Image Compression - Bezier and Splines in Image Processing and Machine Vision - page 95

Contrast Measure
Image quality index (IQI) from equation (2.25) is used as a measure of
contrast.

M

j =1 |

N

B ij | /B

i =1

− h ij

IQI = .

MN

Texture Measure
To compare the texturedness of the reconstructed image with the original
image, we examine the fractal dimension ( FD ) of the reconstructed as well
as of the original images. In general, fractal dimension provides a measure
of irregularities and, therefore, it can be used very effectively as one of the
means to compare the texture quality of two images, provided one of them
is obtained after some operation on the other. This is because two images
having the same fractal dimension does not necessarily mean that they have
the same surface irregularities. In our case, the change in fractal dimension of
the reconstructed image from that of the original image indicates the extent
of damage in texture of the input image due to approximation. The concept
of self-similarity can be used to estimate the fractal dimension. A bounded
set A in Euclidian n-space is self-similar if A is the union of N r distinct
(non-overlapping) copies of itself scaled up or down by a ratio r . The fractal
dimension D of A is given by the relation [117] 1 = N r r D , i.e.,

log( N r )
log(1 /r ) .

D = (4.23)

There exist several approaches to estimate the FD of an image. We have used
[36] to compute the fractal dimension.
Thus, we get the fidelity vector,

F v =[ MSE,PSNR,ρ xy ,H (1) ,H (2) ,IQI,FD ] T . (4.24)

4.4 Results and Discussion

In the SLIC algorithm, subimages obtained through segmentation have been
used for gray encoding while their contour maps are encoded after remov-
ing redundancy. For each subimage, the order of the approximating Bezier-
Bernstein polynomial is computed. We have followed the IQI based approach
for order computation because of psychovisual reasons. For the Lincoln im-
age, local correction is not needed for the residual surface of any region in any
subimage, while for both Lena and Girl images, local corrections are required.
The Girl image is found to have local correction for 18 patches while the Lena
image requires local correction for 31 patches. For the Lincoln image, we have
obtained eight subimages corresponding to seven thresholds. Orders of the
polynomials for these subimages, computed by the IQI based approach, were