cvpr cvpr2013 cvpr2013-265 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Florent Couzinié-Devy, Jian Sun, Karteek Alahari, Jean Ponce
Abstract: This paper addresses the problem of restoring images subjected to unknown and spatially varying blur caused by defocus or linear (say, horizontal) motion. The estimation of the global (non-uniform) image blur is cast as a multilabel energy minimization problem. The energy is the sum of unary terms corresponding to learned local blur estimators, and binary ones corresponding to blur smoothness. Its global minimum is found using Ishikawa ’s method by exploiting the natural order of discretized blur values for linear motions and defocus. Once the blur has been estimated, the image is restored using a robust (non-uniform) deblurring algorithm based on sparse regularization with global image statistics. The proposed algorithm outputs both a segmentation of the image into uniform-blur layers and an estimate of the corresponding sharp image. We present qualitative results on real images, and use synthetic data to quantitatively compare our approach to the publicly available implementation of Chakrabarti et al. [5].
Reference: text
sentIndex sentText sentNum sentScore
1 The estimation of the global (non-uniform) image blur is cast as a multilabel energy minimization problem. [sent-2, score-0.914]
2 The energy is the sum of unary terms corresponding to learned local blur estimators, and binary ones corresponding to blur smoothness. [sent-3, score-1.64]
3 Its global minimum is found using Ishikawa ’s method by exploiting the natural order of discretized blur values for linear motions and defocus. [sent-4, score-0.838]
4 Once the blur has been estimated, the image is restored using a robust (non-uniform) deblurring algorithm based on sparse regularization with global image statistics. [sent-5, score-1.18]
5 The proposed algorithm outputs both a segmentation of the image into uniform-blur layers and an estimate of the corresponding sharp image. [sent-6, score-0.24]
6 Short exposures and small apertures can be used to limit motion blur and increase depth of field, but this may result in noisy images, especially under low light conditions. [sent-12, score-0.856]
7 It is therefore desirable to model the blurring process, and use the image content itself to estimate the corresponding parameters and restore a sharp image. [sent-13, score-0.254]
8 This problem is known as blind deblurring (or blind deconvolution), and it is the topic of this presentation. [sent-14, score-0.574]
9 1In contrast, non-blind deblurring refers to the simpler (but still quite challenging) problem of recovering the sharp image when the blur parameters are known. [sent-16, score-1.283]
10 Two images demonstrating defocus and motion blur, with an out-of-focus swan in the foreground (left), and a moving bus before a static background (right) respectively. [sent-18, score-0.243]
11 Related Work There have been many attempts in the past to solve the image deblurring problem. [sent-25, score-0.358]
12 Amongst these, it is commonly assumed that the blur kernel is spatially uniform [4, 7, 15, 18, 26, 37, 38], which allows it to be estimated from global image evidence. [sent-26, score-0.868]
13 [27] argue that it is desirable to first estimate the blur kernel before using it to deblur the image. [sent-28, score-0.817]
14 Statistical gradient priors [33], sharp edge assumptions [22, 36], and non-convex regularization [24] have also been imposed on the latent sharp image for blur estimation. [sent-31, score-1.159]
15 Although these approaches may give impressive results, they assume that the blur kernel is uniform which, as demonstrated by Figure 1, is not realistic in many settings involving out-of-focus regions or blur due to moving objects. [sent-32, score-1.619]
16 1 1 10 0 07 7 735 3 The uniform kernel assumption has recently been relaxed in several blind deblurring methods that assume instead that blur is mostly due to camera rotation, which is realistic for camera shake in long exposures [6, 8, 16, 17, 21, 35]. [sent-33, score-1.453]
17 In this case, the blurry image can be seen as an integral over time of images related to each other by homographies [34, 35]. [sent-34, score-0.256]
18 An effective framework has also been proposed in [17] to approximate the spatially-varying blur kernels by combining a set of localized uniform blur kernels. [sent-35, score-1.555]
19 Such works handle a specific type of non-uniform blur, where a global camera motion constraint can be imposed over the kernels, which simplifies the problem of kernel estimation. [sent-36, score-0.201]
20 Proposed Approach We propose a method for joint image segmentation and deblurring under defocus and linear (say, horizontal) motion blur. [sent-40, score-0.594]
21 [28] detect blurry regions, but do not estimate the exact kernels that affect them. [sent-43, score-0.305]
22 The algorithms proposed in [1, 8] rely on multiple blurry images or video frames to reduce the ambiguity of motion blur estimation and segmentation. [sent-44, score-1.098]
23 [5] show interesting results for separating the blur and sharp regions in an image, but do not address deblurring itself, which is equally challenging. [sent-46, score-1.319]
24 Dai and Wu [9] and Levin [25] rely on different local spectral or gradient cues, as well as natural image statistics for motion blur estimation. [sent-47, score-0.839]
25 In summary, previous approaches to our deblurring problem either (i) fall short in the estimation or the deblurring step, (ii) require multiple images, or (iii) consider a limited set of blur types (e. [sent-49, score-1.48]
26 We aim to overcome these limitations, and cast the estimation of the global (non-uniform) image blur as a multilabel energy minimization problem (Section 2). [sent-52, score-0.914]
27 The energy is the sum of unary terms corresponding to learned local blur kernel estimators (Section 2. [sent-53, score-1.009]
28 Its global minimum is found using Ishikawa’s method by exploiting the natural order of discretized blur values for linear motions and defocus. [sent-55, score-0.838]
29 Once the blur has been estimated, the image is restored using a robust (non-uniform) deblurring algorithm based on sparse regularization with global image statistics (Section 3). [sent-56, score-1.18]
30 The proposed algorithm outputs both a segmentation of the image into uniform-blur layers and an estimate of the corresponding sharp image. [sent-57, score-0.24]
31 Estimating the Image Blur We show in this section that estimating the non-uniform blur of an image can be cast as a segmentation problem, where uniform regions correspond to homogeneous blur strength. [sent-61, score-1.628]
32 Local (but noisy) blur estimators are learned using logistic regression. [sent-62, score-0.878]
33 A robust global estimate of the image blur is then obtained by combining the corresponding local estimates with smoothness constraints in a multi-label energy minimization framework, where labels correspond to integer (rounded) blur strengths. [sent-63, score-1.688]
34 Since integer labels admit a natural order, it is then possible to find the global minimum of the energy using appropriate smoothness terms and Ishikawa’s method [10, 19]. [sent-64, score-0.18]
35 Learning Local Blur Estimators For simplicity, we model horizontal blur as a moving average, and defocus by a Gaussian filter. [sent-67, score-0.969]
36 Training data is obtained by (globally) blurring a set of natural sharp images for each value of σ. [sent-73, score-0.248]
37 We represent the local grey level pattern around each pixel in a blurry image by a feature vector x of dimension L 1obtained by pooling the responses of a fixed bank of L multi-scale filters. [sent-75, score-0.281]
38 2 The filters used in our framework are a combination of 64 Gabor filters and of atoms of a dictionary learned on blurry and sharp natural images since these have been shown to prove useful in many image restoration tasks [11]. [sent-78, score-0.698]
39 The dictionary is learned such that some of its atoms represent blurry patches. [sent-79, score-0.388]
40 This is achieved by first learning a small dictionary [11] from blurry image patches alone. [sent-80, score-0.318]
41 We then learn the complete dictionary, where the initial atoms are fixed to those learned from blurry patches, with sharp image patches. [sent-81, score-0.531]
42 Figure 2 (left) shows an illustration of dictionary-based filters learned for the horizontal motion blur case. [sent-82, score-0.992]
43 Note that the atoms shown here in the top few rows correspond to blurry patches. [sent-83, score-0.313]
44 + 2Our filters are designed to give zero values on uniform patches since the overall grey level is irrelevant for blur estimation. [sent-84, score-0.9]
45 Left: a dictionary learned on blurry (horizontal motion blur in this case) and sharp natural images. [sent-88, score-1.355]
46 In practice, we divide the useful range [0, Σ] of blur values into K intervals Ik = [σk−1 , σk] for k = 1, . [sent-94, score-0.76]
47 3The observant reader may have noticed that since the k estimators are learned independently, the function fk − fk−1 is not guaranteed to be positive. [sent-108, score-0.203]
48 Given a fixed number P of integer labels, we split the blur parameter space into P bins and predict a bin for each pixel. [sent-110, score-0.805]
49 The function U is the unary cost of assigning label yi to the feature xi, as derived in the previous section, and B is a pairwise smoothness term that ensures that nearby pixels have consistent blur values. [sent-124, score-0.886]
50 After obtaining the optimal kernel labels yi for each pixel i, the local blur for the pixel will be represented by the motion or defocus kernel with corresponding value σi. [sent-128, score-1.1]
51 Deblurring the Image We now address the problem ofdeblurring the blurry image. [sent-130, score-0.256]
52 Given the blur kernel estimated for each pixel in the previous section, we can construct a non-uniform blur kernel matrix Kˆ. [sent-131, score-1.58]
53 Using this model, the blurry image f = Kˆg + u + μ, where f and g are the blurry and sharp images in vector form respectively, and Kˆg denotes the spatially-varying blurring process in matrix form. [sent-133, score-0.739]
54 By further assuming that the error term u is sparsely distributed in the 1 1 10 0 07 7 757 5 with only the unary cost, blur estimation with unary and binary costs, which corresponds to the global minimum of the energy function (3). [sent-136, score-0.998]
55 image domain, we estimate the sharp image g by optimizing: mg,iun12||Kˆg+u−f||22+λ1(||F1g||αα+||F2g||αα)+λ2||u||1, (5) where | |Fig| |αα = ? [sent-137, score-0.212]
56 Experiments Obtaining a quantitative evaluation of algorithms for spatially-varying blur is a difficult task. [sent-155, score-0.74]
57 The results of [5] are shown for both its steps, using blur cues only (which is comparable to our method), and with blur and object cues. [sent-162, score-1.511]
58 We also tested our multi-label framework, which handles images with multiple blur levels, in a binary setting, where there are exactly two labels – one to describe the sharp regions, and another for the blurry areas. [sent-163, score-1.259]
59 way of obtaining a ground truth to evaluate the blur estimation or the deblurring results. [sent-164, score-1.122]
60 Thus, we have built a synthetic dataset, where the region blurred and the strength of the blur are known. [sent-166, score-0.878]
61 We evaluate our approach for non-uniform blind deblurring at several levels. [sent-169, score-0.466]
62 First, we evaluate our energy formulation for blur prediction (Section 2. [sent-170, score-0.815]
63 Given this blur estimation, we then evaluate the proposed deconvolution method, and compare with the popular Richardson-Lucy algorithm [29, 32]. [sent-172, score-0.855]
64 We also compare the quality of the resulting sharp image with that obtained from two baseline deblurring algorithms based on [13, 33]. [sent-173, score-0.543]
65 Datasets For a quantitative evaluation of our blur prediction and deblurring methods, we introduce a synthetic dataset. [sent-176, score-1.202]
66 It consists of 4 sharp images, which were subjected to different levels of horizontal and Gaussian blurs. [sent-177, score-0.363]
67 In essence, this produces ground truth (blur estimate) segmentations and corresponding blurred images for each sharp image. [sent-181, score-0.23]
68 From top to bottom: input image, estimated blur (regions shown in red) with unary and binary costs, the result of [5] using only blur cues, and [5] with blur as well as object cues. [sent-185, score-2.304]
69 that this synthetic dataset may not very accurate, in particular, near the blur boundaries. [sent-187, score-0.812]
70 4 In our experiments, we used a bank of 64 Gabor filters, with different orientations and frequencies, and a dictionary of 320 atoms learned on a set of blurry and sharp natural images to generate the feature set for an image. [sent-193, score-0.594]
71 Here we show the average values for three images from our synthetic dataset, each subjected to six levels of horizontal blur. [sent-206, score-0.27]
72 Blur Estimation We evaluated our local blur estimators (i. [sent-209, score-0.82]
73 In the horizontal blur case, the task is to predict one value from the set σi = {1 3 5 7 9 11 13}, and in the Gaussian blur case, we us=ed a 1se 3t o5f 7 79 9 bl 1u1rs 1o3f} }v,a arinadn ciens t uheni Gfoarumslsyia spread between 0 and 4. [sent-212, score-1.579]
74 We predicted the blur at each pixel individually, with an accuracy of 72% and 62% in the horizontal and Gaussian blurs respectively. [sent-213, score-0.892]
75 A visualization of blur prediction on an entire image using unary costs alone, i. [sent-214, score-0.856]
76 We introduce the smoothness term B (4) to ensure that nearby pixels have consistent blur values. [sent-218, score-0.792]
77 The method by [5] uses a two-step process: (i) blur cues are first used to construct an initial blur estimate segmentation; and then (ii) a color model is learned for each region to yield the final segmentation. [sent-223, score-1.571]
78 Since our approach only uses blur cues, it would be fair to compare it with the results from step (i). [sent-225, score-0.74]
79 Our framework handles images with multiple blur levels (see Figure 3 (right) for example, which shows three distinct blur regions). [sent-229, score-1.548]
80 We tested this generic framework in a binary setting, where only one blur level is assumed, with the other label corresponding to sharp regions, similar to [5]. [sent-230, score-0.946]
81 PSNR values obtained with our method and two stateof-the-art uniform blind deconvolution algorithms on the bus, car, and horse images from our synthetic dataset (see Figures 4, 5). [sent-235, score-0.368]
82 We provide a good approximation for uniform (horizontal) blur regions with a manually marked bounding box enclosing the blurry object. [sent-236, score-1.11]
83 Our method, despite the lack of such ‘ground truth’ blur regions, performs better than the two other methods here. [sent-237, score-0.74]
84 2-label approach shows a performance comparable to [5] with object cues, and outperforms it when only blur cues are used. [sent-241, score-0.771]
85 Deblurring Given the computed non-uniform blur in an image, we estimate the sharp image with our deblurring method. [sent-244, score-1.31]
86 Since there appear to be no deconvolution methods that handle gracefully non-uniform blurs considered here, we adapted three methods to make our baseline comparisons. [sent-245, score-0.189]
87 We show this comparison as average PSNR values, computed on three synthetic images with six strengths of blur each, in Table 2. [sent-247, score-0.812]
88 We also compared our deblurring results with two state-of-the-art uniform blind deblurring algorithms [13, 33]. [sent-248, score-0.877]
89 We observe that our method, which requires no such ‘ground truth’ blur regions, outperforms [13] significantly, and is comparable to or better than [33]. [sent-251, score-0.74]
90 In Table 4 we compare the PSNR values of blurred and estimated sharp image. [sent-252, score-0.25]
91 We also evaluated our blur estimation and deconvolution methods qualitatively on real images from other [5, 25], as well our own datasets. [sent-253, score-0.879]
92 A selection of these results are shown in Figures 6, 7, and 8 for horizontal motion and defocus blurs. [sent-254, score-0.307]
93 Average PSNR values on the synthetic dataset for horizontal and Gaussian blur types. [sent-259, score-0.931]
94 Discussion We presented a novel approach for first estimating nonuniform blur caused by horizontal motion or defocus, and then the sharp (deconvolved) image. [sent-264, score-1.131]
95 A promising direction future work is the construction of a tree structure estimator to be able to handle two different types of blur in the same image. [sent-267, score-0.74]
96 Blind motion deblurring from a single image using sparse approximation. [sent-295, score-0.436]
97 Horizontal blur: Sample deblurring results on two real images from [5] and on one synthetic image. [sent-352, score-0.43]
98 From left to right: blurry image, deblurred image, close-up corresponding to the boxes shown in red. [sent-447, score-0.32]
99 Richardson-lucy deblurring for scenes under a projective motion path. [sent-499, score-0.436]
100 Deconvolving psfs for a better motion deblurring using multiple images. [sent-526, score-0.436]
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