Image Segmentation - Bezier and Splines in Image Processing and Machine Vision - page 54

the regions separately for their gray information. This is an important rea-
son, responsible for providing advantage to image compression. However, the
graylevel distribution over some of the image surface patches may be such
that the global approximation is not adequate for them. One can call such
patches, under a given threshold, busy patches. To overcome this diculty, a
lower order (compared to that of the global approximation) polynomial func-
tion can be used for local approximation of each of the residual surface patches
in the subimage. Therefore, a subimage can be reconstructed using the global
surface, along with the local residual surfaces for the busy patches if they are
really present. Such a hybrid approximation scheme helps to improve the com-
pression ratio. Note that exactly the same kind of approximation is used to
guide the segmentation process, which ensures that the extracted subimages
can be modeled by low order polynomials resulting in better compression.
To more clearly visualize the advantage of the algorithm to image com-
pression, one can consider the following example.
Suppose in a threshold band limited subimage F ( x, y )wehave N surface
patches, then for the local quadratic approximation one requires 6 N coe-
cients. On the other hand, if we have the global quadratic approximation of
the subimage and local planar approximation of the residual surface patches,
the total number of coecients is 3 N + 6. For an improvement in compression
ratio of the global-local approximation over the conventional local approxi-
mation, we must have 6 N> 3 N + 6, i.e., N> 2. This implies a positive gain
in storage if the subimage has more than two surface patches, which is usually
the case. Thus, it is evident that for polynomial approximation, we need fewer
numbers of bits for any segmentation based lossy image compression technique
where regions or patches are approximated separately. Compression factor, as
a result, would improve (assuming the same contour coding scheme as in the
concerned method).
2.8 Concluding Remarks
It is always desirable to break up an image into different regions. Later on,
these regions can be processed either separately or collectively. We must al-
ways keep in mind that segmentation should fulfill our purpose. One segmen-
tation technique may be found to be very good in one application while it may
be completely unsuitable for the other. However, a knowledge based segmen-
tation is expected to yield semantically meaningful regions, which can find
many new applications in a wider scale. Such segmentation can be viewed as
an intelligent segmentation.