無參考圖像質量評價算法(BRISQUE):No-Reference Image Quality Assessment in the Spatial Domain

paper:No-Reference Image Quality Assessment in the Spatial Domain
author:Anish Mittal etc
date:2012
code:BRISQUE

1.Introduction

作者提出的方法 Blind/Referenceless Image Spatial QUality Evaluator (BRISQUE)是基於自然圖像的統計特征(NSS,natural scene statistics)，對於失真圖像，這些特征可能會改變，據此得到了無參考圖像評價的算法。這種方法是在空間域上做的(transform free)，不像之前一些算法要轉換到小波域或者 DCT 域。

2.BRISQUE

A.Natural Scene Statistics in the Spatial Domain

對於圖像\(I(i,j)\),經正則化得到mean subtracted contrast normalized(MSCN)系數

\[\hat{I}(i,j)=\frac{I(i,j)-\mu(i,j)}{\sigma(i,j)+C} \]

其中,\(i \in 1,2,\dots,M,j\in 1,2,\dots,N\),\(M,N\)是圖像的高和寬，\(C=1\)是為了數值穩定的常數。

\[\mu(i,j)=\sum_{k=-K}^{K}\sum_{l=-L}^{L} \omega_{k,l}I_{k,l}(i,j)\\ \sigma(i,j)=\sqrt{\sum_{k=-K}^{K}\sum_{l=-L}^{L}\omega_{k,l}(I_{k,l}(i,j)-\mu(i,j))^2} \]

其中\(\omega=\{ \omega_{k,l}\vert k=-K,\dots,K,l=-L,\dots,L\}\)是高斯核。

Our hypothesis is that the MSCN coefficients have characteristic statistical properties that are changed by the presence of distortion, and that quantifying these changes will make it possible to predict the type of distortion affecting an image as well as its perceptual quality.

使用generalized Gaussian distribution(GGD)建模MSCN系數直方圖,

\[f(x;\alpha,\sigma^2)=\frac{\alpha}{2\beta \Gamma(1/\alpha)}exp(-(\frac{\vert{x}\vert}{\beta})^{\alpha}) \]

其中

\[\beta=\sigma\sqrt{\frac{\Gamma(1/\alpha)}{\Gamma(3/\alpha)}}\\ \Gamma(a)=\int_0^{\infty}t^{a-1}e^{-t}dt \quad a>0 \]

\(GGD(\alpha,\sigma^2)\)的兩個參數可以使用moment-matching based approach計算出來(詳見原論文)。擬合出的兩個參數作為兩個特征量。
另一方面，為了描述相鄰像素之間的統計關系，計算相鄰MSCN系數的pairwise products,共四個方向，水平(H),數值(V),主對角線(D1),次對角線(D2)，得到4個系數矩陣:

\[H(i,j)=\hat{I}(i,j)\hat{I}(i,j+1) \\ V(i,j)=\hat{I}(i,j)\hat{I}(i+1,j)\\ D1(i,j)=\hat{I}(i,j)\hat{I}(i+1,j+1)\\ D2(i,j)=\hat{I}(i,j)\hat{I}(i+1,j-1) \\ for \quad i\in\{1,\dots,M\} \quad and \quad j\in \{1,\dots,N\} \]

下圖顯示了自然圖像和不同失真下這4個矩陣的統計直方圖:

用asymmetric generalized Gaussian(AGGD)distribution對以上四個系數矩陣建模。

\[f(x;\nu,\sigma_l^2,\sigma_r^2)=\left\{ \begin{aligned} \frac{\nu}{(\beta_l+\beta_r)\Gamma(\frac{1}{\nu})}exp(-(\frac{-x}{\beta_l})^{\nu}) & , & x<0, \\ \frac{\nu}{(\beta_l+\beta_r)\Gamma(\frac{1}{\nu})}exp(-(\frac{x}{\beta_l})^{\nu}) & , &x\ge0. \end{aligned} \right. \]

其中

\[\beta_l=\sigma_l\sqrt{\frac{\Gamma(1/\alpha)}{\Gamma(3/\alpha)}}\\ \beta_r=\sigma_r\sqrt{\frac{\Gamma(1/\alpha)}{\Gamma(3/\alpha)}} \]

\(AGGD(\nu,\sigma_l^2,\sigma_r^2)\)的3個參數可以使用moment-matching based approach計算出來(詳見原論文)。
對於H,W,D1,D2四個矩陣，可以提取AGGD分布的參數\((\eta,\nu,\sigma_l^2,\sigma_r^2)\)作為特征，其中

\[\eta = (\beta_r-\beta_l)\frac{\Gamma(\frac{2}{\nu})}{\Gamma(\frac{1}{\nu})} \]

4x4可以得到16維特征，加上GGD提取出的2個參數，共18維特征，然后對原始圖像降分辨率(low pass filtered and downsampled by a factor 2)得到低尺度下的圖像，再仿照上面的計算出18維特征，共36維特征。
下圖顯示了自然圖像和不同失真圖像計算出的GGD和AGGD參數在空間中的分布。

B.Quality Evaluation

使用上面計算出的36維特征訓練出一個回歸分數的SVR模型，學習特征空間到質量分數的映射。

3.Experiments

結果如下