cvpr cvpr2013 cvpr2013-68 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Yi Zhang, Keigo Hirakawa
Abstract: We propose a notion of double discrete wavelet transform (DDWT) that is designed to sparsify the blurred image and the blur kernel simultaneously. DDWT greatly enhances our ability to analyze, detect, and process blur kernels and blurry images—the proposed framework handles both global and spatially varying blur kernels seamlessly, and unifies the treatment of blur caused by object motion, optical defocus, and camera shake. To illustrate the potential of DDWT in computer vision and image processing, we develop example applications in blur kernel estimation, deblurring, and near-blur-invariant image feature extraction.
Reference: text
sentIndex sentText sentNum sentScore
1 edu / ˜ I SL S Abstract We propose a notion of double discrete wavelet transform (DDWT) that is designed to sparsify the blurred image and the blur kernel simultaneously. [sent-3, score-0.766]
2 DDWT greatly enhances our ability to analyze, detect, and process blur kernels and blurry images—the proposed framework handles both global and spatially varying blur kernels seamlessly, and unifies the treatment of blur caused by object motion, optical defocus, and camera shake. [sent-4, score-1.353]
3 To illustrate the potential of DDWT in computer vision and image processing, we develop example applications in blur kernel estimation, deblurring, and near-blur-invariant image feature extraction. [sent-5, score-0.417]
4 Introduction Image blur is caused by a pixel recording lights from multiple sources. [sent-7, score-0.412]
5 Illustrated in Figure 1 are three common types of blur: defocus, camera shake and object motion. [sent-8, score-0.102]
6 Defocus blur is caused by a wide aperture that prevents light rays originating from the same point from converging. [sent-9, score-0.424]
7 Camera motion during the exposure produces global motion blur where the same point on the scene is observed by multiple moving pixel sensors. [sent-10, score-0.567]
8 Object motion causes each pixel to observe multiple points on the scene that produces spatially-variant motion blur. [sent-11, score-0.145]
9 Assuming Lambertian surfaces, blur is typically represented by the implied blur kernel that acts on the unobserved sharp in-focus image. [sent-12, score-0.817]
10 On one hand, long exposure is needed to overcome poor lighting conditions, but it increase the risk of camera shake and object motion blurs that severely deteriorate the sharpness of the image. [sent-14, score-0.209]
11 On the other hand, professional photographers use well-controlled blur to enhance the aesthetics of a photograph. [sent-18, score-0.401]
12 Thus the ability to manipulate blur in postprocessing would offer a greater flexibility in consumer and professional photography. [sent-19, score-0.401]
13 a scene with multiple mov- (a) Defocus(b) Camera shake(c) Object motion Figure 1. [sent-23, score-0.065]
14 We may learn the temporal state of the camera and the scene from blur caused by camera shake or object motion, respectively. [sent-28, score-0.536]
15 The defocus blur kernel varies with the object distance/depth, which can be useful for three dimensional scene retrieval from a single camera[23]. [sent-29, score-0.548]
16 Blur also interferes with recognition tasks, as feature extraction from blurry image is a real challenge. [sent-30, score-0.071]
17 In this paper, we propose a novel framework to address the analysis, detection, and processing of blur kernels and blurry images. [sent-31, score-0.472]
18 Central to this work is the notion of double discrete wavelet transform (DDWT) that is designed to sparsify the blurred image and the blur kernel simultaneously. [sent-32, score-0.766]
19 We contrast DDWT with the work of [3], which regularizes image and blur kernel in terms of their sparsity in linear transform domain. [sent-33, score-0.465]
20 The major disadvantage of regularization approach is that the image/blur coefficients are not directly observed, hence requiring a computationally taxing search to minimize some “cost” function. [sent-34, score-0.088]
21 On the other hand, out DDWT provides a way to observe the wavelet coefficients of image and blur kernel directly. [sent-35, score-0.62]
22 This gives DDWT coefficients a very intuitive interpretation, and simplify the task of decoupling the blur from the signal, regardless of why the blur occurred (e. [sent-36, score-0.844]
23 object motion, defocus, and camera shake) or the type of blur (e. [sent-38, score-0.415]
24 Although the primary goal of this article is to develop the DDWT as an analytical tool, we also show example applications in blur kernel estimation, deblurring, and near-blur-invariant image feature extraction to illustrate the potential of DDWT. [sent-42, score-0.417]
25 dj) to the observed blurry image y, (b) is the interpretation we give to the DDWT coefficients. [sent-46, score-0.073]
26 Related Work Recent advancements on blind and non-blind deblurring have enabled us to handle complex uniform blur kernels (e. [sent-48, score-0.553]
27 By comparison, progress in blind and non-blind deblurring for spatially varying blur kernel (e. [sent-51, score-0.619]
28 [16, 17, 4, 6]) has been slow since there are limited data availability to support localized blur kernel. [sent-53, score-0.378]
29 Approaches to computational solutions include supervised [16] or unsupervised [17, 10] foreground/background segmentation, statistical modeling [4], homography based blur kernel modeling methods [24, 15] and partial differential equation (PDE) methods [6]. [sent-55, score-0.417]
30 In particular, sparsifying transforms have played key roles in the detection ofblur kernels—gradient operator [4, 6, 10, 9] and wavelet/framelet/curvelet transforms [3, 11] have been used for this purpose. [sent-56, score-0.075]
31 However, existing works have shortcomings, such as problems with ringing artifact in deblurring [20, 5] or inability to handle spatially varying blur [19, 12, 3, 2, 21, 22, 9]. [sent-57, score-0.565]
32 It is also common for deblurring algorithms to require iteration [3, 20, 5, 12, 24, 15], which is highly undesirable for many real-time applications. [sent-58, score-0.139]
33 Besides PDE, authors are unaware of any existing framework that unify analysis, detection, and processing of camera shake, object motion, defocus, global, and spatially varying blurs. [sent-59, score-0.101]
34 Definitions We begin by defining single discrete wavelet transform (DWT) and the proposed double discrete wavelet transform (DDWT). [sent-63, score-0.47]
35 Denote by dj : Z2 →→ RR a w aanv iemleatg analysis fainltder n nof ∈ jth Z subband. [sent-70, score-0.11]
36 y}(n) is the jth subband, nth location over-complete single discrete wavelet transform coefficient of an image y(n), where ? [sent-72, score-0.236]
37 The over-complete double discrete wavelet transform is defined by the relation vij(n) := {di ? [sent-75, score-0.296]
38 wj}(n), where vij (n) is the transform coefficient of the image y(n) in the (i, j)th subband and location n. [sent-76, score-0.291]
39 In the special case that dj (n) is a 1D horizontal wavelet analysis filter and di (n) is a vertical one, then vij (n) is an ordinary separable 2D wavelet transform. [sent-77, score-0.579]
40 In our work, however, we allow the possibility that dj (n) and di (n) to be arbitrarily defined (e. [sent-78, score-0.15]
41 Technically speaking, the DWT/DDWT definitions above may apply to nonwavelet transforms dj and di, so long as they are invertible. [sent-81, score-0.136]
42 DDWT Analysis Of Blurred Image Assuming Lambertian reflectance, let x : Z2 → R be latent sharp image, y : Z2 → R is the observe→d blurry image, and n ∈ Z2 is the pixel Rloc iastio thne i ondbesxer. [sent-84, score-0.094]
43 However, hn may take a parametric form in the case of motion blur (by object speed and direction) or defocus blur (by aperture radius or depth). [sent-90, score-1.036]
44 In order for the convolution model of (1) to hold, the Lambertian reflectance assumption is necessary since objects may be observed from a different angle (e. [sent-91, score-0.071]
45 When DDWT is applied to the observation y, the corresponding DDWT coefficients vij is related to the latent sharp image x and the blur kernel h by: vij(n) ={di ? [sent-96, score-0.708]
46 Example of DWT and DDWT coefficients using real camera sensor data. [sent-106, score-0.146]
47 The motion blur manifests itself as a double edge in DDWT, where the distance between the double edges (yellow arrows in (c)) correspond to the speed of the object. [sent-107, score-0.663]
48 Average velocity of the moving pixels in (d) is 38 pixels, and the direction of motion is 40 degrees above the horizontal. [sent-108, score-0.105]
49 h are the DWT decompositions of x and h, respectively; and ηij := di ? [sent-111, score-0.054]
50 By the commutativity and associativity of convolution, the processes in 2(a) and 2(b) are equivalent—2(a) is the direct result of applying DDWT on the observed blurry image,1 but 2(b) is the interpretation we give to the DDWT coefficients (though 2(b) is not directly computable). [sent-115, score-0.175]
51 Then DDWT coefficients vij is the result of applying a “sparse filter” qi to a “sparse signal” uj . [sent-117, score-0.568]
52 1 When K is small, vij is nothing more than a sum of a K DWT coefficients uj . [sent-126, score-0.448]
53 Thanks to sparsity, many of uj are already zeros, and so vij is actually a sum of only a few (far less than K) DWT coefficients uj . [sent-127, score-0.627]
54 In this paper, we call a DDWT coefficient aliased if vij is a sum of more than one “active” uj coefficients. [sent-128, score-0.393]
55 One can reduce the risk of aliasing when the choice of dj and di makes uj and qi as sparse as possible. [sent-129, score-0.465]
56 By symmetry, one may also interpret DDWT coefficients as vij = {qj ? [sent-130, score-0.269]
57 But in practice, the= “ {cqonfusio}n +” ηb etween (qi, uj) and (qj , ui) does not seem to be a concern for algorithm development when qi is more sparse than qj . [sent-132, score-0.155]
58 Recovery of uj from vij leads to image deblurring, while reconstructing qi is the blur kernel detection problem. [sent-133, score-0.897]
59 Clearly, it is easy to decouple uj and qi if vij is unaliased, and reasonably uncomplicated when uj and qi are sufficiently sparse. [sent-134, score-0.794]
60 One can circumvent this problem by using demosaicking method in [13] designed to recover DWT coefficients wj from color filter array data directly. [sent-136, score-0.155]
61 the power of DDWT by analyzing specific blur types and designing example applications. [sent-137, score-0.378]
62 Owing to page limit, we describe object motion blur processing at length. [sent-138, score-0.459]
63 DDWT treatment of other blur types are brief, but their details follow the examples of object motion processing closely. [sent-139, score-0.475]
64 DDWT Analysis Consider for the moment the horizontal motion blur kernel. [sent-144, score-0.461]
65 Assuming constant velocity of the object during exposure, the blur kernel can be modeled as: h(n) = step(n +? [sent-145, score-0.439]
66 Letting di denote a Haar wavelet transform [−1, 1], the DWT coefficient qi is just a wdifavfeerleentc tera onfs tfworom impulse ,fu thnect DioWnsT: q(n) = δ(n +? [sent-150, score-0.399]
67 Recall that DWT coefficients u typically captures directional image features (say vertical edges). [sent-163, score-0.088]
68 By (7), we intuitively expect DDWT of moving objects to yield “double edges” where the distance between the two edges2 correspond exactly to the speed of the moving object. [sent-164, score-0.058]
69 Indeed, detection 2Red lines denote positive DDWT coefficients while blue lines ative. [sent-165, score-0.088]
70 are neg- 1 1 10 0 09 9 913 1 (a) DWT (or DDWT with no blur) (b) DDWT with object motion blur (c) DDWT with defocus blur Figure 4. [sent-166, score-0.952]
71 of local object speed simplifies to the task of these detecting double edges. [sent-171, score-0.114]
72 Deblurring is equally straightforward: double edges in DDWT coefficients v are the copies of u. [sent-172, score-0.194]
73 For computational object motion detection, our ability to detect complex motion is limited primarily by the capabilities of the computer vision algorithms to extract local image features from DDWT, and find similar features that is located unknown (k pixel) distance away. [sent-176, score-0.13]
74 A more advanced image feature extraction strategy founded on computer vision principles would likely improve the overall performance of the object motion detection—we leave this as future research plan. [sent-178, score-0.093]
75 (8) On the other hand, in the presence of motion blur, Rv (? [sent-200, score-0.065]
76 hic =h produces smallest secondary aHuetnoccoer trheela ctiaonnd yields wtheh iechsti pmrao-tion of the blur kernel length: ± kˆ = arg? [sent-221, score-0.417]
77 aTuhsee autocorrelation function of (9) is essentially the indicator function for the double edges evidenced in Figure 3(c). [sent-227, score-0.179]
78 To estimate the local object motion, autocorrelation needs to be localized also. [sent-228, score-0.073]
79 ) that favors piecewiseconstant object motion speed over more complex ones. [sent-279, score-0.087]
80 For non-horizontal/vertical motion, we use image shearing to skew the input image y by angle φ ∈ [0, π] (compared iton image wrot tahteio inn,p shearing ayv boyid asn interpolation e (crroomr). [sent-280, score-0.102]
81 ) the autocorrelation function of v(n) in the sheared direction φ, we detect the local blur angle θ and length k by: (ˆθn,kˆn) = arg(φ,? [sent-282, score-0.471]
82 (12) Figure 3(d) shows the result of estimating the angle θ and the length k of the blur at every pixel location, corresponding to the input image Figure 3(a). [sent-285, score-0.413]
83 Object Motion Deblurring Complementary to the detection of qi from vij is the notion of recovering uj from vij . [sent-288, score-0.679]
84 In the discussion below, we assume that the motion blur angle θ and length k are already known via (12). [sent-292, score-0.463]
85 We first note that noise ηij can be accounted for by applying one of many standard wavelet shrinkage operators to DDWT coefficients vij [14]. [sent-295, score-0.384]
86 Result of object motion deblurring using real camera sensor data with (top row) global and (bottom row) spatially varying blurs. [sent-301, score-0.31]
87 The bottom row was rendered with average velocity of moving pixels for [5, 20, 22] and using Figure 3(d) for the proposed deblurring method. [sent-303, score-0.179]
88 Such procedure effectively removes noise ηij in vij to y? [sent-304, score-0.181]
89 that DWT coefficients u of a natural image x are indeed sp? [sent-345, score-0.088]
90 (13) Since this deblurring scheme improves if P[u(n) = 0] = ρ ≈ 1(i. [sent-402, score-0.139]
91 more sparse), the choice of sparsifying transform dρj ≈ ≈is 1th (ei. [sent-404, score-0.071]
92 determining fea),ct toher fcohro tihcee oefffe spcativrseinfyeisnsg go tfr athnsef proposed DDWT-based blur processing. [sent-405, score-0.408]
93 We highlight a few notable features of the proposed deblurring scheme. [sent-406, score-0.139]
94 First, the recovery of uj in (13) is simple, and works regardless of whether the blur kernel is global or spatially varying (simply replace k with kn). [sent-407, score-0.644]
95 Second, the deblurring technique in (13) is a single-pass method. [sent-408, score-0.139]
96 Finally, one can easily incorporate any wavelet domain denoising scheme into the design of the deblurring algorithm. [sent-417, score-0.254]
97 Reconstructions using real camera sensor data in Figure 5 shows superiority of the proposed DDWT approach. [sent-418, score-0.058]
98 Optical Defocus Blur In this section, we extend DDWT analysis to optical defocus blur. [sent-420, score-0.131]
99 The support of the defocus blur kernel takes the shape of the aperture opening, which is a circular disk in most typical cameras (supp{h} = {n : ? [sent-421, score-0.575]
100 r (14) 1 1 10 0 09 9 935 3 Letting di denote a Haar wavelet transform [−1, 1], the corresponding sparse ab Hluara kre wrnaevle qleit i tsr a(snseefo Figure 16,(1a]),) qi(n)≈⎨⎪ ⎧0π −r1 2 ioft ? [sent-428, score-0.234]
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