Graphics Reference
In-Depth Information
We classify the quality assessment indices into two categories: (say) x and
y. The classification is based on mathematical and physical features. The in-
dices based on mathematical features take care of accuracy in approximation
while the indices based on physical features take care of the preservation of
physical features present in the reconstructed image. In x, we compute indices
taking into account both the images (input and reconstructed) together. MSE
and PSNR are in this category. Image correlation between the input and re-
constructed images is also included in the category of x. In y, we compute
various indices, each characterizing a different image attribute such as homo-
geneity, contrast, and fractal dimension for the two images separately. The
above indices are all concerned with pixel intensities of the image.
A good quality reconstructed image should preserve all these components
in the fidelity vector of the input image. Thus, the closeness between two such
fidelity vectors for the input and reconstructed images indicates the closeness
between them.
Different components of the fidelity vector F v are given below.
MSE
The mean squared error
T otal squared error
Number of data points .
MSE =
(4.18)
PSNR
The normal procedure to evaluate the image quality is to compute the peak
signal to noise ratio (PSNR) value of the original as well as of the reconstructed
image. PSNR value is defined as
1) 2
MSE
( L
PSNR ( dB ) = 10 log 10
.
(4.19)
Correlation
The coecient of correlation ρ xy for two sets of data X =
{
x 1 ,x 2 ,
···
,x N }
and Y =
{
y 1 ,y 2 ,
···
,y N }
is given by
N
1
N
x i y i
xy
i =1
ρ xy =
x 2
,
(4.20)
N
N
x i 2
y i 2
y 2
1
N
1
N
i =1
i =1
N
N
1
N
1
N
where x =
x i and y =
y i . The correlation coecient ρ xy takes
i =1
i =1
on values from +1 to -1, depending on the type and extent of correlation
between the sets of data. We use correlation measure between the input and
reconstructed image. This provides a measure of nearness of two images.
 
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