图像质量评估算法
MAD(Mean Absolute Difference):平均绝对差值
SAD(Sum of Absolute Difference):绝对误差和
SATD(Sum of Absolute Transformed Difference):哈达玛变换算法
SSD(Sum of Squared Difference):差值平方和
MSD(Mean Squared Difference):平均平方误差
SSIM(Structural Similarity Index):结构相似性
MS-SSIM(Multi-Scale-Structural Similarity Index):多层级结构相似性
MAD
D = 1 W ∗ H ∑ x = 1 W ∑ y = 1 H ∣ S ( x , y ) − T ( x , y ) ∣ D = \frac{1}{W*H}\sum_{x=1}^{W}\sum_{y=1}^{H}|S(x,y)-T(x,y)| D=W∗H1x=1∑Wy=1∑H∣S(x,y)−T(x,y)∣
S(x,y)S(x,y) 表示原始图像在坐标(x,y)(x,y)的像素值,T(x,y)T(x,y)为待评价图像在坐标(x,y)(x,y)的像素值。WW代表图像宽度,HH代表图像高度。DD代表待评估图像与原始图像质量区别(或称失真度),越小越好。
SAD
D = ∑ x = 1 W ∑ y = 1 H ∣ S ( x , y ) − T ( x , y ) ∣ D = \sum_{x=1}^{W}\sum_{y=1}^{H}|S(x,y)-T(x,y)| D=x=1∑Wy=1∑H∣S(x,y)−T(x,y)∣
变量意义同MAD.
SATD
SAD是两幅图像差值的绝对值的和,SATD为两幅图像差值进行哈达玛变化后系数的绝对值的和。
SSD
D = ∑ x = 1 W ∑ y = 1 H ∣ S ( x , y ) − T ( x , y ) ∣ 2 D = \sum_{x=1}^{W}\sum_{y=1}^{H}|S(x,y)-T(x,y)|^2 D=x=1∑Wy=1∑H∣S(x,y)−T(x,y)∣2
变量意义同MAD.
MSD
D = 1 W ∗ H ∑ x = 1 W ∑ y = 1 H ∣ S ( x , y ) − T ( x , y ) ∣ 2 D = \frac{1}{W*H}\sum_{x=1}^{W}\sum_{y=1}^{H}|S(x,y)-T(x,y)|^2 D=W∗H1x=1∑Wy=1∑H∣S(x,y)−T(x,y)∣2
变量意义同MAD。
SSIM结构相似性
首先计算图像均指
u X = 1 R ∗ C ∑ i = 1 R ∑ j = 1 C X ( i , j ) u_X = \frac{1}{R*C}\sum_{i=1}^{R}\sum_{j=1}^{C}X(i,j) uX=R∗C1i=1∑Rj=1∑CX(i,j)
u Y = 1 R ∗ C ∑ i = 1 R ∑ j = 1 C Y ( i , j ) u_Y = \frac{1}{R*C}\sum_{i=1}^{R}\sum_{j=1}^{C}Y(i,j) uY=R∗C1i=1∑Rj=1∑CY(i,j)
计算图像的方差
σ X 2 = 1 R ∗ C − 1 ∑ i = 1 R ∑ j = 1 C ( X ( i , j ) − u X ) \sigma^2_X = \frac{1}{R*C-1}\sum_{i=1}^{R}\sum_{j=1}^{C}(X(i,j)-u_X) σX2=R∗C−11i=1∑Rj=1∑C(X(i,j)−uX)
σ Y 2 = 1 R ∗ C − 1 ∑ i = 1 R ∑ j = 1 C ( Y ( i , j ) − u Y ) \sigma^2_Y = \frac{1}{R*C-1}\sum_{i=1}^{R}\sum_{j=1}^{C}(Y(i,j)-u_Y) σY2=R∗C−11i=1∑Rj=1∑C(Y(i,j)−uY)
σ X = σ X 2 \sigma_X = \sqrt{\sigma^2_X} σX=σX2
σ Y = σ Y 2 \sigma_Y = \sqrt{\sigma^2_Y} σY=σY2
计算图像的协方差
σ X Y = 1 R ∗ C − 1 ∑ i = 1 R ∑ j = 1 C ( X ( i , j ) − u X ) \sigma_{XY} = \frac{1}{R*C-1}\sum_{i=1}^{R}\sum_{j=1}^{C}(X(i,j)-u_X) σXY=R∗C−11i=1∑Rj=1∑C(X(i,j)−uX)
计算中间方程组
L ( X , Y ) = 2 u X u Y + C 1 u X 2 + u Y 2 + C 1 L(X,Y) = \frac{2u_Xu_Y + C_1}{u_X^2 + u_Y^2 + C_1} L(X,Y)=uX2+uY2+C12uXuY+C1
C ( X , Y ) = 2 σ X σ Y + C 2 σ X 2 + σ Y 2 + C 2 C(X,Y) = \frac{2\sigma_X\sigma_Y + C_2}{\sigma_X^2 + \sigma_Y^2 + C_2} C(X,Y)=σX2+σY2+C22σXσY+C2
S ( X , Y ) = σ X Y + C 3 σ X σ Y + C 3 S(X,Y) = \frac{\sigma_{XY}+C_3}{\sigma_X\sigma_Y + C_3} S(X,Y)=σXσY+C3σXY+C3
其中L(X,Y)是亮度对比因子,C(X,Y)是对比度因子,S(X,Y)是结构对比因子。
计算SSIM:
S S I M ( X , Y ) = L ( X , Y ) × C ( X , Y ) × S ( X , Y ) SSIM(X,Y)=L(X,Y)×C(X,Y)×S(X,Y) SSIM(X,Y)=L(X,Y)×C(X,Y)×S(X,Y)
当设定C3=C2∖2公式可以简写为如下形式:
S S I M ( X , Y ) = ( 2 u X u Y + C 1 ) ( 2 σ X Y + C 2 ) ( u X 2 + u Y 2 + C 1 ) ( σ X 2 + σ Y 2 + C 2 ) SSIM(X,Y) = \frac{(2u_Xu_Y + C_1)(2\sigma_{XY}+C_2)}{(u_X^2 + u_Y^2 + C_1)(\sigma_X^2 + \sigma_Y^2 + C_2)} SSIM(X,Y)=(uX2+uY2+C1)(σX2+σY2+C2)(2uXuY+C1)(2σXY+C2)
MS-SSIM多层级结构相似性
宽高以\(2_{M-1}\)为因子进行缩小。当M=1时,表示原始图像大小;当M=2时,表示原始图像缩小一半,以此类推。
S S I M ( X , Y ) = [ L M ( X , Y ) ] α M ∑ J = 1 M [ C J ( X , Y ) ] β j [ S J ( X , Y ) ] γ j SSIM(X,Y) = [L_M(X,Y)]^{\alpha M}\sum_{J=1}{M}[C_J(X,Y)]^{\beta_j}[S_J(X,Y)]^{\gamma_j} SSIM(X,Y)=[LM(X,Y)]αMJ=1∑M[CJ(X,Y)]βj[SJ(X,Y)]γj