Image Compression - Bezier and Splines in Image Processing and Machine Vision - page 99

image are, respectively 7398 and 3538. The number of bits for starting pixels
were found to be 5328 for 333 pixels while 600 bits were required for status
words. Graylevel values altogether needed 111 coecients for global approxi-
mation and 124 coecients for local corrections. An overhead of 198 bits were
required for graylevel approximation. Figures 4.5(a), 4.5(b), and 4.5(c) show
the reconstructed Lena images for the input image as shown in Figure 1.1(a).
For the Girl image (Figure 4.6(a)), the number of pixels approximated by line
and arc segments were 6041 and 4016, respectively. 4720 bits were required for
the starting pixels, while 912 bits were required for the status words. For the
local corrections of 18 patches, 72 coecients or 576 bits were required. The
reconstructed images due to two different approaches are shown in Figures
4.6(b), 4.6(c), and 4.6(d), respectively.
To examine the performance of the proposed algorithm on a 256 256

image, we examined the compression ratio as well as compared the result with
that of JPEG algorithm [169]. Note that due to different versions of JPEG
algorithm, results may slightly vary. In order to compute the compression
ratio by the JPEG algorithm, we chose the quality factor in such a way that
the PSNR value of the decompressed images remains as close as possible to
that of the reconstructed images due to our proposed algorithm. For the Lena
image, the quality factors are 50 and 30, respectively, for the JPEG result 1
and JPEG result 2 (Figures 4.5(b) and (c)); for the Girl image, the quality
factors are 32 and 30 (Figures 4.6(c) and 4.6(d)).

×

Table 4.3. Bit requirements.

Image β gr ν γ 256 X 256 Total no. of bits

from eqn.(4 . 8) from eqn.(4 . 12) from eqn.(4 . 17)

Lena 2238 26122 19820.02 48180.02

Girl 1742 20123 17866.14 39731.14

Table 4.4. Comparison of compression ratio.

Image compression ratio

Approach 1 JPEG result 1 JPEG result 2

Lena 10.88 8.86 10.92

Girl 13.20 13.12 13.63

In order to evaluate the quality of the reconstructed images, we present
below the values of the different indices of the fidelity vector F v . To compare
the performance of our method we used the JPEG algorithm. Table 4.5 shows