Image Compression - Bezier and Splines in Image Processing and Machine Vision - page 103

larger for the size of 512 512, while from the work of [75] and [108], we see

that an increase of 4.15 times is possible. In our opinion, one can obtain a
compression ratio larger by a factor between 3.5 and 4.0 simply by increasing
the size of an image from 256

×

512. Thus, it is expected that our
developed method will provide a compression ratio in the range 38.0-43.52
for the Lena and 46.2-52.8 for the Girl image, respectively.

× 256 to 512 ×

4.5 Concluding Remarks

The algorithm, SLIC, uses a segmentation scheme that is suitable for image
compression. The segmentation scheme provides a number of similar gray re-
gions corresponding to each threshold, instead of a single region. Consequently,
a global surface fit (high possibility due to similar gray regions) becomes most
economical. When the order of a polynomial for approximating a subimage
goes beyond a preassigned positive integer, say q (which may happen due to
the physical configuration of regions or large variation on region boundaries),
we need to compute local corrections over the residual surfaces for which the
mean squared error with respect to the global surface of order q exceeds a cer-
tain limit. Computing the order of the polynomial by the IQI based approach
is simple as well as effective. A remarkable gain in compression ratio is found
when encoded in terms of surface points, with the quality of reconstructed
images almost the same as that found for reconstruction from control points.
It is seen that texture regions require the largest number of bits during their
encoding (Lena and Girl images). Examination of the quality of reconstructed
images through the fidelity vector is to quantitatively determine the fidelity
of images.
The approximation for hierarchical segmentation is different from approx-
imation of subimages for their encoding. The former examines the segmen-
tation of subimages, with the assurance that more psychovisually appealing
reconstruction can be made while the latter actually does the approximation.
The components of the fidelity vector are different objective measures that
examine different important features of images. Thus, the smaller the val-
ues of the components of the fidelity vectors of two images, the larger the
resemblance between the two images.