Image Compression - Bezier and Splines in Image Processing and Machine Vision - page 92

a line segment is small enough to maintain high accuracy of the curvature of
contour lines. Here, we encode straightaway the absolute difference ( x d ,y d )
between the start and end points of the line segment. Thus, we need the
following bits for images of two different sizes.

64 × 64 image 256 × 256 image

identity (line or arc): 1 bit. identity (line or arc): 1 bit.
x d : 3 bits; x d : 3 bits;
y d : 3 bits; y d : 3 bits;
quadrant information: 2 bits; quadrant information: 2 bits;
This gives a total of 9 bits, i.e., a maximum of (9/4) or 2.25 bits/pixel
and a minimum of (9/8) or 1.125 bits/pixel. One can also find the number of
bits for line segments of all possible lengths. Here, the number of types of line
segments of different lengths is 8-4+1=5. The total number of pixels for these
types of line segments is 4+5+6+

+8=5/2(8+4)=30. Considering all such
types of line segments are equally probable, we have an average of 5

···

∗ 9/30 bits

or 1.5 bits for a contour pixel on line segments.
Starting pixels
For a 64

256 image, 16
bits per starting pixel. Therefore, the number of bits for contour pixels can
be computed using the following equations:

× 64 image, we consider 12 bits and for a 256 ×

γ 64 × 64 = N bp +12 N sp +0 . 97 N ca +1 . 5 N cl (4.16)

γ 256 × 256 = N bp +16 N sp +0 . 79 N ca +1 . 5 N cl (4.17)
where N sp is the number of starting pixels on contours. The number of contour
pixels on arc and line segments are represented respectively by N ca and N cl .

4.3 Quantitative Assessment for Reconstructed Images

In order to check the quality of the reconstructed images, most of the authors
compute the mean squared error (MSE), although it is clear that MSE does
not always reflect the quality of visual images. A reconstructed image with
low MSE may psychovisually appear to be distorted compared to another one
with high MSE. For this reason, many authors have felt the need of some
other measures for the image quality assessment. Since the mechanism of un-
derstanding image quality is not yet fully known, it is very hard to devise a
perfectly complete quantitative measure for quality judgment. But one can
always consider a measure that depends on some important attributes (de-
pending on local and global properties) present in the input image. We have,
therefore, proposed in our investigation, a fidelity vector F v whose components
are indices of different measures. Here, in addition to MSE and PSNR, we use
image correlation, homogeneity, contrast, and fractal dimension to assess the
quality of the reconstructed image.