cvpr cvpr2013 cvpr2013-449 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Li Xu, Shicheng Zheng, Jiaya Jia
Abstract: We show in this paper that the success of previous maximum a posterior (MAP) based blur removal methods partly stems from their respective intermediate steps, which implicitly or explicitly create an unnatural representation containing salient image structures. We propose a generalized and mathematically sound L0 sparse expression, together with a new effective method, for motion deblurring. Our system does not require extra filtering during optimization and demonstrates fast energy decreasing, making a small number of iterations enough for convergence. It also provides a unifiedframeworkfor both uniform andnon-uniform motion deblurring. We extensively validate our method and show comparison with other approaches with respect to convergence speed, running time, and result quality.
Reference: text
sentIndex sentText sentNum sentScore
1 We propose a generalized and mathematically sound L0 sparse expression, together with a new effective method, for motion deblurring. [sent-6, score-0.211]
2 Our system does not require extra filtering during optimization and demonstrates fast energy decreasing, making a small number of iterations enough for convergence. [sent-7, score-0.232]
3 It also provides a unifiedframeworkfor both uniform andnon-uniform motion deblurring. [sent-8, score-0.155]
4 blind deconvolution, was extensively studied in these a few years and has achieved great success with a few milestone solutions. [sent-14, score-0.142]
5 Because naive maximum a posterior (MAP) inference could fail on natural images, state-of-the-art methods either maximize marginalized distributions [5, 17, 18, 6] or propose novel techniques in MAP to effectively avoid trivial delta kernel estimates [11, 20, 3, 25, 4, 10]. [sent-15, score-0.146]
6 The particularly useful techniques include adaption of the energy function during optimization [20], explicit sharp edge pursuit [11, 13, 19, 3, 25, 4, 10], edge selection [25], and employment of normalized sparsity measure [16]. [sent-18, score-0.29]
7 Intermediate unnatural image representation exists in many state-of-the-art approaches. [sent-25, score-0.205]
8 [11, 13, 19, 3, 25, 9, 23], which are referred to as semi-blind schemes, and those [20, 16] implicitly incorporating special regularization to remove detrimental structures in early stages and gradually enrich image details in iterations. [sent-26, score-0.11]
9 These maps are vital to make motion deblurring accomplishable in different MAP-variant frameworks. [sent-28, score-0.581]
10 This method, in the first a few iterations, uses a large regularization weight to suppress insignificant structures and preserve strong ones, creating crisp-edge image results, as exemplified in Fig. [sent-31, score-0.121]
11 This scheme is useful to remove harmful subtle image structures, making kernel estimation generally follow correct directions in iterations. [sent-33, score-0.214]
12 Explicit Filter and Selection In [19, 3], shock filter is introduced to create a sharpened reference map for kernel estimation. [sent-41, score-0.483]
13 Cho and Lee [3] performed bilateral filter and edge thresholding in each iteration to remove small- and medium-amplitude structures (illustrated in Fig. [sent-42, score-0.239]
14 These two schemes have been extensively validated in motion deblurring. [sent-46, score-0.136]
15 Unnatural Representation The above techniques enable several successful MAP frameworks in motion deblurring. [sent-47, score-0.1]
16 All of them have their intermediate image results or edge maps different from a natural one, as shown in Fig. [sent-48, score-0.123]
17 We generally call them unnatural representation, which is the key to robust kernel estimation in motion deblurring. [sent-50, score-0.483]
18 Our Contribution Based on the step-edge properties in unnatural representation, we in this paper propose a new sparse L0 approximation scheme to generalize these frameworks. [sent-53, score-0.28]
19 Compared to local shock filter, our edges are not explicitly created by filtering in extra steps. [sent-54, score-0.333]
20 Instead, we incorporate a new regularization term consisting of a family of loss functions to approximate the L0 cost into the objective, which, during optimization, leads to consistent energy minimization and accordingly fast convergence. [sent-55, score-0.327]
21 Besides this new sparse image representation, we also contribute a unified framework for both uniform and nonuniform deblurring, which no longer relies on ad-hoc edge selection, spatial filtering, or edge re-weighting. [sent-58, score-0.289]
22 This framework does not sacrifice the competency in solving the challenging deblurring problem. [sent-59, score-0.528]
23 Given a family of loss functions, based on which a graduate non-convexity could be applied, significant edges quickly improve kernel estimates in only a few iterations. [sent-60, score-0.314]
24 This is most beneficial for non-uniform deblurring where intensive computation is needed in each iteration. [sent-61, score-0.481]
25 Other Related Work In non-uniform deblurring, considering 3D camera rotation, Shan et al. [sent-64, score-0.1]
26 [22] solved non-blind deconvolution with a general projective motion model. [sent-69, score-0.31]
27 [12] advocated a hardware solution that physically captures camera rotation. [sent-71, score-0.1]
28 For acceleration, locally uniform approximation was adopted by Harmeling et al. [sent-75, score-0.091]
29 [9], which combines the patch-based model and a global 3D camera motion one. [sent-77, score-0.2]
30 Shock filter is applied to generate sharp edge prediction. [sent-80, score-0.189]
31 In dealing with depth variation, a tree structure was proposed in [26] to hierarchically estimate blur kernels with scale change. [sent-81, score-0.333]
32 Framework ×× We denote by x the latent image and y the blurred observation. [sent-83, score-0.12]
33 The discrete blur model for camera shake can be expressed as y= ? [sent-85, score-0.457]
34 Hm is a N N transformation matrix, which corresponds to either camera rotation or translation for pose m. [sent-90, score-0.231]
35 km denotes the time that camera pose m lasts and is a weight in this function. [sent-91, score-0.1]
36 (1) models the blurred image as summing unblurred images from all camera poses, which approximates continuous integral on light receival for each pixel. [sent-93, score-0.238]
37 Because H can be camera rotation R or translation M, we discuss these two cases. [sent-94, score-0.231]
38 Camera rotation with 3 degree 1 1 1 1 1 10 0 08 6 6 of freedoms (DoF) is generally sufficient to model nonuniform deblurring [14]. [sent-95, score-0.59]
39 Each Rm thus corresponds to a camera rotation pose, sampled in 3D. [sent-96, score-0.164]
40 Blur with in-plane translation M is referred to as uniform blur. [sent-108, score-0.122]
41 Each Mm is thus a sample in 2D and its total number is called kernel size. [sent-109, score-0.146]
42 In camera translation, we similarly substitute Mm for Hm in Eq. [sent-110, score-0.1]
43 m where BM and AM are block Toeplitz with Toeplitz blocks (BTTB) matrices, since camera translation is linear translation invariant (LTI). [sent-113, score-0.234]
44 New Sparsity Function Our framework contains a sparse φ0(·) loss function, which can effectively approximate L0 sparsity during iterative optimization. [sent-114, score-0.167]
45 A few other sparsity-pursuit functions used in deblurring [20, 16] are also plotted in this figure. [sent-127, score-0.521]
46 Final Objective φ0 (·) is incorporated in our method to regularize optimization, which seeks an intermediate sparse representation ˜x containing only necessary edges. [sent-129, score-0.119]
47 Our objective to estimate the blur kernel from the input image is m( x˜,ikn)⎨⎧? [sent-130, score-0.411]
48 Hm could be either Rm or Mm depending on solving the uniform or non-uniform deblurring problem, as shown in Eqs. [sent-138, score-0.536]
49 φ0 (∂∗ x˜) is the new regularization term, which is instrumental in our method, to guide kernel estimation. [sent-153, score-0.22]
50 The unnatural L0 representation computed from our method is image ˜x produced in iterations to solve Eq. [sent-166, score-0.276]
51 Compared to employing shock filter [19, 3] as an extra step that cannot fit into the overall function for consistent energy minimization, φ(·) and ˜x are elegantly incorporated in one objective, optimizing which monotonically decreases energy. [sent-170, score-0.428]
52 Meanwhile, x˜ is not produced by local filtering, which thus guarantees to contain only necessary strong edges, regardless of blur kernels. [sent-171, score-0.265]
53 , (8) in each iteration t + 1, where the information of kt and x˜t is embedded in the blur matrices Bt and At respectively. [sent-183, score-0.349]
54 By convention, blur kernels are estimated in a coarse-tofine manner in an image pyramid. [sent-184, score-0.333]
55 We employ a similar scheme that minimizes a family of loss functions. [sent-196, score-0.129]
56 (1⎭0) We a⎩lternate between computing ˜x and updating lhi and ⎭lvi in iterations for each loss function controlled by ? [sent-233, score-0.366]
57 Update l Solving for lhi in the function { |lhi |0 + 1/? [sent-235, score-0.176]
58 It is efficient when dealing with in-plane translational camera motion M, as the matrix-vector production with regard to the BTTB matrix can be achieved using FFTs. [sent-246, score-0.234]
59 )λ2 +F FD2(∂v) · F(lv) , (12) where F(·) is the FFT operator, which takes an image vector or a BTTB kernel matrix as input. [sent-249, score-0.146]
60 lh and lv are vectors concatenating all lhi and lvi respectively. [sent-253, score-0.368]
61 When considering non-uniform blur caused by camera rotation, which is spatially variant, the blur matrix BR is no longer block Toeplitz with Toeplitz blocks (BTTB). [sent-255, score-0.63]
62 In this approximation, each patch has one blur kernel basis ARδ, generated by applying rotation to a special patch containing all black pixels except for a white point at the δ center. [sent-258, score-0.595]
63 A blur kernel for each patch is then formed using ARδk = ? [sent-259, score-0.471]
64 ote by Cp( x˜) and Ck (ARδk) the p-th patch from the latent image and its corresponding kernel ARδk respectively. [sent-265, score-0.242]
65 A blurred patch Cp(y) is generated by convolving Ck (ARδk) and Cp( x˜). [sent-266, score-0.144]
66 This model enables a closed-form approximation of ˜x by deconvolving each patch separately, written as ˜x =W1? [sent-278, score-0.096]
67 1/W is a weight to suppress visual artifacts caused by the window functions [9]. [sent-282, score-0.087]
68 On the con- trary, when the blur is uniform, Eqs. [sent-285, score-0.265]
69 In implementation, we use a family of 4 loss functions with ? [sent-287, score-0.169]
70 We achieve it by setting iteration numbers for different loss functions inversely proportional to ? [sent-299, score-0.111]
71 With the duality of the blur kernel and latent image in convolution, the AM matrix for translational camera motion is BTTB, making blur kernel estimation also find a closedform solution in frequency domain [25]. [sent-312, score-1.124]
72 To further reduce iterations, we introduce a parameter α controlling the “step size” [1], making updating expressed as k(n+1)= k(n)·? [sent-322, score-0.084]
73 “Energy” and ”Kernel Similarity” plots denote resulting energy and kernel similarity to the ground truth in iterations. [sent-327, score-0.23]
74 Our method only needs to perform it 5 times (according to number t in Algorithm 1) in one image level, compared to tens or even hundreds iterations involved in other approaches. [sent-331, score-0.104]
75 In the final step, we restore the natural image by non-blind deconvolution given the final kernel estimate. [sent-335, score-0.324]
76 Image restoration for both the uniform and non-uniform blur is accelerated by FFTs. [sent-338, score-0.398]
77 Discussion Difference to Shock Filter Compared to edge prediction using shock filter and edge thresholding [3, 25], our approach employs Eqs. [sent-340, score-0.534]
78 (11) achieves theoretically sound gradient thresholding without extra ad-hoc operations. [sent-343, score-0.167]
79 In the sequel, our method does not have the edge location problem inherent in shock filter when blur kernels are highly non-Gaussian or the saddle points used in shock filter do not correspond to latent image edges. [sent-344, score-1.118]
80 (12)) can naturally produce a sparse representation faithful to the input, vastly benefitting motion deblurring. [sent-346, score-0.139]
81 In practice, 5-pass kernel estimation in one image level is enough, compared to hundreds ofiterations by variational Bayesian inference [5], and tens of iterations in the methods of [20, 16]. [sent-352, score-0.282]
82 We measure the similarity between the estimated kernels and the ground truth using the maximum correlation, counting in kernel shift. [sent-354, score-0.214]
83 3 manifest that the rapid convergence does not sacrifice the quality of kernel estimates. [sent-372, score-0.193]
84 The finding is that using the image space constraint for updating ˜x and gradient domain energy to update kernel k (middle of Table 1) is better than other alternatives. [sent-375, score-0.316]
85 We compare the running time of several representative deblurring methods, ofwhich implementations are available. [sent-377, score-0.481]
86 The set of [17] contains 32 images of size 255 255 blurred with 8 different kernels. [sent-382, score-0.084]
87 We use the provided script and non-blind deconvolution function to generate the results, for fairness. [sent-387, score-0.178]
88 All the 32 kernel estimates from the proposed method are shown in (b). [sent-396, score-0.146]
89 This dataset con- sists of 4 images, each is blurred with 12 kernels, including several large ones. [sent-401, score-0.084]
90 Quantitative evaluation is conducted by comparing each deblurring result with 199 unblurred images captured along the camera motion trajectory and recording the largest PSNR. [sent-404, score-0.765]
91 Note that all top ranking methods [25, 3, 23] use shock filter except ours. [sent-407, score-0.337]
92 Non-uniform Deblurring Our framework is fully appli- cable to non-uniform deblurring with the model depicted in the paper. [sent-412, score-0.481]
93 Concluding Remarks We have presented a new framework for both uniform and non-uniform motion deblurring, leveraging an unnatural L0 sparse representation to greatly benefit kernel estimation and large-scale optimization. [sent-422, score-0.577]
94 We proposed a unified model, which seeks gradient sparsity close to L0 to remove pernicious small-amplitude structures. [sent-423, score-0.164]
95 The method not only provides a principled understanding of effective motion deblurring strategies, but also notably augments performance based on the new optimization process. [sent-424, score-0.581]
96 Spacevariant single-image blind deconvolution for removing cam- [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] era shake. [sent-492, score-0.284]
97 Recording and playback of camera shake: benchmarking blind deconvolution with a real-world database. [sent-536, score-0.384]
98 Total variation minimizing blind deconvolution with shock filter reference. [sent-570, score-0.621]
99 Rotational motion deblurring of a rigid object from a single image. [sent-584, score-0.581]
100 Richardson-lucy deblurring for scenes under a projective motion path. [sent-592, score-0.613]
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