iccv iccv2013 iccv2013-51 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Radu Timofte, Vincent De_Smet, Luc Van_Gool
Abstract: Recently there have been significant advances in image upscaling or image super-resolution based on a dictionary of low and high resolution exemplars. The running time of the methods is often ignored despite the fact that it is a critical factor for real applications. This paper proposes fast super-resolution methods while making no compromise on quality. First, we support the use of sparse learned dictionaries in combination with neighbor embedding methods. In this case, the nearest neighbors are computed using the correlation with the dictionary atoms rather than the Euclidean distance. Moreover, we show that most of the current approaches reach top performance for the right parameters. Second, we show that using global collaborative coding has considerable speed advantages, reducing the super-resolution mapping to a precomputed projective matrix. Third, we propose the anchored neighborhood regression. That is to anchor the neighborhood embedding of a low resolution patch to the nearest atom in the dictionary and to precompute the corresponding embedding matrix. These proposals are contrasted with current state-of- the-art methods on standard images. We obtain similar or improved quality and one or two orders of magnitude speed improvements.
Reference: text
sentIndex sentText sentNum sentScore
1 First, we support the use of sparse learned dictionaries in combination with neighbor embedding methods. [sent-4, score-0.414]
2 In this case, the nearest neighbors are computed using the correlation with the dictionary atoms rather than the Euclidean distance. [sent-5, score-0.53]
3 Second, we show that using global collaborative coding has considerable speed advantages, reducing the super-resolution mapping to a precomputed projective matrix. [sent-7, score-0.226]
4 That is to anchor the neighborhood embedding of a low resolution patch to the nearest atom in the dictionary and to precompute the corresponding embedding matrix. [sent-9, score-1.123]
5 In general, it takes one or more low resolution (LR) images as input and maps them to a high resolution (HR) output image. [sent-14, score-0.295]
6 Dictionary-based methods use a patch- or feature-based approach to learn the relationship between local image details in low resolution and high resolution versions of the same scene. [sent-31, score-0.273]
7 By searching for nearest neighbors in a low resolution dictionary, a number of corresponding high resolution candidates can be retrieved. [sent-33, score-0.37]
8 Several methods have been proposed to overcome this problem, most notably neighbor embedding and sparse encoding approaches. [sent-37, score-0.293]
9 Sparse coding methods [17, 18] try to find a sparse coding for the input patches based on a compact dictionary (created by applying K-means or a similar algorithm to the training 11992200 patches). [sent-39, score-0.636]
10 [3] compare the running times for several example-based super-resolution algorithms, mentioning minutes to hours for most state-of-the-art methods, depending on the size of the input image. [sent-42, score-0.134]
11 We propose a new method for example-based superresolution that focuses on low computation time while keeping the qualitative performance of recent state-of-the-art approaches. [sent-43, score-0.114]
12 The remainder of the paper is organized as follows: we take a closer look at recent approaches for neighbor embedding and sparse coding for super-resolution in Section 2, we explain our proposed method in Section 3 and show experimental results in Section 4. [sent-45, score-0.322]
13 As we have briefly presented Freeman’s original method [8] in the introduction, here we focus on neighbor embedding and sparse coding approaches. [sent-49, score-0.322]
14 Neighbor embedding approaches Neighbor embedding (NE) approaches assume that small image patches from a low resolution image and its high resolution counterpart form low-dimensional nonlinear manifolds with similar local geometry. [sent-52, score-0.642]
15 The LLE algorithm assumes that when enough samples are available, each sample and its neighbors lie on or near a locally linear patch of the manifold. [sent-55, score-0.148]
16 search for a set of K nearest neighbors for each input patch in LR feature space, compute K appropriate weights for reconstructing the LR patch by finding a constrained least squares solution, and eventually create an HR patch by applying these weights in HR feature space. [sent-58, score-0.4]
17 It is based on the assumption that the local nonnegative least squares decomposition weights over the local neighborhood in LR space also hold for the corresponding neighborhood in HR space. [sent-61, score-0.438]
18 Sparse coding approaches The NE approaches from the previous section use a dictionary of sampled patches from low and high resolution image pairs. [sent-64, score-0.655]
19 These dictionaries can quickly become very large, especially when more or bigger training images are added to improve performance. [sent-65, score-0.112]
20 Sparse coding (SC) approaches try to overcome this by using a learned compact dictionary based on sparse signal representation. [sent-66, score-0.499]
21 Low resolution patches are sparsely reconstructed from a learned dictionary using the following formulation: mαin ? [sent-69, score-0.576]
22 0, (1) where F is a feature extraction operator, Dl is the learned low resolution dictionary, α is the sparse representation, y is the low resolution input patch and λ is a weighting factor. [sent-73, score-0.47]
23 Sparse dictionaries are jointly learned for low and high resolution image patches, with the goal of having the same sparse representation for low resolution patches as their corresponding high resolution patches. [sent-76, score-0.732]
24 This goal is reached for a set of training image patch pairs Xh, Yl (high and low resolution patches resp. [sent-77, score-0.313]
25 2 (2) where N and M are the dimensionality of the low and high resolution patches and Z is the coefficient vector representing the sparsity constraint. [sent-83, score-0.288]
26 The resulting dictionary has a fixed size and thus the algorithm has the capability of learning from many training patches while avoiding long processing times due to an ever growing dictionary. [sent-84, score-0.515]
27 [18] build upon this framework and improve the execution speed by adding several modifications. [sent-87, score-0.117]
28 Proposed Methods We propose an anchored neighborhood regression method that conveys two situations, one being the general behavior where a neighborhood size is set and the other being the so called global case, where the neighborhood coincides with the whole dictionary in use. [sent-92, score-1.105]
29 We can reformulate the problem as a least squares regression regularized by the l2-norm of the coefficients. [sent-99, score-0.119]
30 2, (3) where Nl corresponds to the neighborhood in LR space that we choose to solve this problem, which in the case of neighborhood embedding would refer to the K nearest neighbors of the input feature yF and in the case of sparse coding would refer to the LR dictionary. [sent-105, score-0.696]
31 (4) The HR patches can then be computed using the same coefficients on the high resolution neighborhood Nh x = Nhβ, (5) where x is the HR output patch and Nh the HR neighborhood corresponding to Nl . [sent-108, score-0.642]
32 If we use the whole LR dictionary for this, meaning (Nh, Nl) = (Dh, Dl), we get a global solution for the problem. [sent-109, score-0.364]
33 This means that during the execution of the SR algorithm we only need to multiply the precomputed projection matrix PG with the LR input feature vector, yF, to calculate the HR output patches x. [sent-111, score-0.257]
34 Anchored Neighborhood Regression The Global Regression approach reduces the superresolution process to a projection of each input feature into the HR space by multiplication with a precomputed matrix. [sent-115, score-0.141]
35 If instead of considering the whole dictionary as starting point for computing the projective matrix we consider local neighborhoods of a given size we allow more flexibility of the approach at the expense of increased computation – we will have more than one projective matrix and neighborhoods. [sent-117, score-0.492]
36 We start by grouping the dictionary atoms into neighborhoods. [sent-118, score-0.433]
37 More specifically, for each atom in the dictionary we compute its K nearest neighbors, which will represent its neighborhood. [sent-119, score-0.448]
38 If we start from a learned sparse dictionary, as in the sparsity approaches ofYang et al. [sent-120, score-0.132]
39 [18], we find the nearest neighbors based on the correlation between the dictionary atoms rather than the Euclidean distance. [sent-122, score-0.53]
40 The reason for this is that the atoms are a learned basis consisting of l2-normalized vectors. [sent-123, score-0.125]
41 If, conversely, we have a dictionary of features taken straight from the training patches, like in the NE approaches of Chang et al. [sent-124, score-0.387]
42 Once the neighborhoods are defined, we can calculate a separate projection matrix Pj for each dictionary atom dj, based on its own neighborhood. [sent-127, score-0.491]
43 This can be done in the same way as in the previous section by using only the dictionary atoms that occur in the neighborhood rather than the entire dictionary, and can again be computed offline. [sent-128, score-0.605]
44 The super-resolution problem can then be solved by calculating for each input patch feature yiF its nearest neighbor atom, dj, in the dictionary, followed by the mapping to HR space using the stored projection matrix Pj : xi = PjyiF. [sent-129, score-0.253]
45 (8) This is a close approximation of the NE approach, with a very low complexity and thus a vast improvement in execution time. [sent-130, score-0.109]
46 We call our approach the Anchored Neighborhood Regression (ANR), since the neighborhoods are anchored to the dictionary atoms and not directly to the low resolution patches as in the other NE approaches. [sent-131, score-0.856]
47 l4096 Dictoinary szie 1 03 102 Dictoinary szie a) trained dictionary 28. [sent-141, score-0.569]
48 6482 16324182561 024N0AGbE4 NRci8+ RuLNb SciEL4096 Dictoinary szie 103 102 e(s)gtim1 0 1 n iuRn1 0 − 12bNAGN ENREcEi+R+u+L bNSLciNELS × 10−3 163264128256512102420484096 Dictoinary szie b) random dictionary Figure 2. [sent-143, score-0.569]
49 average PSNR and average running time performance on the 14 images from Set14 with magnification 3. [sent-145, score-0.181]
50 t aheve mraegtheo PdSsN were dus aedve wraigthe trhuenirn i bnegst t neighborhood sciez eo. [sent-150, score-0.172]
51 For the running times we subtracted the shared processing time (collecting patches, combining the output) for all the methods. [sent-154, score-0.112]
52 details surrounding the algorithm such as used features, dictionary choices, similarity measures, size for neighborhood calculation and different patch embeddings. [sent-155, score-0.611]
53 These features are almost always calculated from the luminance component of the image, while the color components are interpolated using a regular interpolation algorithm such as bicubic interpolation [9, 18, 17, 4, 3]. [sent-161, score-0.239]
54 This is because the human visual system is much less sensitive to high frequency color changes than high frequency intensity changes, so for the magnification factors used in most papers the perceived difference between bicubic interpolation and SR of the color channels is negligible. [sent-162, score-0.298]
55 This usually leads to × features of about 30 dimensions for upscaling factor 3 and 3 3 low resolution patch sizes. [sent-173, score-0.261]
56 2 Embeddings Apart from our comparisons with the sparse methods of Yang et al. [sent-182, score-0.099]
57 [18], we also compare our results to neighbor embedding approaches adapted to our dictionary choices. [sent-184, score-0.557]
58 [4] does not use a learned dictionary, instead the dictionary consists simply of the training patches themselves. [sent-186, score-0.469]
59 This makes direct comparison to our method and the sparse methods difficult, because the question then arises “which dictionary should we use to have a fair comparison? [sent-187, score-0.394]
60 The same can be said when we wish to compare to the nonnegative neighbor embedding of Bevilacqua et al. [sent-189, score-0.34]
61 The solution is to use the same learned dictionary as Zeyde et al. [sent-191, score-0.42]
62 l em 10−13 248163264128256512 Neighborhood szie a) trained dictionary of size 1024 28. [sent-197, score-0.479]
63 68241 bNGANciENREu+ RbLNci SEL48163241825612,04 × Neighborhood szie ()e s111000123 m itg 100 nniuRn1100−−12bNAGNNENREcEi+R+u+LLbNSLciNELS 10−3 12481632641282565121,024 Neighborhood szie b) random dictionary of size 1024 Figure 3. [sent-201, score-0.593]
64 average PSNR and average running time performance on the 14 images from Set14 with magnification 3. [sent-203, score-0.181]
65 uses the original dictionary of 1022, while the other ×m3e. [sent-208, score-0.341]
66 tuhsee running tiinmael oifc tiohen a AryNR of m10e2th2,od w hfriolme t h raen odtohmer dictionary experiments is caused by applying a subsampling step of max{1, neighbo3r0hoodsize } for the anchor atoms, while for the trained one tohnea step pise r1i . [sent-213, score-0.428]
67 Feontrs st ihse c running yti ampepsl we s aub sturbascatemdp tlhineg s hstaerped o processing time (collecting patches, combining t,h we output) hfoer aralli ntehed dictionary based methods, leaving only the encoding time for each method. [sent-214, score-0.446]
68 3 Dictionaries × The choice of the dictionary is critical for the performance of any SR method. [sent-218, score-0.341]
69 Usually, the larger the dictionary the better the performance, however this comes with a higher computational cost. [sent-219, score-0.341]
70 The dictionary can be built using the LR input image itself, in this case we have an “internal” dictionary. [sent-220, score-0.363]
71 Also, we consider both randomly sampled dictionaries and learned dictionaries. [sent-227, score-0.145]
72 2 we depict the effect of the dictionary on the performance. [sent-231, score-0.341]
73 Moreover, we see again that using a learned dictionary is highly beneficial for all the methods it allows for a reasonably high performance for small dictionary sizes. [sent-233, score-0.737]
74 One needs a 16 larger random sampled dictionary t soi z reesa. [sent-234, score-0.341]
75 Most of the methods exhibit a similar log-linear increasing trend with the dictionary size and the PSNR difference among ANR, Zeyde et al. [sent-236, score-0.411]
76 and the NE approaches is quite small for their best settings (using optimal neighborhood size). [sent-237, score-0.172]
77 GR is the fastest method, but as a global method it has its weaknesses, and for large dictionaries tends not to reach competitive PSNR levels. [sent-239, score-0.197]
78 2, our ANR algorithm finds the nearest neighbor (atom) in the dictionary for each input feature and borrows the neighborhood and the precomputed projection matrix from this neighbor. [sent-243, score-0.736]
79 The NE approaches also rely on the neighborhood to the input LR feature. [sent-244, score-0.194]
80 The performance of the embedding methods, and hence the performance of the SR method, depends on the dimensionality of these neighborhoods. [sent-245, score-0.154]
81 The computation of the nearest neighbors is based on a similarity measure. [sent-246, score-0.097]
82 In the case of the learned sparse dictionaries, we obtain l2-normalized atoms meant to form a basis spanning the space of the training samples while minimizing the reconstruction error. [sent-249, score-0.178]
83 sT ohef PmSeNthRod (sd sBh)a raen tdh reu same gtr taiimneed ( dictionary goef o10n2 t4h,e except B diactuabseict. [sent-255, score-0.371]
84 27s on average, being 13 times faster than Zeyde et al. [sent-262, score-0.112]
85 [18]GRANRNE+LSNE+NNLSNE+LLE imagesPSNRTimePSNRTimePSNRTimePSNRTimePSNRTimePSNRTimePSNRTimePSNRTime The neighborhood size is the major parameter for the NE techniques and for ANR as well. [sent-266, score-0.196]
86 We show the effect of this size in Figure 3 for dictionaries of size 1024. [sent-267, score-0.16]
87 On the learned dictionary, NN + LS peaks at 12, NE + LLE and NE + NNLS at 24, while ANR peaks at 40. [sent-270, score-0.127]
88 We will use these neighborhood sizes for the further experiments. [sent-272, score-0.172]
89 More specifically, we compare our results to the sparse coding algorithms of Yang et al. [sent-278, score-0.152]
90 The effect of dictionary size is explored in Fig. [sent-288, score-0.365]
91 3 shows the relationship between neighborhood size, PSNR and time. [sent-290, score-0.172]
92 1 Quality When using the optimal neighborhood size for each method the PSNR of Zeyde et al. [sent-293, score-0.242]
93 [3], which is in the order of 10 seconds for a magnification factor of 3 . [sent-312, score-0.124]
94 compare with their algorithm because it is a very recent method aimed at low complexity and high processing speed while still keeping high quality results, and is therefore an ideal candidate for reference. [sent-315, score-0.15]
95 63 seconds of the algorithms (pre/post processing, bicubic interpolation, patch extraction, etc. [sent-319, score-0.127]
96 As lol fth PeS mNReth (oddBs) s ahnadre r tuhnen same mtraein (se)d p dictionary oonf t1h0e24 Se, except sBeitc. [sent-329, score-0.341]
97 For upscaling factor 3, ANR is 5 times faster than Zeyde et al. [sent-334, score-0.155]
98 Conclusions We proposed a new example-based method for superresolution called Anchored Neighbor Regression which focuses on fast execution while retaining the qualitative performance of recent state-of-the-art methods. [sent-429, score-0.149]
99 We also proposed an extreme variant of this called Global Regression which focuses purely on high execution speed in exchange for some visual quality loss. [sent-430, score-0.19]
100 K-SVD: an algorithm for designing overcomplete dictionaries for sparse representation. [sent-439, score-0.165]
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