cvpr cvpr2013 cvpr2013-166 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Jianchao Yang, Zhe Lin, Scott Cohen
Abstract: We propose a fast regression model for practical single image super-resolution based on in-place examples, by leveraging two fundamental super-resolution approaches— learning from an external database and learning from selfexamples. Our in-place self-similarity refines the recently proposed local self-similarity by proving that a patch in the upper scale image have good matches around its origin location in the lower scale image. Based on the in-place examples, a first-order approximation of the nonlinear mapping function from low- to high-resolution image patches is learned. Extensive experiments on benchmark and realworld images demonstrate that our algorithm can produce natural-looking results with sharp edges and preserved fine details, while the current state-of-the-art algorithms are prone to visual artifacts. Furthermore, our model can easily extend to deal with noise by combining the regression results on multiple in-place examples for robust estimation. The algorithm runs fast and is particularly useful for practical applications, where the input images typically contain diverse textures and they are potentially contaminated by noise or compression artifacts.
Reference: text
sentIndex sentText sentNum sentScore
1 Our in-place self-similarity refines the recently proposed local self-similarity by proving that a patch in the upper scale image have good matches around its origin location in the lower scale image. [sent-2, score-0.585]
2 Based on the in-place examples, a first-order approximation of the nonlinear mapping function from low- to high-resolution image patches is learned. [sent-3, score-0.229]
3 Extensive experiments on benchmark and realworld images demonstrate that our algorithm can produce natural-looking results with sharp edges and preserved fine details, while the current state-of-the-art algorithms are prone to visual artifacts. [sent-4, score-0.253]
4 Furthermore, our model can easily extend to deal with noise by combining the regression results on multiple in-place examples for robust estimation. [sent-5, score-0.408]
5 The algorithm runs fast and is particularly useful for practical applications, where the input images typically contain diverse textures and they are potentially contaminated by noise or compression artifacts. [sent-6, score-0.495]
6 Such image priors range from simple analytical “smoothness” priors to more sophisticated statistical priors learned from natural images [16, 5, 7, 19, 10]. [sent-10, score-0.197]
7 As images contain strong discontinuities, such as edges and corners, the simple “smoothness” prior will result in ringing, jaggy and blurring artifacts. [sent-14, score-0.193]
8 Therefore, more sophisticated statistical priors learned from natural images are exs cohen} @ adobe . [sent-15, score-0.138]
9 Alternatively, example-based nonparametric methods [7, 14, 2, 17] were used to predict the missing frequency band of the upsampled image, by relating the image pixels at two spatial scales using a universal set of training example patch pairs. [sent-18, score-0.725]
10 , local image structures tend to recur within and across different image scales [4, 1, 21], and image super-resolution can be regularized based on these self-similar examples instead of some external database [4, 9, 6]. [sent-24, score-0.225]
11 They show that the local selfsimilarity assumption for natural images holds better for small upscaling factors and the patch search can be conducted in a restricted local region, allowing a very fast practical implementation. [sent-28, score-0.871]
12 In this paper, we refine the local self-similarity [6, 21] by in-place self-similarity, by proving that, for a query patch in the upper scale image, patch matching can be restricted to its origin location in the lower scale image. [sent-29, score-0.933]
13 g, cellphone 1 1 10 0 05 5 579 7 cameras) or compression artifacts (e. [sent-32, score-0.273]
14 We propose a new fast super-resolution algorithm based on regression on in-place examples, which, for the first time, leverages the two fundamental super-resolution approaches of learning from externalexamples and learning from self-examples. [sent-36, score-0.329]
15 We prove that patch matching across different image scales with small scaling factors is in-place, which refines and validates the recently proposed local selfsimilarity theoretically. [sent-38, score-0.634]
16 We can easily extend our algorithm to handle noisy input images by combining regression results on multiple in-place examples. [sent-40, score-0.289]
17 Section 3 presents our robust regression model for super-resolution. [sent-44, score-0.289]
18 Preliminaries and Notations ×× This work focuses on upscaling an input image X0 which contains some high-frequency content that we can borrow for image super-resolution, i. [sent-48, score-0.347]
19 We use bolded lower case x0 and x to denote a a image patches sampled from X0 and Xan, respectively, a an×d y0 maandg y atot cdheenso steam a ×le a image patches sampled from Y0 and Ya , respectively. [sent-53, score-0.229]
20 Regression on In-place Examples In this section, we present our super-resolution algorithm based on learning the in-place example regression by referring to an external database. [sent-57, score-0.408]
21 The Image Super-resolution Scheme Similar to [6], we first describe our overall image upscaling scheme in Figure 1, which is based on in-place examples and first-order regression that will be discussed shortly. [sent-60, score-0.696]
22 For each patch y of the upsampled low-frequency band image Y , we find its in-place match y0 from the low-frequency band Y0, and then perform a first-order regression on x0 to estimate the desired patch x for target X. [sent-64, score-1.321]
23 The input image is denoted as X0 ∈ RK1 ×K2, from which we obtain its low-frequency band image Y0 ∈ RK1×K2 by a low-pass Gaussian filtering. [sent-65, score-0.186]
24 We upsample X∈0 using bicubic interpolation by a factor of s to get Y ∈ RsK1 ×sK2. [sent-66, score-0.196]
25 For each image patch y (a a) from the image Y at locaFotiron e (cxh, y im), we pfiantcdh i tys in-place example y0 g(ae ×Y a at) around its origin coordinates (xr, yr) in image Y0(, aw ×her ae) xr = ? [sent-69, score-0.49]
26 a{ ×y0 a, )x f0r}o mco Xnstitutes a low- and high-resolution prior example pair }fro cmon nwsthiitucthe we apply a first-order regression model to estimate the high- + + × resolution image patch x for y. [sent-81, score-0.62]
27 We repeat this procedure for overlapping patches of Y , and the final high-resolution image X is generated by aggregation all the recovered highresolution image patches. [sent-82, score-0.181]
28 For large upscaling factors, we iteratively repeat the above upscaling step by multiple times, each with a constant scaling factor of s. [sent-83, score-0.854]
29 These local singular primitives are more invariant to scale changes, i. [sent-88, score-0.201]
30 , an upper scale image contains singular structures similar to those in its lower spatial scale [9]. [sent-90, score-0.295]
31 Furthermore, we expect a singular structure in the upper scale image will have a similar structure in its origin location on the lower spatial scale. [sent-91, score-0.277]
32 To evaluate such local scale invariance, we compute the matching error between a 5 5 query patch y at (x, y) in Y and 49 patches centering a ×ro u5n qdu e(xryr, p pyart)c hin y image ,Yy0) on tYhe a Berkeley Segmentation Dataset [11]. [sent-92, score-0.528]
33 Figures 2 plots the average matching errors for different scaling factor s, where “blue” denotes small matching error and “red” denotes large matching error. [sent-93, score-0.34]
34 Matching errors of each patch y in an upper-scale image with its in-place neighbors in the lower-scale image for different scaling factors. [sent-97, score-0.399]
35 s center (xr, yr) on average, and the smaller the scaling factor, the lower the matching error, and the more concentrated the area with lower matching error. [sent-98, score-0.303]
36 Therefore, for a small scaling factor, finding a similar match for a query patch y could be extremely localized on Y0. [sent-99, score-0.482]
37 The local scale invariance indicates that we could efficiently find a similar example y0 for y, and thus the corresponding high-resolution patch x0, from which we can infer the high-frequency information of y. [sent-101, score-0.378]
38 For each patch y of size a a (a > 2) from upsampled image Y ea cath l poacatcthio yn (oxf, s yiz)e, containing only one singular primitive, the location (x0, y0) of a close match y0 in Y0 for y will be at most one pixel away from y ’s origin location (x/s, y/s) on Y0, i. [sent-104, score-0.56]
39 , |x0 x/s| < 1and |y0 y/s| < 1, given the scaling factor s −< xa//s(a| <− 1 2). [sent-106, score-0.16]
40 a − − Therefore, the search region for y on Y0 is in-place, and is called an in-place example for patch y. [sent-107, score-0.294]
41 Based on the in-place example pair {y0 , x0}, we perform a first-order regression atom epsletim paatier {thye high-resolution rinmfo arm fiartsito-nor dfeorr patch y in the following section. [sent-108, score-0.583]
42 In-place Example Regression The patch-based single image super-resolution problem can be viewed as a regression problem, i. [sent-111, score-0.289]
43 , finding a mapping function f from the low-resolution patch space to the target high-resolution patch space. [sent-113, score-0.644]
44 However, learning this regression function turns out to be extremely difficult due to the ill-posed nature of super-resolution; proper regularizations or good image priors are need to constrain the solution space. [sent-114, score-0.388]
45 22) ≈x0 + ∇fT(y0)(y − y0), x =f(y) (1) 2This is a reasonable assumption, as one will not expect a dramatic change in the high-resolution patch for a minor change in the lowresolution image patch, especially in the case of small scaling factors. [sent-118, score-0.399]
46 , cn} sampled from the luoews- ornes aol suettio onf patch space. [sent-125, score-0.294]
47 Discussions In previous example-based super-resolution works [7, 6], the high-resolution image patch x is obtained by transferring the high-frequency component from the best prior example pair {y0, x0} to the low-resolution image patch y, aim. [sent-133, score-0.625]
48 th Caot highfrequency component transfer is an approximate of the firstorder regression model by setting the derivative function ∇f to be the identity matrix. [sent-148, score-0.431]
49 1, which does not account for error compensation and thus has larger approximation errors. [sent-156, score-0.15]
50 The results are obtained by recovering overlapping low-resolution image patches which − −x 3Here, x, y, x0 and y0 are in their vectorized form 4The prior in-place example pairs are found based on {yi }im=1 only discuTssheed p brieofror ine. [sent-158, score-0.216]
51 Because the zero-order approximation has large approximation errors, the overlapping pixel predictions do not agree with each other. [sent-164, score-0.197]
52 However, the algorithm still requires a large number of training examples in order to approximate f well, resulting in expensive computations for practical applications. [sent-169, score-0.147]
53 To reduce the regression variance, we can perform regression on each of them and combine the results by a weighted average. [sent-174, score-0.578]
54 By aggregating the multiple regression results, our algorithm can handle different image degradations well in practical applications. [sent-196, score-0.341]
55 It is worthy to note that our formulation only uses regression results on extremely localized in-place examples in a lower spatial scale, which is different from that of the non-local means algorithm [1] that operates on raw image patches in a much larger spatial window at the same spatial scale. [sent-197, score-0.59]
56 Prediction RMSEs for different approaches on testing patches and images for one upscaling step (1. [sent-199, score-0.442]
57 Although simple interpolation methods result in artifacts along the discontinuities, they perform well on smooth regions. [sent-208, score-0.27]
58 This observation suggests that we only need to process the textured regions with our super-resolution model, while leaving the large smooth regions to simple and fast interpolation techniques. [sent-209, score-0.191]
59 To differentiate smooth and textured regions, we do SVD on the gradient matrix of a local image patch, and calculate the singular values s1 ≥ s2 ≥ 0, which represent the energies in the dominant loc≥al gradient wanhdic edge orersieenntta tthioen e. [sent-210, score-0.209]
60 Parameters We choose patch size a = 5 and iterative scaling factor s = 1. [sent-216, score-0.454]
61 The low-frequency band Y of the target high-resolution image is approximated by bicubic interpolation from X0. [sent-218, score-0.327]
62 The low-frequency band Y0 of the input image X0 is obtained by a low-pass Gaussian filtering with a standard deviation of 0. [sent-219, score-0.186]
63 The image patches of Y are processed with overlapping pixels, which are simply averaged to get the final result. [sent-221, score-0.136]
64 1 1 10 0 06 6 602 0 × frequency transfer egres ion Figure 4. [sent-224, score-0.135]
65 Training To train the regression model, we start from a collection of high-resolution natural images {Xi}ir=1 from tchoel Berkeley Segmentation nD naatatuseratl [ i1m m1a]. [sent-227, score-0.333]
66 g eTsh {eX corresponding lower spatial scale images {X0i}ir=1 are generated by blurring arn sdp downsampling tehse { high-resolution images by a factor of s. [sent-228, score-0.223]
67 The two low-frequency band image sets {Yi}ir=1 and {Y0i}ir=1 are generated as described above. [sent-229, score-0.186]
68 {WYe }then randomly sample image patch pairs from {Yi}ir=1 Wande {hXeni} rira=n1d otom loyb staamin ptlhee mlowag-e a pnadt high-resolution patch pairs {Xxi} , yi}im=1, and meanwhile get the corresponding inplace matching image pairs {xi0, yi0}im=1 from {X0i}im=1 apnladc {eY m0ia}trci=h1in . [sent-230, score-0.849]
69 In our experiments, we find that the learned regression model can be very com- × pact; using 27 = 128 anchor points already suffice for our purpose. [sent-236, score-0.379]
70 Regression Evaluations To measure the regression accuracy from the recovery perspective, we first conduct quantitative comparisons for different methods in terms of RMSE. [sent-239, score-0.33]
71 Table 1 reports the results on both testing patches and synthetic images taken from [11] for one upscaling step (1. [sent-240, score-0.48]
72 As shown, zeroforrodmer regression performs nthge s wtepors (1t d. [sent-242, score-0.289]
73 Frequency transfer performs much better than zero-order regression due to the error compensation for Δx by Δy. [sent-245, score-0.415]
74 5 In Figure 4, we show super-resolution results (3 ) on the “Mayan aurrceh 4i,te wcteur seh”o image rw-ritehs frequency utrltasn(s f3e×r )a ondn our regression model, respectively. [sent-247, score-0.37]
75 By comparison, our regression estimation is more accurate and thus can preserve more sharp details compared with frequency transfer. [sent-248, score-0.491]
76 5It is worthy to note that the algorithms discussed here are based on multiple iterative upscaling steps for large scaling factors. [sent-249, score-0.511]
77 Therefore, we only make comparisons for one upscaling step to keep the experiment clean. [sent-252, score-0.388]
78 However, it also creates small artifacts across the image due to the fact that some unique patches to the image cannot be well represented by the universal dictionary, and the algorithm is also much slower than ours. [sent-263, score-0.315]
79 The algorithms of [9] and [6] are based on selfexamples, which tend to create artificially sharp edges and artifacts due to the insufficient number of matched selfexamples. [sent-264, score-0.384]
80 In contrast, by leveraging learning from external examples and learning from self-examples, our algo- ×× rithm can produce sharp details without noticeable visual artifacts. [sent-265, score-0.338]
81 , ghost artifacts along the cheek in “kid”, jaggy artifacts on the long edge in “chip”, and artifacts in the camera area in “cameraman”. [sent-271, score-0.565]
82 [18] are generally a little burry and they contain many small artifacts across the image upon a closer look. [sent-273, score-0.167]
83 , pupil in “kid”, as it is using frequency transfer to generate high-resolution patches. [sent-279, score-0.135]
84 In comparison, our algorithm is able to recover local texture details as well as sharp edges without sacrificing the naturalness. [sent-280, score-0.177]
85 Most previous super-resolution works focus on synthetic test examples with simple edge structures, but the large body of natural images typically contain diverse textures and rich fine structures. [sent-281, score-0.238]
86 , images captured by low cost sensors are typically contaminated by some amount of sensor noise and internet images with JPEG compression artifacts. [sent-292, score-0.317]
87 By averaging the regression results on multiple in-place self-examples, our algorithm can naturally handle noisy inputs. [sent-294, score-0.289]
88 Figure 7 shows one more set of super-resolution results (3 ) on real-world images that are corrupted uwtiitohn e riethseurlt sensor onnois ree or compression a thrtai-t × facts. [sent-295, score-0.153]
89 As shown, the algorithms in [9] and [6] cannot distinguish noise from the signal and thus enhance both, resulting in magnified noise artifacts, while our algorithm almost completely eliminates the noise and at the same time preserves sharp image structures. [sent-296, score-0.298]
90 Computational Efficiency With fast in-place matching and selective patch processing, our algorithm is much faster than Glasner’s algorithm [9], is at least one order of magnitude faster than Yang’s algorithm [18], and is comparable with Freedman’s algorithm [6]. [sent-298, score-0.431]
91 Conclusions In this paper, we propose a robust first-order regression model for image super-resolution based on justified in-place self-similarity. [sent-305, score-0.289]
92 Taking advantage of the in-place examples, we can learn a fast and robust regression function for the otherwise ill-posed inverse mapping from low- to high-resolution patches. [sent-307, score-0.385]
93 On the other hand, by learning from an external training database, the regression model can overcome the problem of insufficient number of self-examples for matching. [sent-308, score-0.448]
94 Compared with previous example-based approaches, our new approach is more accurate and can produce natural looking results with sharp details. [sent-309, score-0.203]
95 In many practical applications where images are contaminated by noise or compression artifacts, our robust formulation is of particular importance. [sent-310, score-0.322]
96 The results of [18] contain small artifacts along edges (best perceived in zoomed PDF). [sent-314, score-0.27]
97 Imag and video upscaling [7] [8] [9] [10] [11] [12] [13] [14] [15] from local self-examples. [sent-360, score-0.347]
98 In order to get sharp results for singular structure (p, q), we want to match (p, q) with (p? [sent-445, score-0.243]
99 Given a patch y (a a) from the low-frequency band image nY a ace pnattecrhed y ya t( a(x ×, y a),) fsrhoomwn t hine Figure 8, we assume it has a singular structure centered at (p, q). [sent-477, score-0.637]
100 This point has a shift from the patch center by p = x + tx and q = y + ty (|tx |, |ty | < a/2). [sent-478, score-0.294]
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