Image Compression - Bezier and Splines in Image Processing and Machine Vision - page 88

must be able to express the block size compatible to Hilbert image. Therefore,
the choice of the window size for extraction of texture blocks can be made
very easily. We have chosen the block size equal to 16. The number of bits for
texture coding is the total number of bits required for all the blocks, i.e., ν in
equation (4.4) is given by

N tb

ν = ν i , (4.12)

i =1

where ν i is the number of bits for the i th texture block and N tb is the total
number of texture blocks.

4.2.3 Contour Coding

Contours of segmented regions are coded using the methodologies described in
[26] and [23]. [26] uses 1-dimensional Bezier-Bernstein polynomial while [23]
uses stretched discrete circular arcs for encoding contour images. In encoding
contours of segmented regions, they are processed once again, as described
below, to remove redundancy. Regions in each of the k subimages ( k -1 being
the number of thresholds) have their own contours labeled respectively from
1to k . All these contours need not be coded because of redundancy. We
have reduced this redundancy in two stages. In the first stage, we remove the
contours of all regions in the subimage with maximum boundary or contour
length compared to those in other subimages. The reason behind this removal
is that the contours of ( k -1) subimages uniquely define the contour geometry
for the remaining subimage. In the second stage, the contour map for ( k -
1) subimages is examined to get a representation suitable for coding. Since
the regions are adjacent to each other and each region is defined by its own
boundary, we have “double contouring” in the contour map of an image. Note
that the contour of one region defines part of other adjacent regions. In order
to remove double contouring, we consider the following contour processing
scheme. The part of a contour, which is defined by contour of some other
regions, is deleted and the non-deleted contour fragments are encoded. Let us
now elaborate on it.
Removal of double contouring :
Let us first consider a particular region (say, the j th region of l th subimage)
Ω lj of a fixed label l and examine if the regions of other labels are adjacent
to Ω lj . We call the contour of Ω lj the primary contour and contours of the
adjacent regions the adjacent contours. The primary contour is first encoded.
The part of adjacent contours defined by the primary contour is then ex-
amined and deleted. Also, different parts of a higher labeled contour defined
by its adjacent lower labeled contours are deleted, provided the deleted seg-
ments are all connected. Thus, the deletion is always done by lower labeled
adjacent contours. Non-deleted contour fragments are then encoded. Lower
labeled contours are encoded first. The process is repeated until all contours
of different labels adjacent to a primary contour are examined for deletion and