> technique. 
base colors. 
he encoded 
| JPEG. We 
onclusion is 
articular for 
age, the Y 
ince of the 
'dges in the 
nage while 
: gmentation 
t appears as 
> undesired 
(Wang and 
s: 
ce, of each 
ie sharpness 
nto contour 
s the image 
ind smooth. 
camines the 
ring pixels 
region. The 
e criteria to 
's the image 
n ratio, the 
nformation. 
> number of 
f the small 
ons. 
using chain 
of the first 
. Then the 
transmitted 
e chain is 
er than the 
¢ assumes 8 
  
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
adjacent neighbours, i.e., allowing 8 possible directions from 
each pixel. Once a complete chain (region) is transmitted, the 
starting point of the next region has to be coded. Here to save 
bits, only the distance (vertically and horizontally) between the 
new starting point and the previous one are transmitted instead. 
Since the number of bits allocated to this part of the algorithm 
is significant (typically some 50% of the bit budget) it is of 
interest to consider the factors that affect this part of the coding. 
The number of bits needed to code each direction is estimated 
as follows: 
bpd = pL, (1) 
where bpd is the number of bits per direction, 
piis the frequency of each change in direction, 
L; is the length of each code word; i=0, 1, 2, ..7. 
Then, 
bsc = ceiling(log, (max _ dist)) , (2) 
where  bsc is the number of bits per each starting point, 
max dist is the maximum distance between 
consecutive two starting points of chains. 
From (1) and (2) we can calculate the number of bits per 
contour (bpc): 
= * . 3% £ 
bpc = bpd T [CN us 1) bsc Tz fsb] : (3) 
contour 
  
here Nehnain 18 the number of chains, 
Neontour 18 the number of contour points, and 
fsb is the number of bits needed to code the first 
starting point. 
Texture coding — since each region is relatively smooth, the 
color components in each region is described using a smooth 
two-dimensional polynomial function. The order of the 
polynomial function is determined according to the 
approximation error and the number of bits needed to code the 
region information. In our algorithm, we use one of the primary 
colors of the image (R,G,B) to represent the brightness. In most 
cases we select the Green, which is closely related to the gray 
level (Y) information (Goffman and Porat, 2002). 
The coefficients of each polynomial are calculated so that the 
error between the approximation and the original region is 
minimized. 
For a zero order polynomial function the coefficient is the 
average value. For a first order polynomial function the 
approximation and the error are: 
=a, +a,X, +a,X, (4) 
aprox 
705 
n 
. 
SE = >, = UX X. 
l 
where — Y, is the approximation of Y 
Xj, X» are axes of the polynomial function 
ay, az, a5, are the approximation coefficients 
SE represents the Squared Error 
The coefficients that minimize the SE are found based on 
n S S is a S y (5) 
A . 
> X S xus a li- a, 
S y Ses SS as > va, 
For a second order polynomial function the approximation is 
=a, +a,X, +a, X, +a, X} +a, X?, (6) 
aprox 
and the coefficients that minimize the SE are found using 
2 : 
7 S S ei S Sx a S 7 
= 2 2 3 2 ? ( ) 
xy Sx Sex NX NY a, a, Sun, 
2 2 3 
Ë SN ts Sx 3x Ns ges Se 
3 2 4 2.2 2 
S NS > > x a, Sal 
2 a 342 4 2 
i NS S vu S ds S 
A 
= 
MI 
ve 
Color coding - The two additional subordinate colors are 
coded using a polynomial expansion of the base color as 
follows: 
DA 
C mM PCysaCita CU Y. aC rd, (8) 
k=0 
k 
C => PC, )-hC +5 10} + +HC,+h, 
k=0 
where C. is the base color, 
C, , are the interpolated subordinate colors, 
k is the order of the polynomial expansion, and 
as b, are the coefficients of the polynomial 
expansion. 
Quantization - the coefficients of the color polynomial 
expansion and the polynomial coefficient of each region are 
quantized and transmitted to the receiver along with contour 
information. 
The decoder reverses the order of the above procedure.