Image Compression - Bezier and Splines in Image Processing and Machine Vision - page 97

reconstruction 1 and reconstruction 2, while the number of bits, γ 64 × 64 for
contour encoding, can be computed using the equation (4.16). The Lincoln
image was found to have 442 contour pixels on line segments and 348 contour
pixels on arc segments. Nine status words, each 9 bits long, provided region
adjacency information during decoding of the Lincoln image, and the number
of starting pixels was found to be 38. So, the overhead due to contour encod-
ing is 9 38 bits or 537 bits. For gray encoding, the overhead due

to order of approximation from equation (4.3) is β =8

∗ 9+12 ∗

2 = 16 bits (since,
β c = 0). The number of coecients for approximation of Lincoln image is
64. Thus, we get the total bit requirements and compression ratio as shown
in Table 4.1. From Table 4.1, it is seen that for reconstruction 2, the gain

∗

Table 4.1. Bit requirements.

Image β gr γ 64 X 64 Total no. of bits C.R C.R

Recon. 1 Recon. 2 from eq.(4 . 16) Recon. 1 Recon. 2 1 2

from eq.(4 . 3) from eq.(4 . 8)

Lincoln 784 336 1537.56 2321.56 1873.56 8.82 10.93

in compression ratio is higher than that for reconstruction 1 by roughly 25
percent. One can notice the total number of bits for contour coding is not an
integer. This is because we computed an average estimate for them instead of
actual number of bits. Hence the total number of bits is also not an integer.
For the quality of reconstructed images, we consider the following tables for
different values of the components of the fidelity vectors. From the evaluation

Table 4.2. Evaluation of reconstructed image.
Components of F v

Lincoln image
Input Approach 1

recons. 1 recons. 2

MSE 0 7.438 7.884

PSNR ∞ 21.388 21.135

ρxy 1.0 0.958 0.958

H (1)

3.432 2.693 2.646

H (2) 0.1005 0.144 0.054

IQI 6959.24 6973.53 6985.07

FD 2.577 2.547 2.555

Table 4.2, it is clear that the coecient based reconstructions for the two dif-
ferent approaches are very close to each other, though the PSNR value when
the contours are encoded and reconstructed by 1-d B-B polynomial is slightly