Methods

1. Liu et al’s (1997) BMR (blocking-to-masking ratio) measure can be divided into 4 steps:

1) Evaluating the block difference

Let S(i,j,n,m) refers to pixel value at (n,m) (0<=n,m<8) of block(i,j), then blocking degree in the left boundary is

2) Including the perceptual effects

where is the threshold of the just-noticeable-difference (JND), which can be derived from contrast sensitivity models. Scaling factor 50 is used to adjust the range. If is less than , this blocking artifact will be invisible. Hence, BMR(i,j)=0.

3) Separating the blocking and blurring measure

Let OBMR(i,j) be the BMR in the original image, PBMR(i,j) the BMR in the processed image. We will have two sets:

a). PBMR(i,j) > OBMR(i,j). It means the blocking effects in processed image is larger than that of the original image.

b). PBMR(i,j) <= OBMR(I,j). It indicates processed image is blurred.

blocking strength = mean(|OBMR(i,j)-PBMR(i,j)|) for set a)

blurring strength = mean(|OBMR(i,j)-PBMR(i,j)|) for set b)

4) Step 4: Constructing the single BMR

BMR= blocking strength + blurring strength

BMR is an indicator for the whole image perceived quality

The separating of artifact into blocking strength and blurring strength is superior to MSE. Actually, a simple test proves that the blurring and blocking strength do go in the right direction. Left figure shows how the blocking strength decreases with lower JPEG compression ratio (higher quality). Right figure shows the blurring strength increases with larger and larger smooth filter size.

Figure 1: JPEG images at different quality level Figure 2: Blurred JPEG images with different filter size

2. Eskicioglu’s EOBD (1995):

with

3. RMSE (root-mean-square-error)

4. The metrics that I propose here is based on the subjective experiment. RMSE is pixel-based metrics while BMR is block-based that’s why both of they didn’t perform quite well in subjective experiments. The combination of these two should be able to do a better job.

Mix = RMSE + BMR;

5. Chou et al’s de-blocking algorithm (1998).

This algorithm is not an image quality metrics. What makes it attractive is that the author claims it performs equally well for removing blocking artifacts as other much more complicated algorithms. I include it here because I want to evaluate it in the subjective experiments. It takes following steps to remove blocking artifacts.

a) Set a threshold for distinguishing artificial edges.

b) Form a difference d=x-y across the block boundary.

c) If d<=t, the replace x and y with x’=x-a*d and y’=y+a*d respectively.

d) Else replace x and y with x’=x-a*t and y’=y+a*t respectively.