Image Segmentation - Bezier and Splines in Image Processing and Machine Vision - page 35

always produce disconnected edges. For background reading in this area, read-
ers can consult [33, 97, 98, 152], whereas a broad over-view of segmentation
can be found in [68, 133, 144].
To get compact homogeneous regions (or patches), we describe a segmen-
tation method that recursively uses an object/background thresholding algo-
rithm [130]. Unlike the region growing [133] or adaptive region growing [97]
technique, it provides a number of compact regions of similar graylevels for
a given threshold. We call this collection of regions for a given threshold a
subimage . This segmentation method produces a number of subimages de-
pending on the number of computed thresholds. Then it merges small regions
depending on a criterion, and uses some quantitative indices for objective
evaluation of the segmented regions.
2.4 Extraction of Compact Homogeneous Regions
Segmentation is objective oriented. Assume for illustration purposes, that we
are using segmentation for image compression. We can think of a compression
scheme that is based on modeling compact homogeneous regions or patches
using Bezier-Bernstein polynomial function. Given an image, we therefore first
try to extract from it the homogeneous subimages. There are many approaches
[173, 65, 74] to achieve this goal. For example, it can be based on pixel level
decision making such as iterative pixel modification, region growing, or adap-
tive region growing, or it can be based on multilevel thresholding. Each of
these categories of algorithms, except multilevel thresholding, produces one
region of similar graylevels at a time and, therefore, it forces local approxi-
mation for a region. Such methods may be called local thresholding schemes
as a decision is made at the pixel level. It does not provide any information
about other regions of similar gray values. Hence, from the standpoint of com-
pression, segmentation algorithms based on local region growing are not very
attractive. On the other hand, global thresholding based segmentation algo-
rithms, (where the entire image is partitioned by one or a few thresholds),
such as multilevel thresholding algorithms [174, 58, 35], depend on the num-
ber of local minima in the one or two dimensional histogram of gray values
in the image. The extraction of these minima from the histogram information
sometimes may not be very reliable, because all desirable thresholds may not
be reflected as deep valleys in the histogram. Also, the detection of thresholds
is influenced by all pixels in the image.
Several authors [1, 87, 131, 132, 135, 136] have used entropy as the criterion
for object/background classification. All methods described in [87, 135, 136]
use only the entropy of the histogram, while the methods in [1, 131, 132] use
the spatial distribution of gray levels, i.e., the higher order entropy of the
image. For the set of images reported in [130], authors found that conditional
entropy of the objects and background based on Poisson distribution produced
better results compared to the methods in [135, 136, 87, 91]. All these methods