Fuzzy Clustering and Genetic Algorithms - Biomedical Signal Analysis: Contemporary Methods and Applications - page 251

Tabl e 7 . 3
Approximation of the size of the search space, assuming independent subregions
[103].

Size No. of Regions No. of Combinations Search Space

256 × 256 2 65536

> 10 19728

1

2 16364 10 4932

128 × 128 4 > 4 ·

2 4096 > 10 1234

64 × 64 16

2 1024 > 10 310

32 × 32 64

2 256 > 10 79

16 × 16 256

2 64 > 10 22

8 × 8 1024

2 16 > 10 8

4 × 4 40960

the binary edge image and the original one.
The search and solution space for the edge-detection problem is huge
as shown in table 7.3. The table shows, for different image sizes, the
number of combinations and the corresponding search space. In order
to reduce the sample space and simplify the optimization problem, the
original image has to be split into linked regions.
It has been shown in [103] that the GA for edge detection works best
for regions sized 4 4 and larger. Thus, for each subregion we have a

single independent GA which tries to optimize the edge configuration
within the subregion.
Pratt's figure of merit [211] provides a quantitative comparison of
the results of different edge detectors by measuring the deviation of the
output edge from a known ideal edge:

×

I A

1
max ( I A , I I )

1
1+ αd 2 ( i )

P = (7.94)

i=1

with I A being the number of detected edge points, I I the edge points in
the ideal image, α a scaling factor, and d ( i ) the distance of the detected
edge pixel from the nearest ideal edge position. Thus, Pratt's figure of
merit represents a rough indicator of edge quality in the sense that a
higher value denotes a better edge image.
The results shown in [103] demonstrate that GA improved Pratt's
figure of merit from 0.77 to 0.85 for ideal images and detected most of
the basic edge features (thin, continuous, and well-localized) for MR,
CT, and US images.