Image Compression - Bezier and Splines in Image Processing and Machine Vision - page 81

Bezier-Bernstein polynomial, contours by 1-d Bezier-Bernstein polynomial,
and texture by Huffman coding scheme using Hilbert scan on texture blocks.

4.2 SLIC: Subimage-based Lossy Image Compression

In the approximate coding of digital still images, one is mainly concerned
with the compression ratio and the fidelity of the reconstructed images. We
show how compression can be made by globally approximating many seg-
mented patches by a single polynomial function together with local correc-
tion, if needed. For this, all such patches should have similar graylevels, and
one can extract the segmented patches under approximation by a single poly-
nomial using a single threshold. Such segmented patches can be viewed as
different surface patches of almost similar gray values, and the collection of all
such patches under a single threshold is defined as a subimage. The segmenta-
tion scheme [24] recursively uses an object/background thresholding algorithm
based on conditional entropy. Thresholding based segmentation strategy pro-
vides an advantage over that done by the split and merge technique [133]. The
latter does not provide any group of patches or regions of similar graylevels at
a time. It is, therefore, preferable to choose a thresholding based segmentation
strategy for coding application. However, the graylevel distribution over some
of the image surface patches may be such that the global approximation is
not adequate for them. We call such patches, under a given threshold, busy
patches. To overcome this diculty under such circumstances, a lower order
(compared to that of the global approximation) polynomial function is used
for local approximation of each of the residual surface patches in the subim-
age. Therefore, the subimage is 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 compression ratio.
Note that this is exactly the same kind of approximation one can use during
segmentation of an image [24]. Thus, compression can use necessary infor-
mation of approximation from the segmentation of images. Contours can be
coded by line and arc segments. Sometimes very small regions are found in
images in the form of a texture, and region contours are found to fluctuate
very rapidly so that a large number of knots or key pixels is required on con-
tours for approximation. Under such conditions, encoding of contours by line
and arc segments is not economical. Such regions can be separated out in
the form of blocks from images, if they are really present. These blocks are
then suitably encoded. Figure 4.1 shows the 8-bit Lena image of size 256

×
256 and its segmentation without and with texture regions. Contour images
for some hierarchical thresholds are shown in Figure 4.2. In Figure 4.1(b),
all the gray values in thresholded regions are replaced by the corresponding
threshold value. This approach is simple and straightforward, and displays
the segmented image noticeably well, provided the difference of gray values at
respective pixel positions between the two images is adequate to be visually