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1 LOW-COMPLEXITY SINGLE-IMAGE SUPER-RESOLUTION BASED ON NONNEGATIVE NEIGHBOR EMBEDDING Marco Bevilacqua 1,2, Aline Roumy 1, Christine Guillemot 1, Marie-Line Alberi Morel 2 1 Inria Rennes - Bretagne Atlantique 2 Alcatel-Lucent - Bell Labs France British Machine Vision Conference (BMVC) 2012 September 6, 2012
2 Overview Single-image Super-Resolution What is it? Methods used Neighbor embedding SR Proposed algorithm [KP1] Feature representation [KP2] Neighbor embedding method [KP3] Choice of the dictionary Results Conclusions BMVC Low-Complexity Single-Image SR September 6,
3 Single-image Super-Resolution What is it? Given a low resolution (LR) input image, the aim is to produce an enhanced upscaling (high resolution - HR). Our target I Design a low-complexity yet efficient single-image SR algorithm BMVC Low-Complexity Single-Image SR September 6,
4 Methods Single-image SR Inverse problem methods Machine Learning methods Example-based methods ( correspondences of LR/HR patches ) Direct local Learning (Support Vector Regression, Ridge Regression...) Nearest Neighbor (NN) estimation BMVC Low-Complexity Single-Image SR September 6,
5 Nearest Neighbor SR 1. Dictionary learning Learning correspondences of LR/HR patches training images external dictionary [Freeman et al., 2002, Yang et al., 2008, Chang et al., 2004] correspondences learnt exploiting image self-similarities [Glasner et al., 2009] 2. NN search Search for best matching patches for the LR input patches 3. Weight computation Compute the weights of the patch combinations by using the selected LR candidates 4. HR patch reconstruction Combine the corresponding HR candidates to reconstruct the HR output patches, according to the weights computed The whole procedure is carried out in a feature space One-pass or multi-pass approach BMVC Low-Complexity Single-Image SR September 6,
6 LLE-based Nearest Neighbor SR In [Chang et al., 2004] an example-based SR algorithm, inspired by LLE (Locally Linear Embedding), is proposed: The weights for the linear combination (3. Weight computation), like in LLE, are the results of a LS problem that minimizes the approximation error with a sum-to-1 constraint (SUM1-LS) w i = arg min xt i Xd i w 2 s.t. 1 T w = 1. (1) w Gradient features are used for the LR patches; mean-subtracted luma values are used as features for the HR patches. BMVC Low-Complexity Single-Image SR September 6,
7 Key points Three key points KP1 Features used to represent the LR and HR patches KP2 Method used to compute the neighbor embedding (i.e. the weights of the patch combination) KP3 Nature of the dictionary: external or internal? BMVC Low-Complexity Single-Image SR September 6,
![[KP1] Representation by features Each patch is represented by a feature vector Role of the features To catch the most salient information in the LR patches in order to predict the HR details To](/docs-images/88/116249070/images/8-0.jpg "enforce the hypothesis of manifold similarity Various possibilities Simple luminance values Centered luminance values (with mean removal) Gradient values.")
8 [KP1] Representation by features Each patch is represented by a feature vector Role of the features To catch the most salient information in the LR patches in order to predict the HR details To enforce the hypothesis of manifold similarity Various possibilities Simple luminance values Centered luminance values (with mean removal) Gradient values... BMVC Low-Complexity Single-Image SR September 6,
9 [KP1] Analysis of the features F1 1st order gradient F2 Centered luminance values F1+F2 Concatenation of F1 and F2 All curves present a fall (even dramatic in case of F2) We decide to use F2: low-cost and best performing overall Can we avoid the fall? BMVC Low-Complexity Single-Image SR September 6,
![[KP1] Why the fall? Observation 1 d: dimension of the LR vectors; K: number of neighbors The ith neighborhood matrix Xd i has the highest possible rank w.h.p., i.e. r i = min(d 1, K).](/docs-images/88/116249070/images/10-0.jpg "Observation 2 For K = d the SUM1-LS problem is equivalent to a square linear system, as we have d equations in K = d unknowns unique solution in the LR domain.")
10 [KP1] Why the fall? Observation 1 d: dimension of the LR vectors; K: number of neighbors The ith neighborhood matrix Xd i has the highest possible rank w.h.p., i.e. r i = min(d 1, K). Observation 2 For K = d the SUM1-LS problem is equivalent to a square linear system, as we have d equations in K = d unknowns unique solution in the LR domain. Here, experimentally we have a critical point in the performance. The fall is because of an overfitting problem! BMVC Low-Complexity Single-Image SR September 6,
11 [KP2] A nonnegative embedding? Idea: replace the sum-to-1 equality constraint by an inequality constraint to avoid the unique solution problem Patches reconstructed only by additive combinations according to the intuitive notion of combining parts to form a whole The LS problem (1) becomes a nonnegative least squares (NNLS) problem: w i = arg min xt i Xd i w 2 s.t. w 0. (2) w BMVC Low-Complexity Single-Image SR September 6,
12 [KP2] Analysis of the weights Distribution of the weights SUM1-LS NNLS Distance between the actual LR weights and the ideal HR weights BMVC Low-Complexity Single-Image SR September 6,
13 [KP3] Choice of the dictionary Two possibilities build an external dictionary from a set of training images (from the original HR images, generate the LR versions, and extract HR and LR patches, respectively) learn the patch correspondences in a pyramid of recursively scaled images, starting from the LR input image, in the way of [Glasner et al., 2009] Internal DB Ext DB esa Ext DB wiki Image Scale PSNR DB size PSNR DB size PSNR DB size Head Baby Eyetest bird Woman In our case the dictionary derived from the pyramid is insufficient. BMVC Low-Complexity Single-Image SR September 6,
14 Algorithm: summary KP1 Features used to represent the LR and HR patches Centered luminance features (F2) KP2 Method used to compute the neighbor embedding (i.e. the weights of the patch combination) Nonnegative embedding (NNLS weights) KP3 Nature of the dictionary: external or internal? External BMVC Low-Complexity Single-Image SR September 6,
15 Experiments: algorithms considered Name Procedure LR features Patch reconstruction method Chang et al. (LLE) Glasner et al. (Pyramid) Tang et al. (KRR) Our algorithm single-step gradient (1st-2nd) NN embedding with SUM1-LS weights multi-pass luminance NN embedding with exponential weights single-step gradient (1st-2nd) kernel ridge regression single-step centered luminance NN embedding with NNLS weights BMVC Low-Complexity Single-Image SR September 6,
16 Results 1/3 Our algorithm Chang et al. Glasner et al. Tang et al. Image Scale PSNR Time PSNR Time PSNR Time PSNR Time baby bird butterfly head woman baby bird butterfly head woman baby bird butterfly head woman Higher PSNR for scale = 2; Glasner et al. outperforming for larger scale factors. BMVC Low-Complexity Single-Image SR September 6,
17 Results 2/3 Our algorithm Chang et al. Glasner et al. Tang et al. Image Scale PSNR Time PSNR Time PSNR Time PSNR Time baby bird butterfly head woman baby bird butterfly head woman baby bird butterfly head woman Computational time sensibly reduced, thanks to 1) one-pass procedure or 2) shorter feature vectors. BMVC Low-Complexity Single-Image SR September 6,
18 Results 3/3 Our algorithm Chang et al. Glasner et al. Tang et al. Lin. Regr. + F2 Image Scale PSNR Time PSNR Time PSNR Time PSNR Time PSNR Time baby bird butterfly head woman baby bird butterfly head woman baby bird butterfly head woman Linear Ridge Regression + centered luminance features: promising method! BMVC Low-Complexity Single-Image SR September 6,
19 Visual results: bird 1/6 M. factor: x3 Input image BMVC Low-Complexity Single-Image SR September 6,
20 Visual results: bird 2/6 M. factor: x3 Bicubic interpolation BMVC Low-Complexity Single-Image SR September 6,
21 Visual results: bird 3/6 PSNR: db Time: 47 s. Chang et al. BMVC Low-Complexity Single-Image SR September 6,
22 Visual results: bird 4/6 PSNR: db Time: 281 s. Glasner et al. BMVC Low-Complexity Single-Image SR September 6,
23 Visual results: bird 5/6 PSNR: db Time: 42 s. Tang et al. BMVC Low-Complexity Single-Image SR September 6,
24 Visual results: bird 6/6 PSNR: db Time: 9 s. Our algorithm BMVC Low-Complexity Single-Image SR September 6,
25 Visual results: baby 1/6 M. factor: x3 Input image BMVC Low-Complexity Single-Image SR September 6,
26 Visual results: baby 2/6 M. factor: x3 Bicubic interpolation BMVC Low-Complexity Single-Image SR September 6,
27 Visual results: baby 3/6 PSNR: db Time: 116 s. Chang et al. BMVC Low-Complexity Single-Image SR September 6,
28 Visual results: baby 4/6 PSNR: db Time: 2188 s. Glasner et al. BMVC Low-Complexity Single-Image SR September 6,
29 Visual results: baby 5/6 PSNR: db Time: 111 s. Tang et al. BMVC Low-Complexity Single-Image SR September 6,
30 Visual results: baby 6/6 PSNR: db Time: 27 s. Our algorithm BMVC Low-Complexity Single-Image SR September 6,
31 Conclusions Our method present better results than other one-pass algorithms [Chang et al., 2004, Tang et al., 2011] Results comparable to the multi-pass algorithm of [Glasner et al., 2009] for scale factor of 2 and 3, but much lower computational time Future work Further study regression methods (already promising results) Investigate other strategies for neighbor search BMVC Low-Complexity Single-Image SR September 6,
32 THANKS Questions? BMVC 2012 University of Surrey September 3-7, 2012
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