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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.