iccv iccv2013 iccv2013-135 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Gaofeng Meng, Ying Wang, Jiangyong Duan, Shiming Xiang, Chunhong Pan
Abstract: unkown-abstract
Reference: text
sentIndex sentText sentNum sentScore
1 cn Abstract—Images captured in foggy weather conditions often suffer from bad visibility. [sent-6, score-0.215]
2 In this paper, we propose an efficient regularization method to remove hazes from a single input image. [sent-7, score-0.271]
3 Our method benefits much from an exploration on the inherent boundary constraint on the transmission function. [sent-8, score-0.662]
4 Experimental results on a variety of haze images demonstrate the effectiveness and efficiency of the proposed method. [sent-12, score-0.289]
5 INTRODUCTION When one takes a picture in foggy weather conditions, the obtained image often suffers from poor visibility. [sent-14, score-0.247]
6 This is because the reflected light from these objects, before it reaches the camera, is attenuated in the air and further blended with the atmospheric light scattered by some aerosols (e. [sent-16, score-0.309]
7 Early methods for haze removal mainly rely on additional depth information or multiple observations of the same scene. [sent-20, score-0.364]
8 [11] notice that the airlight scattered by atmospheric particles is partially polarized. [sent-23, score-0.232]
9 Based on this observation, they develop a quick method to reduce hazes by using two images taken through a polarizer at different angles. [sent-24, score-0.228]
10 From left to right: (Top) the foggy image and the dehazing result by our method. [sent-32, score-0.668]
11 (Bottom) the boundary constraint map and the recovered scene transmission. [sent-33, score-0.306]
12 Under the assumption that the two functions are locally statistically uncorrelated, a haze image can be broken into regions of constant albedo, from which the scene transmission can be inferred. [sent-38, score-0.76]
13 Tan [13] proposes to enhance the visibility of a haze image by maximizing its local contrast. [sent-39, score-0.331]
14 [5] present an interesting image prior - dark channel prior for single image dehazing. [sent-43, score-0.256]
15 [7] model an image as a factorial Markov random field, in which the scene albedo and depth are two statistically independent latent layers. [sent-47, score-0.223]
16 Following this idea, we begin our study in this paper by deriving an inherent boundary constraint on the scene transmission. [sent-52, score-0.276]
17 This constraint, combined with a weighted L1−norm based contextual regularization between neighboring pixels, is formalized into an optimization problem to recover the unknown transmission. [sent-53, score-0.194]
18 Figure 1 illustrates an example of our dehazing result. [sent-55, score-0.567]
19 Our second contribution is a new contextual regularization that enables us to incorporate a filter bank into image dehazing. [sent-59, score-0.211]
20 The transmission function t(x) (0 ≤ t(x) ≤ 1) itrsa cnosmrreilssaiteodn . [sent-64, score-0.395]
21 Fctuirotnhe tr( assuming xth)a ≤t th 1e) haze is homogenous, we can express t(x) as follows: + t(x) = − e−βd(x), (2) where β is the medium extinction coefficient, and d(x) is the scene depth. [sent-66, score-0.402]
22 The goal of image dehazing is to recover the scene radiance J(x) from I(x) based on Eq. [sent-67, score-0.757]
23 This requires us to estimate the transmission function t(x) and the global atmospheric light A. [sent-69, score-0.622]
24 Once t(x) and A are estimated, the scene radiance can be recovered by: J(x) =[maIx(x(t)( −x) A,? [sent-70, score-0.234]
25 For each x, we require the extrapolation of J(x) cannot cross over the boundary of the radiance cube. [sent-73, score-0.296]
26 Jb (x1) and Jb (x2) are the corresponding boundary constraint points. [sent-74, score-0.204]
27 However, dehazing from a single image is highly underconstrained, since the number of unknowns is much greater than the number of available equations. [sent-79, score-0.544]
28 (1), a pixel I(x) contaminated by fog will be “pushed” towards the global atmospheric light A (see Figure 2). [sent-83, score-0.289]
29 (4) Consider that the scene radiance of a given image is always bounded, that is, C0 ≤ J(x) ≤ C1,∀x ∈ Ω, (5) where C0 and C1 are two constant vectors that are relevant to the given image. [sent-86, score-0.208]
30 Consequently, for any x, a natural requirement is that the extrapolation of J(x) must be located in the radiance cube bounded by C0 and C1, as illustrated in Figure 2. [sent-87, score-0.23]
31 The above requirement on J(x), in turn, imposes a boundary constraint on t(x). [sent-88, score-0.225]
32 Suppose that the global atmospheric light A is given. [sent-89, score-0.227]
33 Thus, for each x, we can compute the corresponding boundary constraint point Jb(x) (see Figure 2). [sent-90, score-0.204]
34 (5), leading to the following boundary constraint on t(x): 0 ≤ tb(x) ≤ t(x) ≤ 1, (6) 618 where tb(x) is the lower bound of t(x), given by tb(x) = min? [sent-93, score-0.204]
35 The boundary constraint of t(x) provides a new geometric perspective to the famous dark channel prior [5]. [sent-98, score-0.438]
36 Let C0 = 0 and suppose the global atmospheric light A is brighter than any pixel in the haze image. [sent-99, score-0.54]
37 (1) by assuming the pixel-wise dark channel of J(x) to be zero. [sent-101, score-0.212]
38 Similarly, assuming that the transmission in a local image patch is constant, one can quickly derive the patch-wise transmission t˜(x) in He et al. [sent-102, score-0.842]
39 It is worth noting that the boundary constraint is more fundamental. [sent-106, score-0.204]
40 In most cases, the optimal global atmospheric light is a little darker than the brightest pixels in the image. [sent-107, score-0.318]
41 In these cases, the dark channel prior will fail to those pixels, while the proposed boundary constraint still holds. [sent-111, score-0.438]
42 It is also worthy to point out the commonly used constant assumption on the transmission within a local image patch is somewhat demanding. [sent-112, score-0.445]
43 For this reason, the patch-wise transmission t˜(x) based on this assumption in [5] is often underestimated. [sent-113, score-0.42]
44 The new patch-wise transmission is given as below: tˆ(x) =y m∈ωinxzm∈aωxytb(z). [sent-115, score-0.395]
45 (9) Fortunately, the above patch-wise transmission tˆ(x) can be conveniently computed by directly applying a morphological closing on tb(x). [sent-116, score-0.395]
46 Figure 3 illustrates a comparison of the dehazing results by directly using the patch-wise transmissions derived from dark channel prior and the boundary constraint map, respectively. [sent-117, score-1.134]
47 One can observe that the patchwise transmission from dark channel prior works not well in the bright sky region. [sent-118, score-0.697]
48 In comparison, the new patch-wise transmission derived from the boundary constraint map can handle the bright sky region very well and also produces fewer halo artifacts. [sent-120, score-0.837]
49 Based on this assumption, we have derived a patch-wise transmission from the boundary constraint. [sent-123, score-0.532]
50 Image dehazing by directly using the patch-wise transmissions from dark channel prior and boundary constraint map, respectively. [sent-125, score-1.086]
51 From left to right: (top) the foggy image, the dehazing result by dark channel prior and the dehazing result by boundary constraint. [sent-126, score-1.558]
52 (bottom) the boundary constraint map, the patch-wise transmission from dark channel and the patch-wise transmission from boundary constraint map (C0 = (20, 20, 20)T, C1 = (300, 300, 300)T, δ = 1. [sent-127, score-1.41]
53 patches with abrupt depth jumps, leading to significant halo artifacts in the dehazing results. [sent-129, score-0.795]
54 When W(x, y) = 0, the corresponding contextual constraint of t(x) between x and y will be canceled. [sent-134, score-0.187]
55 Notice the facts that the depth jumps generally appear at the image edges, and that within local patches, pixels with a similar color often share a similar depth value. [sent-139, score-0.287]
56 is the log-luminance channel of the image I(x), the exponent α > 0 controls the sensitivity to the luminance difference of two pixels and ? [sent-149, score-0.189]
57 619 Integrating the weighted contextual constraints in the whole image domain leads to the following contextual regularization on t(x): ? [sent-152, score-0.253]
58 (3) requires to estimate an appropriate transmission function t(x) and the global atmospheric light A. [sent-197, score-0.622]
59 We find an optimal transmission function t(x) by minimizing the following objective function: 2λ? [sent-210, score-0.415]
60 t part is the data term, which measures the fidelity of t(x) to the patch-wise transmission tˆ(x) derived from the boundary constraint map, the second part models the contextual constraints of t(x), and λ is the regularization parameter for balancing the two terms. [sent-218, score-0.782]
61 More specifically, we introduce the following auxiliary variables, denoted by uj (j ∈ ω) and convert (19) to a new cost function as below: ⎛ ⎞ λ2? [sent-221, score-0.205]
62 Minimizing (20) for a fixed β can be performed by an alternating optimization with respect to uj and t. [sent-234, score-0.205]
63 That is, we first solve for each optimal uj by fixing t, and then solve for an optimal t by fixing uj . [sent-235, score-0.496]
64 620 Optimizing uj : With t fixed in (20), we solve for (j ∈ ω) by minimizing the following function: ? [sent-238, score-0.205]
65 22, uj (21) The above problem consists of solving a series of independent 1D problems of the following forms, i. [sent-242, score-0.205]
66 Figure 5 illustrates an example of the estimation process of scene transmission function. [sent-272, score-0.47]
67 The intermediate estimations of t(x) and the final dehazing result are shown in the figure. [sent-275, score-0.544]
68 Example Results Figure 6 illustrates some examples of our dehazing results and the recovered scene transmission functions. [sent-279, score-1.064]
69 As can be seen from the results, our method can recover rich details of images with vivid color information in the haze regions. [sent-288, score-0.389]
70 It should be pointed out that the estimated transmissions of the right three images in the figure cannot be regarded as a scaling version of the depth map, since the hazes in the images are not homogeneous. [sent-289, score-0.407]
71 Actually, the transmission function reflects the density of the hazes in the captured scene. [sent-291, score-0.623]
72 However, the colors in the recovered images are often over saturated, since the method is not a physically based approach and the transmission may thus be underestimated. [sent-303, score-0.501]
73 Moreover, some significant halo artifacts usually appear around the recovered sharp edges (e. [sent-304, score-0.226]
74 In comparison, our method can improve the visuality of image structures in very dense haze regions while restoring the faithful colors. [sent-307, score-0.348]
75 The halo artifacts in our results are also quite small. [sent-308, score-0.211]
76 They estimate the atmospheric veil by applying a fast median filter to the minimum components of the observed image. [sent-313, score-0.191]
77 The biggest advantage of their method is its linear complexity and can be implemented in real time, while the weakness is the dehazing results are not quite visually compelling. [sent-314, score-0.599]
78 If the haze is very dense, the color information will be very faint and the transmission may thus be wrongly estimated, leading to erroneous enhancement on the image. [sent-316, score-0.792]
79 For example, the hill enhanced by Fattal’s method in Figure 8 is too dark (bottom image) and some hazes still remain among the underbrush (top image). [sent-317, score-0.333]
80 By exploiting the priors of natural images and depth statistics, they can factorize the image into its scene albedo and depth via an EM algorithm. [sent-324, score-0.307]
81 Moreover, the dehazing results also contain some halo artifacts. [sent-326, score-0.689]
82 Based on the hue disparity between the original image and its semi-inverse, they can quickly identify the hazy regions and estimate the global airlight constant and the transmission map. [sent-330, score-0.486]
83 However, due to the ambiguity between color and depth, pixel-wise haze detection is not robust and often suffers from large recognition errors. [sent-333, score-0.421]
84 Therefore, some hazes in the images are not fully removed (e. [sent-334, score-0.228]
85 In contrast, our method can well remove most hazes in the image and produce a clear image with vivid color information. [sent-337, score-0.299]
86 As can be seen from the results, the both methods produce comparable results in regions with heavy hazes (e. [sent-340, score-0.228]
87 Fewer hazes remain in the our dehazing results and the halo artifacts are also smaller. [sent-346, score-0.948]
88 DISCUSSION AND CONCLUSION In this paper, we have proposed an efficient method to remove hazes from a single image. [sent-353, score-0.228]
89 From left to right: input haze images, Tan’s results, our results and the close-up patches of the results, IFCigCuVre’0 89. [sent-357, score-0.289]
90 d F irnom co l eofrt) to right: (top) input haze imag, Kratz et al. [sent-370, score-0.289]
91 (Best viewed in color) much from an exploration on the inherent boundary constraint on the transmission function. [sent-376, score-0.642]
92 In comparison with the state-of-the-arts, our method can generate quite visually pleasing results with faithful color and finer image details and structures. [sent-379, score-0.178]
93 Single image dehazing often suffers from the problem of ambiguity between image color and depth. [sent-380, score-0.676]
94 From a geometric perspective of image dehazing, we have derived a boundary constraint on the transmission from the radiance cube of an image. [sent-385, score-0.802]
95 Although the boundary constraint imposes a much weak constraint on the dehazing process, it proves to be surprisingly effective for the dehazing of most natural images, after combined with the contextual regularization. [sent-386, score-1.5]
96 More generally, one can employ a tighter radiance envelop, not limited to a cubic shape, to provide a more accurate constraint on the transmissions. [sent-387, score-0.224]
97 Another way to address the ambiguity problem is to adopt more sound constraints or develop new image priors, for example, using the scene geometry [2], or directly incorporating the available depth information [6] into the estimation of scene transmission. [sent-389, score-0.234]
98 A fast semi-inverse approach to detect and remove the haze from a single image. [sent-401, score-0.289]
99 Factorizing scene albedo and depth from a single foggy image. [sent-440, score-0.306]
100 An investigation of dehazing effects on image and video coding. [sent-450, score-0.544]
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