cvpr cvpr2013 cvpr2013-169 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Xiaogang Chen, Sing Bing Kang, Jie Yang, Jingyi Yu
Abstract: Patch-based methods such as Non-Local Means (NLM) and BM3D have become the de facto gold standard for image denoising. The core of these approaches is to use similar patches within the image as cues for denoising. The operation usually requires expensive pair-wise patch comparisons. In this paper, we present a novel fast patch-based denoising technique based on Patch Geodesic Paths (PatchGP). PatchGPs treat image patches as nodes and patch differences as edge weights for computing the shortest (geodesic) paths. The path lengths can then be used as weights of the smoothing/denoising kernel. We first show that, for natural images, PatchGPs can be effectively approximated by minimum hop paths (MHPs) that generally correspond to Euclidean line paths connecting two patch nodes. To construct the denoising kernel, we further discretize the MHP search directions and use only patches along the search directions. Along each MHP, we apply a weightpropagation scheme to robustly and efficiently compute the path distance. To handle noise at multiple scales, we conduct wavelet image decomposition and apply PatchGP scheme at each scale. Comprehensive experiments show that our approach achieves comparable quality as the state-of-the-art methods such as NLM and BM3D but is a few orders of magnitude faster.
Reference: text
sentIndex sentText sentNum sentScore
1 In this paper, we present a novel fast patch-based denoising technique based on Patch Geodesic Paths (PatchGP). [sent-13, score-0.317]
2 PatchGPs treat image patches as nodes and patch differences as edge weights for computing the shortest (geodesic) paths. [sent-14, score-0.397]
3 We first show that, for natural images, PatchGPs can be effectively approximated by minimum hop paths (MHPs) that generally correspond to Euclidean line paths connecting two patch nodes. [sent-16, score-0.709]
4 To construct the denoising kernel, we further discretize the MHP search directions and use only patches along the search directions. [sent-17, score-0.486]
5 Along each MHP, we apply a weightpropagation scheme to robustly and efficiently compute the path distance. [sent-18, score-0.143]
6 To handle noise at multiple scales, we conduct wavelet image decomposition and apply PatchGP scheme at each scale. [sent-19, score-0.198]
7 Traditional pixel-based edge-preserving algorithms such as median filters, bilateral filters [34], total variation [33] and anisotropic diffusion [33] have long served as workhorses in denoising tasks. [sent-23, score-0.543]
8 The core of these approaches is to use patches similar to the noisy one within the image as cues. [sent-27, score-0.137]
9 For example, in NLM and BM3D, denoising each patch requires computing its similarity with all other patches in a predefined search window. [sent-29, score-0.638]
10 [4] show that one can use the K most similar patches instead of all patches within the window which is equivalent to solving the K-nearest neighbor (K-NN) problem in the high dimensional patch space. [sent-32, score-0.491]
11 In this paper, we present a novel fast patch-based denoising technique based on Patch Geodesic Paths (PatchGP). [sent-34, score-0.317]
12 PatchGP extends the pixel geodesic paths (PixelGP) [5] by treating image patches as nodes and assigning patch differences as edge weights for computing the shortest (geodesic) paths. [sent-35, score-0.762]
13 We first show that for natural images, PatchGPs can be effectively approximated by minimum hop paths (MHPs) that generally correspond to Euclidean line paths connecting two patch nodes. [sent-39, score-0.709]
14 To construct the denoising kernel, we further discretize the MHP search directions and use only patches along the search directions. [sent-40, score-0.486]
15 Along each MHP, we apply a weight propagation scheme to robustly and efficiently compute the path distance. [sent-41, score-0.166]
16 Finally, to handle noise at multiple scales, we conduct wavelet image decomposition and apply PatchGP scheme at each scale. [sent-42, score-0.198]
17 Related work Image denoising is a long standing problem. [sent-45, score-0.276]
18 [24] discussed the the relation between the patch complexity of natural images, patch size, and restoration errors. [sent-51, score-0.513]
19 A widely used class of pixel-based algorithms is edge-preserving filters such as anisotropic diffusion [28] and bilateral filters [29]. [sent-55, score-0.326]
20 They can be viewed as convolving the noisy image with a special smoothing kernel [29] [34]: ˆ퐼(푖) =푍(1푖)푗∑∈Ω푖푤(푖,푗)퐼(푗), (1) where 푤 is the smoothing kernel, Ω푖 is the spatial support of 푤 or a neighbo∑rhood of pixel 푖, and 푍(푖) is the normaliza- tion factor as푗∑∈Ω푖푤(푖,푗). [sent-56, score-0.204]
21 Anisotropic diffusion uses similar local filte(rs∣푣 t(o푖 s)u−cc푣e(s푗s)i∣vely produces a family of parameterized images where new images at each iteration are computed by applying diffusion filters to the ones from the previous iteration [29]. [sent-58, score-0.143]
22 For example, NLM uses patch similarity instead of pixel similarity for constructing the smoothing kernel: 푖. [sent-60, score-0.321]
23 − 푤푁퐿푀(푖,푗) = 퐺휎(∣푁퐼(푖) − 푁퐼(푗)∣2), (3) 푖 where 푁퐼 (푖) and 푁퐼 (푗) represent patches centered at and 푗 and ⋅ ∣2 is the sum of squared differences (SSD) between the patches. [sent-61, score-0.134]
24 More sophisticated schemes [32] [36] [41] further utilize image statistics within patches to improve the denoising results. [sent-64, score-0.426]
25 (1), whether pixel or patch based, are computational expensive. [sent-68, score-0.271]
26 The original bilateral filters have computational complexity of 푂(푟2) for each pixel, where 푟 is radius of the spatial support. [sent-69, score-0.188]
27 Despite great advances on pixel-based denoising, accelerating patch-based denoising remains as an open problem. [sent-78, score-0.301]
28 This is mainly due to the high dimensionality of patch space. [sent-79, score-0.237]
29 We, in contrast, explore the problem from the perspective of natural image patch statistics. [sent-83, score-0.258]
30 Patch Geodesic Paths The core of our approach is to accelerate patch-based denoising by only conducting patch comparisons on the geodesic paths. [sent-85, score-0.776]
31 Pixel Geodesic Distance In a graph, the geodesic distance between two nodes is the accumulative edge weights in a shortest path connecting them. [sent-88, score-0.481]
32 The pixel geodesic distance corresponds to Γ 1 1 12 2 21 1 102 0 the shortest path in terms of image gradients, i. [sent-90, score-0.422]
33 The concept of pixel geodesic distance has been successfully applied to colorization [39], segmentation and matting [5, 18, 12], texture removal and non-photorealistic rendering [13], and most recently, denoising [13, 17]. [sent-93, score-0.604]
34 (4) to: 푑퐺퐷(푠,푡) = mΓin푁∑푖=Γ−11∣퐼(Γ(푝푖+1)) − 퐼(Γ(푝푖))∣, (5) where Γ denotes a path starting from the patch centered at 푠 to the patch centered at 푁Γ denotes the hops of the path Γ. [sent-95, score-0.805]
35 To apply pixel geodesic distance for image denoising, one can compute the smoothing ker- 푡. [sent-97, score-0.326]
36 This is often referred to as Pixel Geodesic Path (PixelGP) denoising [17]. [sent-100, score-0.276]
37 Specifically, we treat each image patch as a node and define the geodesic distance between two patches 푠 and as: 푡 푑푝푎푡푐ℎ퐺푃(푠,푡) = mΓin푁푖∑=Γ−11∣∣푁퐼(Γ(푝푖+1)) − 푁퐼(Γ(푝푖))∣∣, (6) where 푁퐼 (푥) is the patch centered at 푥, . [sent-106, score-0.85]
38 h We pea ctcalhl tcheen tsehroerdte astt path ∣Γ∣ m beetawseuerens tw thoe patches the Patch Geodesic Path (PatchGP). [sent-108, score-0.216]
39 However, the brute-force implementation of PatchGP is very expensive because weight computation requires pairwise patch comparisons. [sent-112, score-0.283]
40 Minimal Hop Paths (MHP) Consider two patches centered at pixel 푠 and 푡. [sent-116, score-0.168]
41 We define the Minimum Hop Path (MHP) as the path with the minimal number of hops connecting two nodes. [sent-117, score-0.196]
42 Among all paths connecting 푝 and 푞, the diagonal red path is the corresponding MHP under 8connectivity. [sent-120, score-0.261]
43 For each configuration (patch size, window size, noise variance), we find PatchGP between every pair ofpatches and verify ifit is an MHP. [sent-131, score-0.148]
44 The percentage ofPatchGP being MHP is shown in (a) 5 5 patch size and (b) 7 ×7patch size. [sent-132, score-0.255]
45 We add white Gaussian noise to the images and test different patch sizes. [sent-136, score-0.339]
46 For a fixed noise variance and patch size, we first compute the ground truth PatchGPs between all patches. [sent-137, score-0.367]
47 In Fig 2, the Y-axis is the percentage of MHPs being PatchGPs averaged over all 200 images and the X-axis is the spatial support (the maximum hop allowed between the nodes). [sent-139, score-0.17]
48 The results hold for noisy images: even with noise variance 휎푛 = 15 and spatial support 7 (15 15 window), over 90% Pat=chG 1P5s a are pMatHiaPls s, as osrhto 7w (n1 5in× Fig 2i(nad)o awn)d, (vbe). [sent-141, score-0.163]
49 Nevertheless, for images with small noise variances, the smaller window is required for smoothing and MHP approximation is mostly reserved (over 95% for window radius 5). [sent-146, score-0.244]
50 (a) shows the cameraman image and two central patches (5x5) we aim to denoise. [sent-149, score-0.135]
51 For each patch ,w witeh uisn eth ae s wpaintidaolw su, we fti (ndw i ntsd oPwatc shizGeP) otof 1t3he× c1e3n. [sent-151, score-0.237]
52 (d) and (g) show the color-coded path hop maps for the corresponding PatchGPs. [sent-155, score-0.282]
53 In the extreme case when patch size is 1 1, PatchGP degenerates xtotr PemixeelG caPse ew whhereen M paHtcPh his s nizoet longer c,o PnasticshteGnPt with PixelGP. [sent-158, score-0.255]
54 Since most patch-based denoising schemes (NLM, BM3D, etc) use a large patch size, MHPs thus still provide good approximations to PatchGPs. [sent-159, score-0.559]
55 For each patch, we compute its PatchGP to all other patches within a window of 13 13. [sent-163, score-0.15]
56 3 (c) and (f) show the patch geodesic doiwsta onfce 1 map w. [sent-165, score-0.456]
57 They form concentric squares and are nearly identical to the MHP hop maps under 4-way connectivity. [sent-170, score-0.17]
58 1(b), in order to denoise patch 푥0, we need to compute the path distances from 푁(푥0) to patches 푁(푥1), 푁(푥2), . [sent-182, score-0.502]
59 ) This indicates the patch geodesic distance can be computed progressively: we can first compute 1-hop path distance and then propagate it to 2-hop, 3-hop, and so on. [sent-189, score-0.614]
60 Under our direction and hop discretization, we can reformulate the denoising filter as: 퐼ˆ(푖) =푧(1푖)휃∑∈Θ푟∑=푅1푤(푖,푖휃,푟)퐼(푖휃,푟푅), (9) where thenˆ ormalization factor 푧(푖) = ∑푟∑=1푤(푖,푖휃,푟). [sent-190, score-0.464]
61 , patches that do not lie on the predefined directions will not be used. [sent-198, score-0.138]
62 This can potentially affect the patch-based denoising performance as some of the missing patches may be critical for denoising the central patch. [sent-199, score-0.656]
63 We also implement a multi-scale denoising scheme to compensate for sparse patch sampling. [sent-201, score-0.544]
64 Reusing Fig 1, if 푁(푥1 ) is significantly differ- ent from 푁(푥0) while 푁(푥2) is highly similar to 푁(푥0), patch 푁(푥2) should be assigned a large weight for denoising 푁(푥0). [sent-205, score-0.536]
65 To compute 1-hop patch distance ∣푁(푥푟) − 푁(푥푟−1) , we can oemitpheurt etr 1ea-ht pixels wh idthisinta ntchee patch equally or adopt a Gaussian weighting [10]. [sent-215, score-0.532]
66 The former (we call uniform weighting) is faster as its computation is independent of the patch size by using Integral Histogram [30]. [sent-216, score-0.32]
67 8), we use patch size 7 ×7 and Gaussian weighting fwoirth F 휎푤푒푖푔ℎ푡 =e u2s. [sent-219, score-0.29]
68 A common challenge in pixel-based denoising is reducing low frequency noise: properly handling low frequency noise requires using ultralarge spatial support. [sent-221, score-0.42]
69 4 (c) and (e) show the denoising results using the PixelGP [17] vs. [sent-224, score-0.276]
70 We resolve this problem by using a coarse-to-fine denoising scheme. [sent-227, score-0.276]
71 The Harr wavelet transformation provides two advantages: it is faster compared with the Gaussian pyramid and does not affect noise statistics. [sent-231, score-0.175]
72 4 compares the denoising results of PixelGP [17], PatchGP, F-PatchGP and FM-PatchGP. [sent-237, score-0.307]
73 The noisy image (b) is synthesized by adding Gaussian noise with variance 20. [sent-238, score-0.163]
74 Specifically, we compare FM-PatchGP against the FoE, NLM, BM3D, PixelGP, and fast bilateral filters (F-BL) [38]. [sent-244, score-0.229]
75 For each image, we synthesize 6 noisy versions by adding Gaussian noise with different variances between 5 and 30. [sent-252, score-0.171]
76 5 corresponds to a specific image where the X-axis is the noise variance and Y-axis the PSNR. [sent-254, score-0.13]
77 6 compares the visual quality, the PSNR, and the processing time of different denoising algorithms on the ’man’ image (with added Gaussian noise 휎푛=15). [sent-257, score-0.409]
78 We downsample a clean image of resolution 4032× 6048 fWroem d [w22n]s tmo dlieff aer celneta rnes imolaugtieon osf a rendso lthuteino nad 4d0 3G2a×us6s0ia4n8 noise 휎푛 = 15. [sent-267, score-0.133]
79 Our experiments suggest that FM-PatchGP can be potentially used for real-time denoising on mobile devices with relatively low computational power. [sent-290, score-0.276]
80 Finally, we compare FM-PatchGP with two commercial denoising tools “Neat Image” [2] and “Noise Ninja” [3]. [sent-291, score-0.327]
81 Both tools automatically estimate the noise profile to account for intensity-dependent noise variances [25]. [sent-292, score-0.262]
82 We then use their identified ’uniform’ regions to estimate noise variance 휎푛 to determine the window size and then apply FMPatchGP with uniform weighting. [sent-293, score-0.23]
83 Limitations and Future work We have presented a new patch-based image denoising algorithm based on the observation that patch geodesic paths (PatchGP) can be approximated by the minimal hop paths (MHP). [sent-309, score-1.146]
84 Comprehensive experiments on a broad range of natural images demonstrate that our new fast multi-scale PatchGP or FM-PatchGP is comparable to or outperforms state-of-the-art algorithms in terms of quality, and is orders of magnitude faster. [sent-310, score-0.134]
85 Similar to most denoising schemes, FM-PatchGP requires using good parameters, e. [sent-312, score-0.276]
86 , the patch size, the window size, the discretized search directions, etc. [sent-314, score-0.329]
87 Similar to BM3D and NLM, we usually fix the search directions and patch sizes and exhaust different window sizes. [sent-315, score-0.376]
88 For example, FM-PatchGP can be used to quickly locate similar patches for conducting PCA-based denoising [40]. [sent-321, score-0.405]
89 Finally, in our solution, we separately denoise each color channel and then combine the three channoise level 10 noise level 20 noise level 30 oisy imageN LNM TPimSeN:R0:. [sent-322, score-0.253]
90 Comparisons between FM-PatchGP and two commercial denoising tools Noise Ninja [3] and Neat Image [2] on real images. [sent-342, score-0.327]
91 11111222221111157755 fast bilateral filter (F-BL) [38], and our FM-PatchGP with uniform and Gaussian weighting at different image resolutions. [sent-351, score-0.259]
92 A geodesic framework for fast interactive image and video segmentation and matting. [sent-375, score-0.284]
93 A fundamental relationship between bilateral filtering, adaptive smoothing, and the nonlinear diffusion equation. [sent-388, score-0.171]
94 Fast bilateral filtering for the display of high-dynamic-range images. [sent-438, score-0.15]
95 Pointwise shapeadaptive dct for high-quality denoising and deblocking of grayscale and color images, 2006. [sent-444, score-0.276]
96 Edge-preserving smoothing using a similarity measure in adaptive geodesic neighbourhoods. [sent-456, score-0.269]
97 [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] Image denoising with block-matching and 3d filtering. [sent-482, score-0.276]
98 A fast approximation of the bilateral filter using a signal processing approach. [sent-524, score-0.188]
99 Image denoising using scale mixtures of Gaussians in the wavelet domain. [sent-553, score-0.32]
100 Two-stage image denoising by principal component analysis with local pixel grouping. [sent-614, score-0.31]
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