Image Compression - Bezier and Splines in Image Processing and Machine Vision - page 89

encoded. Note that the same primary contour may be considered more than
once to examine and encode all adjacent contours, but the primary contour
is to be encoded only once. This happens if a primary contour has more than
one adjacent contour of the same label. All other primary contours having the
same label are then sequentially considered. The entire process is repeated
for regions of different labels. To explain the contour processing scheme more
clearly, we consider a ( k + 1) bit status word W s = X s ,X 1 X 2 ··· X k . It indi-

cates the status of the primary and adjacent contours. The first bit, X s in W s ,
always shows the status of the primary contour. X s = 1 indicates that the
primary contour is to be encoded along with adjacent contours but X s =0
indicates the primary contour is already encoded and only the adjacent con-
tours need to be examined and encoded. The position of the first non-zero bit
in X 1 X 2 ··· X k denotes the label of the primary contour. For example, con-

sider W s =1 , 111101101. According to the status word, the primary contour
has label 1 and adjacent contours have labels 2, 3, 4, 6, 7, and 9. Further,
the adjacent contours with labels 2, 3, 4, 6, 7, and 9 must have some part
of their contours defined by the primary contour. The defined part must be
deleted in each case. Since X s = 1, the primary contour must also be encoded.
Similarly, W s =0 , 101100101 indicates that the primary contour has label
1. The primary contour must not be encoded because it has the status word
X s = 0. Contours with labels 3, 4, 7, and 9 are to be examined for deletion
and encoded if required. Note that we consider, sequentially, all the primary
contours of a fixed label. As a result, when we move on to a primary contour
of label k , all the bits in W s from2to( k

1) are zeros. Therefore, if N p is
the number of primary contours, the number of bits N bp , required to preserve
the region adjacency information, is given by

−

N bp =( k +1) N p . (4.13)

Encoding of primary and adjacent contours using 1-d
Bezier-Bernstein polynomial :
Key pixels are detected on the primary contour as well as on the non-
deleted contour fragments to serve as knots. Key pixels are basically points
of high curvature and inflexion points. The key pixels on contours are such
that an arc between any two key pixels always remains confined within a right
triangle, with its base as the line joining the two key pixels. As a result, be-
tween two consecutive key pixels, contour fragments are decomposed either
into straight line or arc segments [26, 27]. Each of the arcs is approximated by
a1-dBezier-Bernstein polynomial and so can be viewed as a Bezier-Bernstein
arc. We consider the parametric representation of arcs because it is axis inde-
pendent. Given the starting point, each line segment requires one point while
an arc needs two points for their description. Since the selection of key pix-
els depend on high curvature, any segment with rapid changes of curvature
will have more number of key points (dense) than a segment with less curva-
ture change. Note that line and arc segments between knots, therefore, are of
variable sizes. Obviously, the line and arc segments between key pixels have