Page 134 - 2023-Vol19-Issue2

130 | Al-Furaiji, Tsviatkou & Sadiq

TABLE I.
AVERAGE COMPRESSION RATIOS OF IMAGE BIT PLANES FOR THE RLE CODER

Bit planes Partial and full compression ratios of bit planes of images

7 (15) Grayscale satellite Grayscale portrait Grayscale medical Landscape thermal Differences of spectral channels
6 (14) 1.74466
5 (13) 1.12429 1.56655 10.47579 1.17699 18318.4105 (1.4104)
4 (12) 0.63831
3 (11) 0.42969 0.86344 3.50286 0.5182 18318.8455(50909.6075)
2 (10) 0.39203
1 (9) 0.40096 0.6439 2.12782 0.34866 1157.6183(50909.6075)
0 (8) 0.39986
All 0.40006 0.43127 1.10178 0.36688 1.1011 (50909.6075)
0.51390
0.40328 0.74446 0.33853 0.2947 (50909.6075)

0.48656 0.50431 0.33297 0.2553 (50909.6075)

0.50185 0.38566 0.36361 0.2450(45954.3425)

0.44505 0.33411 0.38925 0.2494(36585.6001)

0.52599 0.73092 0.40438 0.81049

TABLE II.
AVERAGE COMPRESSION RATIOS OF IMAGE BIT PLANES FOR THE ARITHMETIC CODER

Bit planes Partial (full) compression ratios high/low of bit planes of images
(high/low)
7/6–0 Grayscale satellite Grayscale portrait Grayscale medical Landscape thermal
7–6/5–0
7–5/4–0 25.7676/1.0804 (1.2272) 13.0135/1.2382 (1.3941) 13.0135/1.6706 (1.8720) 27.4541/1.1168 (1.2689)
7–4/3–0
7–3/2–0 3.5595/1.0246 (1.2150) 2.2076/1.1635 (1.2982) 6.39613/1.5153 (1.8473) 2.8637/1.0581 (1.2550)
7–2/1–0
7–1/0 3.0243/1.0015 (1.3113) 1.9414/1.1058 (1.2886) 3.9399/1.3923 (1.7935) 2.2112/1.0244 (1.2816)

2.2277/0.9912 (1.3543) 1.7919/1.0650 (1.3209) 3.2933/1.2982 (1.8250) 1.9459/1.0045 (1.3239)

1.8680/0.9870 (1.3905) 1.6408/1.0244 (1.3295) 2.8619/1.2243 (1.8878) 1.7454/0.9925 (1.3578)

1.6625/0.9806 (1.4111) 1.5466/1.0208 (1.3577) 2.5539/1.1666 (1.9586) 1.5976/0.9827 (1.3810)

1.5246/0.9621 (1.4186) 1.4963/0.9358 (1.3821) 2.3217/1.0958 (2.0332) 1.4915/0.9649 (1.3958)

Encoding test images in their entirety (without splitting RY X (6)
into bit planes) using the RLE coder does not result in com- CRRLE (R) = ?Rr=-01 ? fRLE (B (r))?
pression (? fRLE (I (R))? = RY X).
RY X
The arithmetic coder is applied separately for higher CRAC (R) = ? fAC (IC (rHL, rHH ))? + ? fAC (IC (rLL, rLH ))? (7)
( fAC (iC (rHL, rHH , y, x))) and lower ( fAC (iC (rLL, rLH , y, x))) bit
planes (rHH > rHL, rLH = rHL - 1, rLH > rLL, rLL = 0), where Table I shows that the RLE coder allows compressing
fAC is the function of arithmetic coding. Partial compression the two highest (r = 7, 6) medical bit-planes and one high
ratios are calculated using expressions (4) and (5). (r = 7) bit-plane of portrait 8-bit grayscale images, as well as
9–11 high-order bit planes, starting from 14-th, of the differ-
CRAC (rHL, rHH ) = (rHH - rHL + 1)Y X / ? fAC (IC (rHL, rHH ))? ences of the spectral channels of HSI. For the remaining bit
(4) planes will not be used in compression. Moreover, even in the
case of compression, the RLE coder is inferior in efficiency
CRAC (rLL, rLH ) = (rLH - rLL + 1)Y X / ? fAC (IC (rLL, rLH ))? to the arithmetic coder on all types of images (CR RLE (r) >
(5) 1,CRRLE (r) < CRAC (rHL, rHH ) , CRRLE (r) < CRAC (rLL, rLH )),
except for the differences in the HSI channels, which is as-
The bit plane 15 of the differences of the HSI spectral sociated with a high probability of zeros in their higher bit
channels contains the codes of the signs of the values of the planes.
differences: 0 – plus, 1 – minus and is encoded separately
( fAC (B (15))). Tables (I, II, and III) also show the full com- The use of an arithmetic coder for the lower bit-plane of 8-
pression ratios CRRLE (R) and CRAC (R) of all bit-planes of bit grayscale images (? fAC (IC (0, 0))? > Y X ? CRAC (0, 0) < 1)
the images, taking into account the volume of codes of indi- and 2 lower bit planes of 16-bit differences of the HSI chan-
vidual bit-planes and their combinations, which are calculated nels (? fAC (IC (0, 1))? > 2Y X ? CRAC (0, 1) < 1), is usually
using expressions (6) and (7).