Leukocyte Detection Through an Evolutionary Method - Complex System Modelling and Control Through Intelligent Soft Computations - page 140

In symmetry-based detection (Muammar and Nixon 1989 ; Atherton and
Kerbyson 1993 ), the ellipse geometry is taken into account. The most common
elements used in ellipse geometry are the ellipse center and axis. Using these
elements and edges in the image, the ellipse parameters can be found. Ellipse
detection in digital images is commonly solved through the Hough Transform
(Fischer and Bolles 1981 ). It works by representing the geometric shape by its set of
parameters, then accumulating bins in the quantized parameter space. Peaks in the
bins provide the indication of where ellipses may be. Obviously, since the
parameters are quantized into discrete bins, the intervals of the bins directly affect
the accuracy of the results and the computational effort. Therefore, for

ne quan-
tization of the space, the algorithm returns more accurate results, while suffering
from large memory loads and expensive computation. In order to overcome such a
problem, some other researchers have proposed other ellipse detectors following the
Hough transform principles by using random sampling. In random sampling-based
approaches (Shaked et al. 1996 ; Xu et al. 1990 ), a bin represents a candidate shape
rather than a set of quantized parameters, as in the HT. However, like the HT,
random sampling approaches go through an accumulation process for the bins. The
bin with the highest score represents the best approximation of an actual ellipse in
the target image. McLaughlin

'

s work (Han et al. 1993 ) shows that a random
sampling-based approach produces improvements in accuracy and computational
complexity, as well as a reduction in the number of false positives (non existent
ellipses), when compared to the original HT and the number of its improved
variants.
As an alternative to traditional techniques, the problem of ellipse detection has
also been handled through optimization methods. In general, they have demon-
strated to give better results than those based on the HT and random sampling with
respect to accuracy and robustness (Ayala-Ramirez et al. 2006 ). Such approaches
have produced several robust ellipse detectors using different optimization algo-
rithms such as Genetic algorithms (GA) (Lutton and Martinez 1994 ; Yao et al.
2005 ) and Particle Swarm Optimization (PSO) (Cheng et al. 2009 ).
Although detection algorithms based on optimization approaches present several
advantages in comparison to traditional approaches, they have been scarcely
applied to WBC detection. One exception is the work presented by Karkavitsas and
Rangoussi, in 2005 that solves the WBC detection problem through the use of GA.
However, since the evaluation function, which assesses the quality of each solution,
considers the number of pixels contained inside of a circle with

fixed radius, the
method is prone to produce misdetections particularly for images that contained
overlapped or irregular WBC.
In this work, the WBC detection task is approached as an optimization problem
and the differential evolution algorithm is used to build the ellipsoidal approxi-
mation. Differential Evolution (DE), introduced by Storn and Price, in 1995 ,isa
novel evolutionary algorithm which is used to optimize complex continuous non-
linear functions. As a population-based algorithm, DE uses simple mutation and
crossover operators to generate new candidate solutions, and applies one-to-one
competition scheme to greedily decide whether the new candidate or its parent will