cvpr cvpr2013 cvpr2013-131 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Uwe Schmidt, Carsten Rother, Sebastian Nowozin, Jeremy Jancsary, Stefan Roth
Abstract: Non-blind deblurring is an integral component of blind approaches for removing image blur due to camera shake. Even though learning-based deblurring methods exist, they have been limited to the generative case and are computationally expensive. To this date, manually-defined models are thus most widely used, though limiting the attained restoration quality. We address this gap by proposing a discriminative approach for non-blind deblurring. One key challenge is that the blur kernel in use at test time is not known in advance. To address this, we analyze existing approaches that use half-quadratic regularization. From this analysis, we derive a discriminative model cascade for image deblurring. Our cascade model consists of a Gaussian CRF at each stage, based on the recently introduced regression tree fields. We train our model by loss minimization and use synthetically generated blur kernels to generate training data. Our experiments show that the proposed approach is efficient and yields state-of-the-art restoration quality on images corrupted with synthetic and real blur.
Reference: text
sentIndex sentText sentNum sentScore
1 † Microsoft Research Cambridge Abstract Non-blind deblurring is an integral component of blind approaches for removing image blur due to camera shake. [sent-4, score-1.081]
2 Even though learning-based deblurring methods exist, they have been limited to the generative case and are computationally expensive. [sent-5, score-0.571]
3 One key challenge is that the blur kernel in use at test time is not known in advance. [sent-8, score-0.496]
4 From this analysis, we derive a discriminative model cascade for image deblurring. [sent-10, score-0.256]
5 Our cascade model consists of a Gaussian CRF at each stage, based on the recently introduced regression tree fields. [sent-11, score-0.324]
6 We train our model by loss minimization and use synthetically generated blur kernels to generate training data. [sent-12, score-0.786]
7 Image deblurring has thus been an active area of research, starting with the pioneering work of Lucy [21] and Richardson [23]. [sent-18, score-0.53]
8 Recent work has predominantly focused on blind deblurring, particularly on estimating the blur from images (stationary and non-stationary). [sent-19, score-0.52]
9 Yet, this is an important problem since most blind deblurring approaches separate the problem into blur estimation and non-blind deblurring (theoretically justified by Levin et al. [sent-21, score-1.58]
10 To this date, most approaches rely on the classical Lucy-Richardson algorithm as non-blind deblurring component [e. [sent-23, score-0.53]
11 In this paper we introduce a discriminative non-blind image deblurring approach for arbitrary photographic input images and arbitrary blurs. [sent-30, score-0.69]
12 To the best of our knowledge, this is the first time discriminative deblurring has been attempted. [sent-31, score-0.601]
13 the observed image is the result of convolving the unknown original image with a blur kernel (+ noise), but our approach is not limited to this setup and can be extended to non-uniform image blurs. [sent-35, score-0.533]
14 Since it is in general not feasible to train a specialized model for every image blur, it is necessary to train a model that outputs a deblurred image given an arbitrary input image and blur kernel. [sent-37, score-0.687]
15 We address this by effectively parametrizing our discriminative model with the blur kernel. [sent-38, score-0.514]
16 We address this using a model cascade based on regression tree fields [15], which first predicts a relatively crude estimate that removes dominant image blur and is refined further in later stages. [sent-40, score-0.811]
17 We use synthetically generated blur kernels to overcome this limitation. [sent-42, score-0.691]
18 While previous non-blind deblurring approaches have for the most part either been very fast but 666000224 with inferior performance, or slow but with high-quality results [e. [sent-44, score-0.53]
19 25], our approach delivers state-of-the-art deblurring performance with an efficient inference method that allows deblurring even higher-resolution images. [sent-46, score-1.06]
20 In image deblurring, denoising and other restoration applications, sparse image priors are frequently used for regularization [e. [sent-49, score-0.274]
21 I)n =the N case Kofx n,σon-blind deconvolution, we have Kx = k ⊗ x, where K is the bdleucro mnvaotrluixti otnha,t corresponds xto = convolving thhee image sw tihteh a blur kernel k. [sent-61, score-0.533]
22 The image noise is assumed to be pixelindependent additive white Gaussian noise with variance σ2. [sent-62, score-0.216]
23 , MAP estimation) by introducing (independent) auxiliary/latent variables zjc for each filter and image clique, such that the prior is re? [sent-66, score-0.265]
24 Updating z based on p(z|y, x) is easy, since all zjc are independent: p(z|x,y) ∝ ? [sent-112, score-0.208]
25 odtohmingfiebldu,t 666000335 Therefore μx|y,z∗ and Σx|y,z∗ are the mean and covariance parameters yo,zf a multivariate normal distribution defined on the whole image, chosen through so as to hopefully lead to good deblurring results. [sent-152, score-0.559]
26 Non-blind image deblurring is more difficult than image denoising, and it might be difficult to directly regress suitable model parameters. [sent-169, score-0.685]
27 Then, in the generative approach one can think of zjc as modulating pairwise potentials: reducing smoothness constraints in case of large image derivatives of the output image x, and imposing smoothness otherwise. [sent-171, score-0.249]
28 But in the case of deblurring, the image content in y is shifted and combined with other parts of the image, depending on a blur kernel that is different for each image. [sent-175, score-0.496]
29 We believe this is one of the reasons why discriminative non-blind deblurring approaches had not been attempted before. [sent-177, score-0.601]
30 In a standard half-quadratic approach (top), each zjc can only be updated via Eq. [sent-181, score-0.208]
31 In the proposed discriminative cascade (bottom), one can use arbitrary pferaotpuoresse do fd tihscer image over larger areas (large white circles) to find model parameters Θ(i) and via regression. [sent-183, score-0.318]
32 Discriminative model cascade To build a discriminative model for deblurring, we draw inspiration from the iterative refinement of z in halfquadratic regularization. [sent-187, score-0.455]
33 We start with an educated guess of the Gaussian model parameters, regressed from the input image, to obtain a restored image x(1) , which is less corrupted than the original input image. [sent-188, score-0.271]
34 We can then use this as an intermediate result to help regress refined Gaussian model parameters, in order to obtain a better restored image x(2) , etc. [sent-189, score-0.272]
35 Image denoising and other restoration tasks may also benefit from such a model cascade and repeated refinement of the auxiliary variables; we do not consider this here, however. [sent-192, score-0.417]
36 As discussed above, a standard generative halfquadratic approach updates each zjc only based on the local clique of the current estimate of the restored image (cf. [sent-194, score-0.505]
37 In a discriminative approach, we can regress the parameters based on arbitrary local and global properties of the input image as well as the current estimate of the re- Θ(i) 666000446 stored image (see Fig. [sent-197, score-0.254]
38 The proposed discriminative cascade is also related to the active random field [2], which is a multi-stage approach for image denoising that is trained discriminatively. [sent-203, score-0.345]
39 Gaussian CRF for Deblurring As we have seen, a discriminative alternative to halfquadratic MAP estimation is conceptually attractive, but also challenging due to the need of regressing local image models from the blurred input image y. [sent-206, score-0.348]
40 lO Gnaeu challenge i np devising such a model is that we cannot train a different model for every blur matrix K; this difficulty may in fact be the reason why no such approach exists to date. [sent-208, score-0.503]
41 (t h6)a;t tthhee blur is not used as an input feature to the regressor. [sent-221, score-0.439]
42 However, for deblurring this is not feasible, and it is crucial to incorporate a blur component into the model to adapt to arbitrary blurs. [sent-225, score-1.005]
43 We extend these previous RTF-based approaches to our setting by (a) incorporating the blur likelihood for non-blind image deblurring into the prediction as outlined in Eqs. [sent-248, score-1.007]
44 (6) and (7), and (b) by assembling multiple RTFs into a model cascade that iteratively refines the prediction (see Sec. [sent-249, score-0.22]
45 Second, the model parameters of arbitrary pairwise Gaussian potentials (with full mean and covariance) are regressed from the input image, whereas [27] restrict their parameterization to diagonal weighting of filter responses. [sent-254, score-0.269]
46 Since capturing image pairs of blurred and clean images is difficult, one possible avenue is to synthesize training data by blurring clean images with realistic blurs. [sent-262, score-0.296]
47 Unfortunately, existing databases [16, 20] only supply a relatively limited number of blur kernels, and moreover serve also for testing. [sent-263, score-0.414]
48 We address this problem by generating realistic-looking blur kernels by sampling random 3D trajectories using a simple linear motion model; the obtained trajectories are projected and rasterized to random square kernel sizes in the range from 5 5 up to 27 27 pixels (see Fig. [sent-265, score-0.679]
49 r Wealhi slteic i tk weronuellds through more accurate models of camera shake motion3, we find that these synthetic kernels already allow to generalize well to unseen real blur (cf. [sent-268, score-0.706]
50 We synthetically generate blurred images by convolving each clean image with an artificially generated blur kernel, and subsequently add pixel-independent Gaussian noise (using standard deviations σ = 2. [sent-271, score-0.83]
51 2, it is difficult to directly regress good local image models from the blurred input image. [sent-279, score-0.287]
52 Therefore, we employ a cascade of RTF models, where each subsequent model stage uses the output of all previous models as features for the regression (see Fig. [sent-280, score-0.396]
53 We train the first stage of the cascade with minimal conditioning on the input image to avoid overfitting. [sent-282, score-0.303]
54 The parameters of the unary and pairwise potentials are only linearly regressed from the pixels in the respective cliques (plus a constant pseudo-input); we do not use a regression tree. [sent-283, score-0.246]
55 We train this model with 200 pairs of blurred and clean images, which is ample since there are only few model parameters. [sent-285, score-0.26]
56 3We think that on average these synthetic blur kernels more challenging than typical real ones. [sent-287, score-0.597]
57 While we do not expect excellent results from RTF1 , it is able to remove the dominant blur from the input image (cf. [sent-291, score-0.466]
58 6) and makes it much easier for subsequent ×× RTF stages to regress good potentials for the CRF. [sent-294, score-0.276]
59 However, we use a different filter bank here, the 16 generatively trained 5 5 fdiliftefersre nfrot mfil tehre b arencken hte Fields-of-Experts mveoldye trl aoinf [e1d0 5]; we found these filters to outperform other filter banks we have tried, including those used in [14]4. [sent-298, score-0.245]
60 An interesting property of our model cascade is that it yields a deblurred image after every stage, not only at the end. [sent-311, score-0.281]
61 Even if a deep cascade was trained, at test time we can trade off computational resources versus quality of the deblurred image by stopping after a certain stage (cf. [sent-312, score-0.368]
62 when training and testing is carried out with perfect blur kernels. [sent-319, score-0.449]
63 proach by training the model to deal with imperfect blur kernels. [sent-329, score-0.478]
64 This is important for blind deblurring, where the estimated blur kernels mostly contain some errors. [sent-330, score-0.731]
65 Please note that images and kernels are always kept strictly separate for training and testing in all experiments. [sent-332, score-0.218]
66 We trained a six-stage RTF prediction cascade as described in Sec. [sent-334, score-0.232]
67 Training images have been blurred synthetically with 1% additive white Gaussian noise (σ = 2. [sent-336, score-0.371]
68 While we used artifical blur kernels to generate our training data, the test images from [25] have been created with the realistic kernels from [20]. [sent-340, score-0.87]
69 The blur kernels used for deblurring are slightly perturbed from the ground truth to mimic kernel estimation errors, but the perturbation is somewhat minor here. [sent-341, score-1.234]
70 ground truth) blur kernels, as usual for non-blind deblurring, our approach achieves excellent results. [sent-363, score-0.441]
71 our model has been trained on artificially generated blur kernels (Fig. [sent-369, score-0.706]
72 Blind deblurring approaches often produce kernel estimates with substantial errors, which can cause ringing artifacts in the restored image [cf. [sent-372, score-0.772]
73 To train our model for this task, we experimented with adding noise to the ground truth kernels and also used estimated kernels for training. [sent-375, score-0.554]
74 [19] as a benchmark, which provides several kernel estimates besides blurred and ground truth images for 32 test instances, as well as deblurring results with the various kernel estimates. [sent-377, score-0.901]
75 Since the amount of noise in these blurred images is significantly lower than in the benchmark of [25], we only added Gaussian noise with σ = 0. [sent-378, score-0.321]
76 2 show that training with ground truth kernels leads to subpar performance when kernels estimates are used at test time. [sent-382, score-0.472]
77 Adding noise to the ground truth kernels for training leads to improved results of RTF1 with estimated kernels at test time, but performance of our second stage model RTF2 already deteriorates; hence those noisy kernels are not an ideal proxy for real kernel estimates. [sent-383, score-0.914]
78 However, we achieve superior results by training our model with a mix of perfect and estimated kernels (obtained with the method of Xu and Jia [30]), i. [sent-384, score-0.304]
79 for half of the synthetically blurred training images we use an estimated kernel instead of the ground truth kernel5. [sent-386, score-0.4]
80 Compared to the deblurred images from [19] (which used the 5Here, we trained RTF1 and RTF2 with the same 200 images as it was time-consuming to obtain good enough kernel estimates for training. [sent-387, score-0.265]
81 666000779 those in the two rightmost columns: we derived the noisy ground truth (GT) kernels from the provided GT kernels, and estimated kernels with [30]. [sent-388, score-0.419]
82 The last row shows the average performance of deblurring results provided by [19] (using the non-blind approach of [18]). [sent-389, score-0.53]
83 For the kernel estimates of [19] (4th column), we used the “free energy with diagonal covariance approximation” algorithm in the filter domain. [sent-390, score-0.214]
84 non-blind approach of [18]), we achieve substantial performance improvements for deblurring with estimated kernels of up to 0. [sent-391, score-0.741]
85 [16] to demonstrate results on realistic higher-resolution images; these images may substantially violate our model’s stationary blur and Gaussian noise assumptions (which can deteriorate performance [cf. [sent-406, score-0.625]
86 The overall best performing blind deblurring approach in this benchmark is the one by Xu and Jia [30] despite making a stationary blur assumption, i. [sent-409, score-1.126]
87 the same blur kernel is used in all parts of the image. [sent-411, score-0.496]
88 We use the provided kernel estimates by [30] from the benchmark dataset, but with our non-blind method to obtain the deblurred image (treating color channels R, G, and B independently). [sent-412, score-0.259]
89 While Xu 6The result might not be fully comparable, since the blur kernel estimation and non-blind method from [6] may have been used. [sent-415, score-0.496]
90 7Theoretically, in the absence of noise non-blind deblurring can be solved exactly without any regularization by inverting the blur matrix. [sent-416, score-1.071]
91 [16] for each combination of 4 test images and 12 blur kernels. [sent-418, score-0.414]
92 We use the provided blur kernel estimates of [30] with our RTF2 model for non-blind deblurring. [sent-419, score-0.571]
93 3), showing the result of our RTF2 model (right) given the blurred image (left) and the kernel estimates by [30]. [sent-422, score-0.293]
94 trained with a mix of ground truth and estimated kernels (using [30]), and additive Gaussian noise with σ = 0. [sent-430, score-0.417]
95 The first stage RTF1 removes dominant blur from the image (c), but artifacts remain. [sent-434, score-0.53]
96 The blur kernel is shown at the upper left of (b), scaled and resized for better visualization. [sent-438, score-0.496]
97 Summary and Conclusions From a novel analysis of common half-quadratic regularization, we introduced – to the best of our knowledge – the first discriminative non-blind deblurring method. [sent-441, score-0.601]
98 Our proposed cascade model is based on regression tree fields at each stage, which are trained by loss minimization on training data generated with synthesized blur kernels. [sent-442, score-0.859]
99 Our approach is not limited to image deblurring and can readily be extended to other image restoration applications in the future. [sent-444, score-0.648]
100 Motion-aware noise filtering for deblurring of noisy and blurry images. [sent-625, score-0.605]
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