nips nips2006 nips2006-45 knowledge-graph by maker-knowledge-mining

45 nips-2006-Blind Motion Deblurring Using Image Statistics

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Author: Anat Levin

Abstract: We address the problem of blind motion deblurring from a single image, caused by a few moving objects. In such situations only part of the image may be blurred, and the scene consists of layers blurred in different degrees. Most of of existing blind deconvolution research concentrates at recovering a single blurring kernel for the entire image. However, in the case of different motions, the blur cannot be modeled with a single kernel, and trying to deconvolve the entire image with the same kernel will cause serious artifacts. Thus, the task of deblurring needs to involve segmentation of the image into regions with different blurs. Our approach relies on the observation that the statistics of derivative ﬁlters in images are signiﬁcantly changed by blur. Assuming the blur results from a constant velocity motion, we can limit the search to one dimensional box ﬁlter blurs. This enables us to model the expected derivatives distributions as a function of the width of the blur kernel. Those distributions are surprisingly powerful in discriminating regions with different blurs. The approach produces convincing deconvolution results on real world images with rich texture.

Reference: text

Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 Blind Motion Deblurring Using Image Statistics Anat Levin∗ School of Computer Science and Engineering The Hebrew University of Jerusalem Abstract We address the problem of blind motion deblurring from a single image, caused by a few moving objects. [sent-1, score-0.539]

2 In such situations only part of the image may be blurred, and the scene consists of layers blurred in different degrees. [sent-2, score-0.603]

3 Most of of existing blind deconvolution research concentrates at recovering a single blurring kernel for the entire image. [sent-3, score-0.876]

4 However, in the case of different motions, the blur cannot be modeled with a single kernel, and trying to deconvolve the entire image with the same kernel will cause serious artifacts. [sent-4, score-0.913]

5 Thus, the task of deblurring needs to involve segmentation of the image into regions with different blurs. [sent-5, score-0.605]

6 Assuming the blur results from a constant velocity motion, we can limit the search to one dimensional box ﬁlter blurs. [sent-7, score-0.666]

7 This enables us to model the expected derivatives distributions as a function of the width of the blur kernel. [sent-8, score-0.752]

8 1 Introduction Motion blur is the result of the relative motion between the camera and the scene during image exposure time. [sent-11, score-0.972]

9 As blurring can signiﬁcantly degrade the visual quality of images, photographers and camera manufactures are frequently searching for methods to limit the phenomenon. [sent-13, score-0.441]

10 One solution that reduces the degree of blur is to capture images using shorter exposure intervals. [sent-14, score-0.653]

11 An alternative approach is to try to remove the blur off-line. [sent-16, score-0.602]

12 Blur is usually modeled as a linear convolution of an image with a blurring kernel, also known as the point spread function (or PSF). [sent-17, score-0.613]

13 Image deconvolution is the process of recovering the unknown image from its blurred version, given a blurring kernel. [sent-18, score-1.053]

14 In most situations, however, the blurring kernel is unknown as well, and the task also requires the estimation of the underlying blurring kernel. [sent-19, score-0.877]

15 Most of the existing blind deconvolution research concentrates at recovering a single blurring kernel for the entire image. [sent-21, score-0.876]

16 While the uniform blur assumption is valid for a restricted set of camera motions, it’s usually far from being satisfying when the scene contains several objects moving independently. [sent-22, score-0.699]

17 In this work, however, we would like to address blind multiple motions deblurring using a single frame. [sent-24, score-0.481]

18 The ﬁrst assumption is that the image consists of a small number of blurring layers with the same blurring kernel within each layer. [sent-26, score-1.17]

19 Most of the examples in this paper include a single blurred object and an unblurred background. [sent-27, score-0.446]

20 As a result, within each blurred layer, the blurring kernel is a simple one dimensional box ﬁlter, so that the only unknown parameters are the blur direction and the width of the blur kernel. [sent-31, score-1.996]

21 Deblurring different motions requires the segmentation of the image into layers with different blurs as well as the reconstruction of the blurring kernel in each layer. [sent-32, score-1.136]

22 While image segmentation is an active and challenging research area which utilizes various low level and high level cues, the only segmentation cue used in this work is the degree of blur. [sent-33, score-0.485]

23 In order to discriminate different degrees of blur we use the statistics of natural images. [sent-34, score-0.624]

24 Our observation is that statistics of derivatives responses in images are signiﬁcantly changed as a result of blur, and that the expected statistics under different blurring kernels can be modeled. [sent-35, score-0.728]

25 Given a model of the derivatives statistics under different blurring kernels our algorithm searches for a mixture model that will best describe the distribution observed in the input image. [sent-36, score-0.67]

26 This results in a set of 2 (or some other small number) blurring kernels that were used in the image. [sent-37, score-0.44]

27 In order to segment the image into blurring layers we measure the likelihood of the derivatives in small image windows, under each model. [sent-38, score-1.124]

28 Research about blind deconvolution given a single image, usually concentrate at cases in which the image is uniformly blurred. [sent-42, score-0.503]

29 Early deblurring methods treated blurs that can be characterized by a regular pattern of zeros in the frequency domain such as box ﬁlter blurs [26]. [sent-44, score-0.713]

30 Even in the noise free case, box ﬁlter blurs can not be identiﬁed in the frequency domain if different blurs are present. [sent-46, score-0.439]

31 In a creative recent research which inspired our approach, Fergus et al [12] use the statistics of natural images to estimate the blurring kernel (again, assuming a uniform blur). [sent-49, score-0.559]

32 Their approach searches for the max-marginal blurring kernel and a deblurred image, using a prior on derivatives distribution in an unblurred image. [sent-50, score-0.862]

33 They address more than box ﬁlters, and present impressing reconstructions of complex blurring kernels. [sent-51, score-0.52]

34 As the edge’s scale provides some measure of blur this is used for segmenting an image into a focus and out of focus layers. [sent-55, score-0.799]

35 In [4], blind restoration of spatially-varying blur was studied in the case of astronomical images, which have statistics quite different from the natural scenes addressed in this paper. [sent-57, score-0.794]

36 As a scene point focus is a function of its depth, the relative blur is used to estimate depth information. [sent-62, score-0.665]

37 2 Image statistics and blurring Figure 1(a) presents an image of an outdoor scene, with a passing bus. [sent-65, score-0.65]

38 The bus is blurred horizontally as a result of the bus motion. [sent-66, score-0.484]

39 In ﬁg 1(b) we plot the log histogram of the vertical derivatives of this image, and the horizontal derivatives within the blurred area (marked with a rectangle). [sent-67, score-0.831]

40 As can be 0 0 0 vertical horizontal −1 Input 5 taps blur 21 taps blur −2 −2 horizontal blurred vertical −1 −2 −3 −4 −3 −4 −4 −6 −5 −5 −6 −8 −6 −7 −10 −7 −8 −9 −0. [sent-68, score-1.769]

41 (b) Horizontal derivatives within the blurred region versus vertical derivatives in the entire image. [sent-100, score-0.728]

42 (d) Horizontal derivatives within the blurred region matched with blurred verticals (4 tap blur). [sent-102, score-0.728]

43 seen, the blur changes the shape of the histogram signiﬁcantly. [sent-103, score-0.619]

44 This suggests that the statistics of derivative ﬁlters responses can be used for detecting blurred image areas. [sent-104, score-0.509]

45 How does the degree of blur affects the derivatives histogram? [sent-105, score-0.752]

46 We convolve the image with the kernels f k (where k runs from 1 to 30) and compute the vertical derivatives distributions: T pk ∝ hist(dy ∗ fk ∗ I) (1) T where dy = [1 − 1] . [sent-108, score-0.624]

47 As the size of the blurring kernel changes the derivatives distribution, we would also like to use the histograms for determining the degree of blur. [sent-110, score-0.706]

48 For example, as illustrated in ﬁg 1(d), we can match the distribution of vertical derivatives in the blurred area, and p 4 , the distribution of horizontal derivatives after blurring with a 4 tap kernel. [sent-111, score-1.191]

49 1 Identifying blur using image statistics Given an image, the direction of motion blur can be selected as the direction with minimal derivatives variation, as in [28]. [sent-113, score-1.705]

50 For the simplicity of the derivation we will assume here that the motion direction is horizontal, and that the image contains a single blurred object plus an unblurred background. [sent-114, score-0.762]

51 Our goal is to determine the size of the blur kernel. [sent-115, score-0.574]

52 That is, to recover the ﬁlter f k which is responsible for the blur observed in the image. [sent-116, score-0.574]

53 Therefore, without segmenting the blurred areas there is no single blurring model p k that will describe the observed histogram. [sent-119, score-0.724]

54 We deﬁne the log-likelihood of the derivatives in a window with respect to each of the blurring models as: k (i) = log pk (Ix (j)) (2) j∈Wi Where Ix (j) is the horizontal derivative in pixel j, and W i is a window around pixel i. [sent-121, score-0.811]

55 On the other hand, uniform areas receive the highest likelihoods from wide blur kernels (since the derivatives distribution for wide kernels is more concentrated around zero, as can be observed in ﬁgure 1(c)). [sent-124, score-0.883]

56 When the image consists of large uniform areas, this bias the likelihood toward wider blur kernels. [sent-125, score-0.816]

57 In order to make our model consistent, when building the blurred distribution models p k (eq 1), we also take into account only pixels within a window around a vertical edge. [sent-127, score-0.441]

58 2 Segmenting blur layers Once the blurring kernel f k has been found, we can use it to deconvolve the image, as in ﬁg 2(b). [sent-130, score-1.18]

59 While this signiﬁcantly improves the image in the blurred areas, serious artifacts are observed in the background. [sent-131, score-0.49]

60 Therefore, in addition to recovering the blurring kernel, we need to segment the image into blurred and unblurred layers. [sent-132, score-1.126]

61 The ﬁnal restorated image is computed as: R(i) = x(i)I −fk (i) + (1 − x(i))I(i) (7) 3 Results To compute a deconvolved image I −fk given the blurring kernel, we follow [12] in using the matlab implementation (deconvlucy) of the Richardson-Lucy deconvolution algorithm [23, 18]. [sent-143, score-1.035]

62 For the doll example the image was segmented into 3 blurring layers. [sent-145, score-0.679]

63 To determine the blur direction in those images we select the direction with minimal derivatives variation, as in [28]. [sent-148, score-0.872]

64 For each image we show what happens if the segmentation is ignored and the entire image is deconvolved with the selected kernel (for the doll case the wider kernel is shown). [sent-150, score-0.862]

65 In comparison, the third row presents the restorated images computed from eq 7 using the blurring layers segmentation. [sent-152, score-0.641]

66 (e)Segmentation contour The recovered blur sizes for those examples were 12 pixels for the bicycles image and 4 pixels for the bus. [sent-165, score-0.978]

67 For the doll image a 9 pixels blur was identiﬁed in the skirt segment and a 2 pixels blur in the doll head. [sent-166, score-1.611]

68 We note that while recovering big degrees of blur as in the bicycles example is visually more impressing, discriminating small degrees of blur as in the bus example is more challenging from the statistical aspect. [sent-167, score-1.409]

69 This is because the derivatives distributions in the case of small blurs are much more similar to the distributions of unblurred images. [sent-168, score-0.544]

70 For the bus image the size of the blur kernel found by our algorithm was 4 pixels. [sent-169, score-0.945]

71 Segmentation: As demonstrated in ﬁg 2(b) deconvolving the entire image with the same kernel damages the unblurred parts. [sent-175, score-0.522]

72 One obvious solution is to divide the image into regions and match a separate blur kernel to each region. [sent-176, score-0.848]

73 While likelihood measure based on a big window is more reliable, such a window might cover regions from different blurring layers. [sent-180, score-0.53]

74 Another alternative is to brake the image into segments using an unsupervised segmentation algorithm, and match a kernel to each segment. [sent-181, score-0.432]

75 The fact that blur changes the derivatives distributions also suggests that it might be captured as a kind of texture cue. [sent-182, score-0.814]

76 However, as this is an unsupervised segmentation process which does not take into account the grouping goal, it’s hard to expect it to yield exactly the blurred layers. [sent-186, score-0.421]

77 The output over-segments blur layers, while merging parts of blurred and unblurred objects. [sent-188, score-1.02]

78 To do that independently of the segmentation, we manually segmented the bus and applied the matlab blind deconvolution function (deconvblind), initialized with a 1 × 7 box kernel. [sent-195, score-0.495]

79 Yet, the histogram structure of different images is not identical, and we found that trying to deblur one image using the statistics of a different image doesn’t work that well. [sent-199, score-0.516]

80 For example, ﬁgure 5 shows the result of deblurring the bus image using the bicycles image statistics. [sent-200, score-0.814]

81 The selected blur in this case was a 6-tap kernel, but deblurring the image with this kernel introduces artifacts. [sent-201, score-1.122]

82 Our solution was to work on each image using the vertical derivatives histograms from the same image. [sent-203, score-0.497]

83 This isn’t an optimal solution as when the image is blurred horizontally some of the vertical derivatives are degraded as well. [sent-204, score-0.737]

84 (a) (b) (c) (d) Figure 5: Deblurring the bus image using the bicycles image statistics. [sent-206, score-0.54]

85 One failure source is blurs which can’t be described as a box ﬁlter, or failures in identifying the blur direction. [sent-213, score-0.848]

86 Even when this isn’t the case, the algorithm may fail to identify the correct blur size or it may not infer the correct segmentation. [sent-214, score-0.574]

87 The bushes area consists of many small derivatives which are explained better by a small blur model than by a no-blur model. [sent-217, score-0.816]

88 As a result the algorithm selected a 6-pixels blur model. [sent-219, score-0.574]

89 This model might increase the likelihood of the bushes texture and the noise on the road, but it doesn’t remove the blur of the car. [sent-220, score-0.687]

90 4 Discussion This paper addresses the problem of blind motion deconvolution without assuming that the entire image undergone the same blur. [sent-227, score-0.606]

91 Thus, in addition to recovering an unknown blur kernel, we segment the image into layers with different blurs. [sent-228, score-0.953]

92 We treat this highly challenging task using a surprisingly simple approach, relying on the derivatives distribution in blurred images. [sent-229, score-0.441]

93 We model the expected derivatives distributions under different degrees of blur, and those distributions are used for detecting different blurs in image windows. [sent-230, score-0.577]

94 The box ﬁlters model used in this work is deﬁnitely limiting, and as pointed out by [12, 6], many blurring patterns observed in real images are more complex. [sent-231, score-0.524]

95 Stronger models might enable us to identify a wider class of blurring kernels rather than just box ﬁlters. [sent-233, score-0.537]

96 Particularly, they could provide a better strategy for identifying the blur direction. [sent-234, score-0.592]

97 In future work, it will also be interesting to try to detect different blurs without assuming a small number of blurring layers. [sent-236, score-0.61]

98 This will require estimating the blurs in the image in a continues way, and might also provide a depth from focus algorithm that will work on a single image. [sent-237, score-0.422]

99 Local scale control for edge detection and blur estimation. [sent-294, score-0.574]

100 Simultaneous image formation and motion blur restoration via multiple capture. [sent-334, score-0.904]

similar papers computed by tfidf model

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