yang Department of Computing Science University of Alberta, Edmonton, AB, Canada {clei,yang}@cs.ualberta.ca
Signal Reconstruction from Sparse Representations: An Introdu. Sensing
Signal Reconstruction from Sparse Representations: An Introduction to Compressed Sensing December 18, 2009 Digital Data Acquisition Suppose we want to acquire some real world signal digitally. Applications
Ninio, J. and Stevens, K. A. (2000) Variations on the Hermann grid: an extinction illusion. Perception, 29,
Ninio, J. and Stevens, K. A. (2000) Variations on the Hermann grid: an extinction illusion. Perception, 29, 1209-1217. CS 4495 Computer Vision A. Bobick Sparse to Dense Correspodence Building Rome in
Compressive Sensing for Multimedia. Communications in Wireless Sensor Networks
Compressive Sensing for Multimedia 1 Communications in Wireless Sensor Networks Wael Barakat & Rabih Saliba MDDSP Project Final Report Prof. Brian L. Evans May 9, 2008 Abstract Compressive Sensing is an
Nonrigid Surface Modelling. and Fast Recovery. Department of Computer Science and Engineering. Committee: Prof. Leo J. Jia and Prof. K. H.
Nonrigid Surface Modelling and Fast Recovery Zhu Jianke Supervisor: Prof. Michael R. Lyu Committee: Prof. Leo J. Jia and Prof. K. H. Wong Department of Computer Science and Engineering May 11, 2007 1 2
Filter Flow: Supplemental Material
Filter Flow: Supplemental Material Steven M. Seitz University of Washington Simon Baker Microsoft Research We include larger images and a number of additional results obtained using Filter Flow [5]. 1
Supplementary Material : Partial Sum Minimization of Singular Values in RPCA for Low-Level Vision
Supplementary Material : Partial Sum Minimization of Singular Values in RPCA for Low-Level Vision Due to space limitation in the main paper, we present additional experimental results in this supplementary
Lecture 16: Computer Vision
CS4442/9542b: Artificial Intelligence II Prof. Olga Veksler Lecture 16: Computer Vision Motion Slides are from Steve Seitz (UW), David Jacobs (UMD) Outline Motion Estimation Motion Field Optical Flow Field
Computer Vision I - Filtering and Feature detection
Computer Vision I - Filtering and Feature detection Carsten Rother 30/10/2015 Computer Vision I: Basics of Image Processing Roadmap: Basics of Digital Image Processing Computer Vision I: Basics of Image
Introduction. Wavelets, Curvelets [4], Surfacelets [5].
Introduction Signal reconstruction from the smallest possible Fourier measurements has been a key motivation in the compressed sensing (CS) research [1]. Accurate reconstruction from partial Fourier data
Visual Tracking (1) Feature Point Tracking and Block Matching
Intelligent Control Systems Visual Tracking (1) Feature Point Tracking and Block Matching Shingo Kagami Graduate School of Information Sciences, Tohoku University swk(at)ic.is.tohoku.ac.jp http://www.ic.is.tohoku.ac.jp/ja/swk/
Exploring Curve Fitting for Fingers in Egocentric Images
Exploring Curve Fitting for Fingers in Egocentric Images Akanksha Saran Robotics Institute, Carnegie Mellon University 16-811: Math Fundamentals for Robotics Final Project Report Email: asaran@andrew.cmu.edu
CHAPTER 3 DISPARITY AND DEPTH MAP COMPUTATION
CHAPTER 3 DISPARITY AND DEPTH MAP COMPUTATION In this chapter we will discuss the process of disparity computation. It plays an important role in our caricature system because all 3D coordinates of nodes
Edge and corner detection
Edge and corner detection Prof. Stricker Doz. G. Bleser Computer Vision: Object and People Tracking Goals Where is the information in an image? How is an object characterized? How can I find measurements
A Bottom Up Algebraic Approach to Motion Segmentation
A Bottom Up Algebraic Approach to Motion Segmentation Dheeraj Singaraju and RenéVidal Center for Imaging Science, Johns Hopkins University, 301 Clark Hall, 3400 N. Charles St., Baltimore, MD, 21218, USA
Locally Weighted Least Squares Regression for Image Denoising, Reconstruction and Up-sampling
Locally Weighted Least Squares Regression for Image Denoising, Reconstruction and Up-sampling Moritz Baecher May 15, 29 1 Introduction Edge-preserving smoothing and super-resolution are classic and important
Supplementary Material for Zoom and Learn: Generalizing Deep Stereo Matching to Novel Domains
Supplementary Material for Zoom and Learn: Generalizing Deep Stereo Matching to Novel Domains Jiahao Pang 1 Wenxiu Sun 1 Chengxi Yang 1 Jimmy Ren 1 Ruichao Xiao 1 Jin Zeng 1 Liang Lin 1,2 1 SenseTime Research
Image reconstruction based on back propagation learning in Compressed Sensing theory
Image reconstruction based on back propagation learning in Compressed Sensing theory Gaoang Wang Project for ECE 539 Fall 2013 Abstract Over the past few years, a new framework known as compressive sampling
NIH Public Access Author Manuscript Proc Int Conf Image Proc. Author manuscript; available in PMC 2013 May 03.
NIH Public Access Author Manuscript Published in final edited form as: Proc Int Conf Image Proc. 2008 ; : 241 244. doi:10.1109/icip.2008.4711736. TRACKING THROUGH CHANGES IN SCALE Shawn Lankton 1, James
Augmented Reality VU. Computer Vision 3D Registration (2) Prof. Vincent Lepetit
Augmented Reality VU Computer Vision 3D Registration (2) Prof. Vincent Lepetit Feature Point-Based 3D Tracking Feature Points for 3D Tracking Much less ambiguous than edges; Point-to-point reprojection
Continuous and Discrete Optimization Methods in Computer Vision. Daniel Cremers Department of Computer Science University of Bonn
Continuous and Discrete Optimization Methods in Computer Vision Daniel Cremers Department of Computer Science University of Bonn Oxford, August 16 2007 Segmentation by Energy Minimization Given an image,
What have we leaned so far?
What have we leaned so far? Camera structure Eye structure Project 1: High Dynamic Range Imaging What have we learned so far? Image Filtering Image Warping Camera Projection Model Project 2: Panoramic
Range Imaging Through Triangulation. Range Imaging Through Triangulation. Range Imaging Through Triangulation. Range Imaging Through Triangulation
Obviously, this is a very slow process and not suitable for dynamic scenes. To speed things up, we can use a laser that projects a vertical line of light onto the scene. This laser rotates around its vertical
Autonomous Navigation for Flying Robots
Computer Vision Group Prof. Daniel Cremers Autonomous Navigation for Flying Robots Lecture 7.1: 2D Motion Estimation in Images Jürgen Sturm Technische Universität München 3D to 2D Perspective Projections
Total Variation Regularization Method for 3D Rotational Coronary Angiography
Total Variation Regularization Method for 3D Rotational Coronary Angiography Haibo Wu 1,2, Christopher Rohkohl 1,3, Joachim Hornegger 1,2 1 Pattern Recognition Lab (LME), Department of Computer Science,
Panoramic Image Stitching
Mcgill University Panoramic Image Stitching by Kai Wang Pengbo Li A report submitted in fulfillment for the COMP 558 Final project in the Faculty of Computer Science April 2013 Mcgill University Abstract
Robust Face Recognition via Sparse Representation Authors: John Wright, Allen Y. Yang, Arvind Ganesh, S. Shankar Sastry, and Yi Ma
Robust Face Recognition via Sparse Representation Authors: John Wright, Allen Y. Yang, Arvind Ganesh, S. Shankar Sastry, and Yi Ma Presented by Hu Han Jan. 30 2014 For CSE 902 by Prof. Anil K. Jain: Selected
Limitations of Matrix Completion via Trace Norm Minimization
Limitations of Matrix Completion via Trace Norm Minimization ABSTRACT Xiaoxiao Shi Computer Science Department University of Illinois at Chicago xiaoxiao@cs.uic.edu In recent years, compressive sensing
Flow Estimation. Min Bai. February 8, University of Toronto. Min Bai (UofT) Flow Estimation February 8, / 47
Flow Estimation Min Bai University of Toronto February 8, 2016 Min Bai (UofT) Flow Estimation February 8, 2016 1 / 47 Outline Optical Flow - Continued Min Bai (UofT) Flow Estimation February 8, 2016 2
Notes on Robust Estimation David J. Fleet Allan Jepson March 30, 005 Robust Estimataion. The field of robust statistics [3, 4] is concerned with estimation problems in which the data contains gross errors,
Hand-Eye Calibration from Image Derivatives
Hand-Eye Calibration from Image Derivatives Abstract In this paper it is shown how to perform hand-eye calibration using only the normal flow field and knowledge about the motion of the hand. The proposed
Fast Image Registration via Joint Gradient Maximization: Application to Multi-Modal Data
MITSUBISHI ELECTRIC RESEARCH LABORATORIES http://www.merl.com Fast Image Registration via Joint Gradient Maximization: Application to Multi-Modal Data Xue Mei, Fatih Porikli TR-19 September Abstract We
LOW COMPLEXITY OPTICAL FLOW USING NEIGHBOR-GUIDED SEMI-GLOBAL MATCHING
LOW COMPLEXITY OPTICAL FLOW USING NEIGHBOR-GUIDED SEMI-GLOBAL MATCHING Jiang Xiang *, Ziyun Li, David Blaauw, Hun Seok Kim and Chaitali Chakrabarti * * School of Electrical, Computer and Energy Engineering,
Visual Odometry. Features, Tracking, Essential Matrix, and RANSAC. Stephan Weiss Computer Vision Group NASA-JPL / CalTech
Visual Odometry Features, Tracking, Essential Matrix, and RANSAC Stephan Weiss Computer Vision Group NASA-JPL / CalTech Stephan.Weiss@ieee.org (c) 2013. Government sponsorship acknowledged. Outline The
3D Computer Vision. Dense 3D Reconstruction II. Prof. Didier Stricker. Christiano Gava
3D Computer Vision Dense 3D Reconstruction II Prof. Didier Stricker Christiano Gava Kaiserlautern University http://ags.cs.uni-kl.de/ DFKI Deutsches Forschungszentrum für Künstliche Intelligenz http://av.dfki.de
Structured Light II. Thanks to Ronen Gvili, Szymon Rusinkiewicz and Maks Ovsjanikov
Structured Light II Johannes Köhler Johannes.koehler@dfki.de Thanks to Ronen Gvili, Szymon Rusinkiewicz and Maks Ovsjanikov Introduction Previous lecture: Structured Light I Active Scanning Camera/emitter
Local Image Registration: An Adaptive Filtering Framework
Local Image Registration: An Adaptive Filtering Framework Gulcin Caner a,a.murattekalp a,b, Gaurav Sharma a and Wendi Heinzelman a a Electrical and Computer Engineering Dept.,University of Rochester, Rochester,
Collaborative Sparsity and Compressive MRI
Modeling and Computation Seminar February 14, 2013 Table of Contents 1 T2 Estimation 2 Undersampling in MRI 3 Compressed Sensing 4 Model-Based Approach 5 From L1 to L0 6 Spatially Adaptive Sparsity MRI
A low rank based seismic data interpolation via frequencypatches transform and low rank space projection
A low rank based seismic data interpolation via frequencypatches transform and low rank space projection Zhengsheng Yao, Mike Galbraith and Randy Kolesar Schlumberger Summary We propose a new algorithm