Abstract—Edge detection is the most popular and common
choices for cell image segmentation, in which local searching
strategies are commonly used. In spite of their computational
efficiency, traditional edge detectors, however, may either
produce discontinued edges or rely heavily on initializations. In
this paper, we propose a bacterial foraging based edge detection
(BFED) algorithm for cell image segmentation. We model the
gradients of intensities as the nutrient concentration and propel
bacteria to forage along nutrient-rich locations via mimicking
the behavior of Escherichia coli, including the chemotaxis,
swarming, reproduction, elimination and dispersal. As a nature-
inspired evolutionary technique, this algorithm can identify the
desired edges and mark them as the tracks of bacteria. We have
evaluated the proposed algorithm against the Canny, SUSAN,
Verma's and an active contour model (ACM) based edge
detectors on both synthetic and real cell images. Our results
suggest that the BFED algorithm can identify boundaries more
effectively and provide more accurate cell image segmentation.
I. INTRODUCTION
Separation of cells from background as well as separation
of nuclei from cytoplasm using microscope imaging plays an
essential role in a wide spectrum of clinical and research
settings. Due to the extensive existence of abrupt changes in
intensities at the boundary of cells or nuclei, various edge
detection methods appear to be the most popular and common
choices for this segmentation task in the literature.
Edge detection aims to mark the boundaries of objects in
an image and is a fundamental step in image analysis and
machine vision. Traditionally, edge pixels can be detected on a
pixel-by-pixel basis by using either the first-order or
second-order derivation. The Roberts, Sobel and Prewitt
operators estimate the gradient of intensities and view the
pixels with maximum gradient amplitudes as edges; whereas
the Laplacian operator estimates the second-order derivative
of intensities at each pixel and regards zero-crossings pixels as
edges [1]. These derivative-based edge detectors are simple,
but prone to be affected by noise. Marr and Hildreth [2]
combined the Gaussian filter with Laplacian operator, and
thus proposed the Laplacian of Gaussian (LoG) operator for
edge detection. Canny [3] furthered this trend and developed
*Research supported in part by the National Science Foundation of China
under Grants 61471297 and 81160183, in part by the Natural Science
Foundation of Shaanxi Province, China, under Grant 2015JM6287, in part by
the Natural Science Foundation of Ningxia Autonomous Region, China,
under Grants NZ12179 and NZ14085, and in part by the Fundamental
Research Funds for the Central Universities under Grant 3102014JSJ0006.
Y. Pan and Y. Xia are with the Shaanxi Key Lab of Speech & Image
Information Processing (SAIIP), School of Computer Science, Northwestern
Polytechnical University, Xi'an 710072, China(phone: 86-29-88491533; fax:
86-29-88431518; e-mail: yxia@nwpu.edu.cn).
T. Zhou is with the School of Science, Ningxia Medical University,
Yinchuan 750004, China.
an optimal edge detector, which incorporates both Gaussian
filters and non-maximum suppression into the derivative-
based edge detection. Recent years have witnessed the
prevalent use of non-linear filters in edge detection. Kirsch
operator [
4], for instance, uses eight templates to calculate the
response of each pixel to eight specific directions and selects
the maximum response as the output. Smallest univalue
segment assimilating nucleus (SUSAN) method [5] counts the
pixels that are similar to each center pixel in a small
neighborhood and possesses a strong ability to resist noise.
Since they use only the local information to examine if a
pixel belongs to an edge or not, these methods can only
produce discontinued edges, which have to be linked based on
the heuristic knowledge to form closed contours of objects [6].
To avoid the heuristic-guided edge linking, which is always
troublesome and less-reliable, various active contour models
(ACMs) [7] have been formulated under an energy
minimization framework based on the theory of contour
evolution and geometric flows, which can be solved by
representing the contour as the zero level set of an implicit
function defined in a higher dimension and converting the
motion of the contour as the evolution of the level set function.
In spite of their widespread applications, ACM-based methods
are largely local optimization approaches, which rely heavily
on local image information and initializations.
To search edges globally, an edge detection method has to
explore 2
M×N
possible solutions for an M × N image, which is
computationally intractable. Since edges in an image are
similar to the paths an ant colony searches for, several edge
detection methods were proposed based on the ant colony
optimization (ACO) [8-10]. Besides ACO, other nature
inspired evolutionary methods, such as the genetic algorithm
(GA) [11] and clonal selection algorithm (CSA) [12], have
also been applied to edge detection.
Recently, Passino [13] proposed the bacterial foraging
algorithm (BFA), which is a novel evolutionary optimization
technique inspired by the behavior of Escherichia coli. BFA
searches the optimum through moving a population of bacteria,
each of which encodes a potential solution as its location,
where the nutrient concentration is calculated by
evaluating the objective function at the given solution. Then,
each solution is iteratively evolved towards the global
optimum through mimicking the bacterium's foraging
behavior, i.e. reaching the eutrophication position via
chemotaxis, swarming, reproduction and dispersal. The BFA
terminates when either the desired solution or preset
maximum iteration number is reached. Due to its parallel and
stochastic searching strategy and the ability to jump out of
local optima, BFA has found abundant successful applications,
such as image enhancement [14], registration [15] and edge
detection [16]. However, the BFA-based edge detection
Bacterial Foraging Based Edge Detection for Cell Image