iccv iccv2013 iccv2013-312 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Wufeng Xue, Xuanqin Mou, Lei Zhang, Xiangchu Feng
Abstract: How to measure the perceptual quality of natural images is an important problem in low level vision. It is known that the Mean Squared Error (MSE) is not an effective index to describe the perceptual fidelity of images. Numerous perceptual fidelity indices have been developed, while the representatives include the Structural SIMilarity (SSIM) index and its variants. However, most of those perceptual measures are nonlinear, and they cannot be easily adopted as an objective function to minimize in various low level vision tasks. Can MSE be perceptual fidelity aware after some minor adaptation ? In this paper we propose a simple framework to enhance the perceptual fidelity awareness of MSE by introducing an l2-norm structural error term to it. Such a Structural MSE (SMSE) can lead to very competitive image quality assessment (IQA) results. More surprisingly, we show that by using certain structure extractors, SMSE can befurther turned into a Gaussian smoothed MSE (i.e., the Euclidean distance between the original and distorted images after Gaussian , smooth filtering), which is much simpler to calculate but achieves rather better IQA performance than SSIM. The socalled Perceptual-fidelity Aware MSE (PAMSE) can have great potentials in applications such as perceptual image coding and perceptual image restoration.
Reference: text
sentIndex sentText sentNum sentScore
1 hk Abstract How to measure the perceptual quality of natural images is an important problem in low level vision. [sent-8, score-0.204]
2 It is known that the Mean Squared Error (MSE) is not an effective index to describe the perceptual fidelity of images. [sent-9, score-0.311]
3 Numerous perceptual fidelity indices have been developed, while the representatives include the Structural SIMilarity (SSIM) index and its variants. [sent-10, score-0.311]
4 However, most of those perceptual measures are nonlinear, and they cannot be easily adopted as an objective function to minimize in various low level vision tasks. [sent-11, score-0.149]
5 Can MSE be perceptual fidelity aware after some minor adaptation ? [sent-12, score-0.331]
6 In this paper we propose a simple framework to enhance the perceptual fidelity awareness of MSE by introducing an l2-norm structural error term to it. [sent-13, score-0.369]
7 Such a Structural MSE (SMSE) can lead to very competitive image quality assessment (IQA) results. [sent-14, score-0.116]
8 , the Euclidean distance between the original and distorted images after Gaussian , smooth filtering), which is much simpler to calculate but achieves rather better IQA performance than SSIM. [sent-17, score-0.084]
9 The socalled Perceptual-fidelity Aware MSE (PAMSE) can have great potentials in applications such as perceptual image coding and perceptual image restoration. [sent-18, score-0.313]
10 Introduction In many image processing and low level vision tasks, it is indispensable to find a suitable fidelity measure to measure the fidelity index of the underlying visual signal. [sent-20, score-0.345]
11 cn use of fidelity measure can be generally classified into the following categories. [sent-27, score-0.164]
12 First of all, the fidelity measure is ubiquitously used to evaluate the performance of competing algorithms and to guide the parameter selection, for example, in image denoising [9] and medical image reconstruction [29]. [sent-28, score-0.179]
13 Second, the fidelity measure is used to design the objective function for minimization in applications such as image coding [12,23] and image restoration [17]. [sent-29, score-0.194]
14 Third, the fidelity measure can be used as the rule to make decisions, for example, in content based image retrieval [21] and block matching [16, 27]. [sent-30, score-0.164]
15 The most popular and widely used signal fidelity measure may be the classical Mean Squared Error (MSE), which measures the fidelity of a signal d ∈ RN by ? [sent-31, score-0.349]
16 This is mainly because MSE is pixel-wise and ignores the structural relationship in a neighborhood. [sent-41, score-0.055]
17 The past decades have witnessed the rapid development of image quality assessment (IQA) methods, which aim to gauge the perceptual quality of natural images like human − 770055 does. [sent-43, score-0.287]
18 In the case that the reference image is accessible, the resulting full reference (FR) IQA model can be utilized as an image perceptual fidelity term to mimic the human perception of image quality. [sent-44, score-0.33]
19 Though these IQA models can better predict the perceptual quality of a test image than MSE, they do not profit much the applications such as perceptual image coding, perceptual image representation and restoration, etc. [sent-46, score-0.483]
20 Most of them are not a valid distance metric and have much higher computational complexity than MSE. [sent-48, score-0.06]
21 In perceptual image coding and restoration, more visually comfortable results have been reported by using SSIM to guide the algorithm design [16, 17, 23]. [sent-51, score-0.164]
22 The underlying assumption of SSIM is that the human vision system is highly adapted to extract structural information in the viewing field. [sent-52, score-0.055]
23 For a pair of reference image r and distorted image d, SSIM estimates the perceptual quality of d from three aspects: luminance, contrast and structure. [sent-53, score-0.243]
24 It uses the following formula to compute the perceptual fidelity index of d: SSIM(r,d) =μ2r2μ+rμ μdd2++ c c11·σ2r2σ+r, σdd2++ c2 c2 (1) where μr and μd are the local mean luminance of r and d; σr2 and σd2 are the local variance; σr,d is the local covariance between r and d. [sent-54, score-0.323]
25 It is highly demanded to find an MSE-like fidelity measure, which could inherit some of the appealing merits of MSE while being highly perceptual fidelity aware. [sent-57, score-0.451]
26 This will not only simplify the computation in IQA applications, but also facilitate significantly the use of perceptual fidelity measure in applications such perceptual image coding and perceptual image restoration. [sent-58, score-0.626]
27 With the above considerations, in this work we aim to develop an MSE-like l2-norm perceptual fidelity measure. [sent-59, score-0.294]
28 We propose to introduce an l2-norm structural error term to the original MSE so that the resulting measure can be more perceptual fidelity aware. [sent-60, score-0.388]
29 The structural error term can be simply designed by using the linear gradient operator or Laplacian of Gaussian operator. [sent-61, score-0.152]
30 , the Euclidean distance between reference image r and distorted image d after Gaussian smooth filtering. [sent-65, score-0.102]
31 We call the resulting measure Perceptual-fidelity Aware MSE (PAMSE), which provides a very simple MSE-like formula to calculate the image perceptual fidelity and achieves rather better perceptual consistency than SSIM. [sent-66, score-0.462]
32 In addition, PAMSE can have great potentials in perceptual image coding and restoration. [sent-67, score-0.164]
33 Section 2 presents the framework of SMSE and the setting of its structural term. [sent-68, score-0.055]
34 Since human visual system is sensitive to image local structures, we propose to amend MSE a little so that the modified MSE can count more the structural information in the fidelity estimation. [sent-76, score-0.2]
35 2 2 ) (2) where α is a (negative or positive) constant to adjust the contribution of structural error term ? [sent-91, score-0.075]
36 SMSE is an amendment of MSE by introducing a structural error term. [sent-97, score-0.075]
37 The framework of Structure MSE (SMSE) and Perceptual fidelity Aware MSE (PAMSE). [sent-101, score-0.145]
38 22 (6) The matrix P can be viewed as a new feature extractor (a linear projection/transform) which is able to simultaneously measure the pixel-wise energy preservation and local neighborhood-wise image structure preservation. [sent-119, score-0.108]
39 Linear structure extractor S There are many candidates for the linear structure operator S in the proposed SMSE framework. [sent-123, score-0.146]
40 For instances, S can be chosen as the gradient operator which outputs the abrupt changes of image intensity; S can also be chosen as the Laplacian or Laplacian of Gaussian(LOG) operator which mimics the receptive field of the ganglion cells and the lateral geniculate nucleus (LGN) cells [5]. [sent-124, score-0.133]
41 The linear transforms such as wavelet transform and principle component analysis can also be employed as the feature extractor S. [sent-125, score-0.064]
42 For simplicity, in this paper we only consider the gradient operator and the Laplacian operator. [sent-126, score-0.077]
43 1 Gradient operators Image gradient is a good feature for low level and higher level vision tasks, and gradient priors are widely used in image restoration. [sent-129, score-0.083]
44 Therefore, it is a good choice to employ gradient operators as S in the proposed SMSE framework. [sent-131, score-0.062]
45 That is, we can apply a filter f = [1, −1] horizontally and vertically to the images r afnd = =d 1to, get th hoeirri gradient maps. [sent-134, score-0.056]
46 tTichael yfor towta rhde dimif-ference filtering can be written as a matrix operator, denoted by Sd = [Sxd; Sdy], where Sdx and Sdy denote the corresponding operators along horizontal and vertical directions, respectively. [sent-135, score-0.094]
47 The forward difference operator can be too sensitive to small intensity changes. [sent-136, score-0.07]
48 A more commonly used gradient operator is the Gaussian gradient operator, which actual- ly smoothes the image by using a Gaussian smooth filter h before applying the forward difference filter f. [sent-137, score-0.228]
49 2 Laplacian operators The gradient operator computes the first derivative of images. [sent-141, score-0.132]
50 In comparison, the Laplacian operator, denoted by Sl, exploits the second derivative of images by filtering the images with the Laplacian filter l = [0, 1, 0; 1, −4, 1; 0, 1, 0] . [sent-142, score-0.076]
51 aTghees Laplacian operator nS fli tise very se [0n,si1t,i0ve; 1to, −no4,is1e; a0n,d1 i,m0]-. [sent-143, score-0.056]
52 age small changes, and hence the LOG operator, denoted by Slog, is proposed to smooth the image by Gaussian smooth filter h before applying l. [sent-144, score-0.095]
53 The zero770077 crossings of the LOG filtering response indicate the edge locations, and the LOG based edge map has been successfully used to predict image quality [28, 3 1]. [sent-146, score-0.063]
54 3 The determination of α Given a linear structure extractor S, we need to determine the parameter α to make the proposed SMSE a valid distance metric. [sent-149, score-0.119]
55 Since the operators Sd, Sg, Sl, and Slog can be interpreted as filtering operations, they can be written as a circulant matrix (each row is a cyclic shift of another) of size N N, whose rows are repeated svherisftio onfs a nofo tthheer corresponding Nfil,te wr template. [sent-157, score-0.132]
56 Gaussian smooth MSE: an inherent perceptual fidelity aware MSE In Section. [sent-178, score-0.361]
57 2, we proposed a framework to make MSE be able to characterize image local structural changes while measuring the global energy of image pixel-wise error. [sent-179, score-0.055]
58 With some linear structure extractor S and the associated parameter α determined in Eq. [sent-180, score-0.077]
59 9, the new image fidelity measure SMSE is however still a valid distance metric. [sent-181, score-0.206]
60 The metric is actually characterized by the symmetric PSD matrix M = I αSTS, which can be written as + M = PTP, and consequently the SMSE metric can be written as SMSE(r, d) = N1 ? [sent-182, score-0.076]
61 matrix P is a circulant matrix and each row of it comes from a filter, then the feature extraction by Pr and Pd becomes the linear filtering of images r and d by this filter. [sent-187, score-0.089]
62 The operator P depends on the used linear feature extractor S. [sent-190, score-0.12]
63 We can also use more than one operator in the pro− posed SMSE framework. [sent-193, score-0.056]
64 Suppose that we use the difference operator Sd and the Laplacian operator Sl, and hence the SMSE measure becomes SMSE(r,d) = N1(? [sent-194, score-0.131]
65 Interestingly, it can be proved that (please refer to Appendix A) if we set αd = −2σ2 and αl = σ4, where σ is the scale parameter of a G−a2uσssian smooth filter h and σ is small, then we have S+MσS4E? [sent-201, score-0.065]
66 on: we can simply make MSE perceptual fidelity aware by filtering the images r and d with a Gaussian smooth filter. [sent-211, score-0.388]
67 We call such an image fidelity measure Perceptual-fidelity Aware MSE (PAMSE), defined as PAMSE(r,d) =N1? [sent-212, score-0.164]
68 12 can be written as PAMSE(r, d) = N1(r − d)TPhTPh(r − d), where Ph is the matrix form of filtering by h, PAM(SrE− −is always a (pseudo-)distance metric because PhTPh is a PSD matrix. [sent-217, score-0.071]
69 The images in these databases are generated through different distortion channels and are all assigned with a subjective quality/distortion score. [sent-222, score-0.087]
70 scores and the predicted scores can be examined in terms of Spear rank order correlation coefficient (SRC), Pearson correlation coefficient (PCC) and the root mean squared error (RMSE). [sent-226, score-0.064]
71 Note that PCC and RMSE are calculated after a logistic regression between the predicted scores and the subjective scores [8]. [sent-227, score-0.061]
72 The LIVE database consists of 29 reference images and 779 distorted images generated from JPEG compression (JPEG), JPEG2000 compression (JP2K), additive white noise (AWN), Gaussian blur (GB), and simulated fast fading Rayleigh channel. [sent-229, score-0.058]
73 The CSIQ database consistes of 30 reference images and 866 distorted images of JPEG2000, JPEG, AWN, GB, additive pink Gaussian noise (PGN) and contrast change. [sent-230, score-0.058]
74 There are 25 reference images and 1,700 distorted images of 17 distortion types. [sent-233, score-0.078]
75 Since these operators are actually the matrix form of spatial filters, in implementation we use spatial convolution to compute the structural features Sr and Sd. [sent-238, score-0.108]
76 For SMSE with Sg, we will smooth the images r and d by using a Gaussian smooth filter h(i, j) = 2π1σ2 before applying the forward difference filter efx. [sent-262, score-0.144]
77 For SMSE with Slog, we also need to set the scale parameter of the Gaussian smooth filter h. [sent-293, score-0.065]
78 Implementation and results of PAMSE The implementation of PAMSE is even simpler than SMSE because we only need to set the scale parameter σ of the Gaussian smooth filter h. [sent-325, score-0.065]
79 The key message we would like to convey is that with some small adaptation, an MSE-like image perceptual fidelity measure can be obtained, which is very easy and efficient to implement while offering very competitive IQA results. [sent-343, score-0.327]
80 4 shows the scatter plots of the subjective score versus the predicted score by SSIM and PAMSE on the CSIQ database. [sent-358, score-0.074]
81 MSE measures image distortion equally in all frequencies, and thus over-estimates the perceptual distortion. [sent-403, score-0.169]
82 r d) with the filter corresponding to operator Sro,r a singdn tahle (nr calculating thhee f il 2t-erno cromrr eosfp tohned ifnilgte troing response. [sent-417, score-0.091]
83 The scatter plots of the subjective score versus the results of IQA models on the CSIQ database. [sent-426, score-0.074]
84 Conclusions By adding an l2-norm structure error term to the original Mean Squared Error (MSE) index, in this paper we proposed a simple yet very effective framework, namely Structural MSE (SMSE), for image quality assessment (IQA). [sent-436, score-0.135]
85 When using difference operator and Laplacian operator to extract the structure error, SMSE becomes the MSE between Gaussian smoothed reference and distorted images, and we call the corresponding SMSE measure Percetualfidelity Aware MSE (PAMSE). [sent-437, score-0.214]
86 Meanwhile, SMSE and PAMSE have good potentials to be used as objective functions in perceptual quality based image processing tasks. [sent-440, score-0.185]
87 f Wdifefe uresenc ∇e operator Sod d aenndo Laplacian operator Sl, respectively. [sent-444, score-0.112]
88 On the mathematical properties of the structural similarity index. [sent-478, score-0.07]
89 Perceptual image quality assessment using a geometric structural distortion model. [sent-486, score-0.177]
90 Visible differences predictor: an algorithm for the assessment of image fidelity. [sent-496, score-0.066]
91 Final report from the video quality experts group on the validation of objective models of video quality assessment, phase II. [sent-516, score-0.072]
92 Most apparent distortion: fullreference image quality assessment and the role of strategy. [sent-526, score-0.102]
93 The effects of a visual fidelity criterion of the encoding of images. [sent-540, score-0.145]
94 TID2008-a database for evaluation offull-reference visual quality assessment metrics. [sent-564, score-0.102]
95 An information fidelity criterion for image quality assessment using natural scene statistics. [sent-588, score-0.247]
96 Image quality assessment: From error visibility to structural similarity. [sent-631, score-0.111]
97 Maximum differentiation (mad) competition: A methodology for comparing computational models of perceptual quantities. [sent-637, score-0.149]
98 Patch-based probabilistic image quality assessment for face selection and improved video-based face recognition. [sent-646, score-0.102]
99 An image quality assessment metric based on non-shift edge. [sent-651, score-0.12]
100 Non-shift edge based ratio (nser): An image quality assessment metric based on early vision features. [sent-672, score-0.12]
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