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Upload PDF. Follow this author. New articles by this author. New citations to this author. New articles related to this author's research. Email address for updates. It also implies a high computational time complexity decreasing its processing speed. Also, the method is not resistant to noise thereby resulting in even lower accuracy Atherton and Kerbyson To overcome such a problem, some other approaches based on the Hough transform, for instance the probabilistic Hough transform Fischler and Bolles ; Shaked et al.

In order to overcome the drawbacks of the Hough Transforms, many optimization techniques have been applied to the circle detection problem. These methods have produced much higher accuracy, stability, computational speed and robustness as compared to the discussed Hough Transform as well as other methods like Otsu method based on circular histogram Wu et al. These optimization techniques are nature-inspired methods including genetic algorithms GA Ayala-Ramirez et al. Hereunder each optimization method will be discussed one by one and their possible problems that were unaddressed in the cited literature before introducing our proposed scheme.

In summary, the genetic algorithm is the most favored computational intelligence model for multi-circle detection so far and has been proven to be more suitable for multi-circle detection problem among other computational intelligence based methods. However, due to the nature of global optimization of genetic algorithm, multi-circle detection requires additional processing. The ideal case would be an algorithm with an inbuilt computational intelligence with a niche adaptability and robustness that only needs to run once like regular deterministic approaches.

In Das et al. Although the method here is robust to noise, it fails to detect circle locations with considerable precision, under both clear and noisy conditions seen from their result samples. In ant colony algorithm Chattopadhyay et al. This method is essentially a closed loop tracking method, and its performance is questionable when circular shape edges are not enclosed Chattopadhyay et al. In Cuevas et al. For the fuzzy cellular neural network Wang and Cheng a , b , the basic limitation is that it takes single inputs where only one WBC is analysed.

Moreover, with an exponential increase in the number of iterations the detected circle gets distorted covering the surrounding area, thereby giving more false positives and losing out on the true positives. Also for the adaptive bacterial foraging algorithm in Dasgupta et al. In the clonal selection algorithm for circle detection Isa et al. The PGSA is a stochastic evolutionary computation technique based on the natural growth process of a plant towards the global optimal solution—sunlight. Based on plant phototropism, the PGSA regards the feasible region of Integer programming as plant growth environment and evaluates the probability on different growth points according to the changes in the object function.

It then grows towards the global optimal solution—light source. The plant grows a trunk from its roots; some branches will grow from the nodes on the branches. This repeats until a plant is formed. The plant branches out through a number of iterations which can be considered as generations towards the globally optimal solution, thereby forming an optimal configuration structure that can help it to absorb maximum sunlight for photosynthesis.

In the literature Wang and Cheng a , b , PGSA is compared with other optimization algorithms where the results have shown that the optimal network given by PGSA is the best option as compared to the existing optimization techniques namely genetic algorithms, particle swarm optimization, gradient descent and Tabu search, with a higher rate of accuracy and faster global optimization. As per the analyses, PGSA has the following advantages: 1 the objective function and constraint satisfaction are dealt separately, 2 it does not require any predefined error coefficient, rates of cross-over and mutation therefore resulting in stable solutions, 3 it has a search mechanism with ideal direction and randomness balancing property which is determined by the plant growth hormone morphactin concentration and thus finds the global optimal solution quickly.

In literatures Luo and Yu , Xu et al. The algorithm uses the variable growth rate of the plant vertex to reduce the search time and uses the vertical growth characteristics of the early growth to reduce search space; hence, it is possible to obtain a more optimal solution in less time. Thus, PGSA gives minimum loss while showing greater convergence stability. The PGSA based circle detector uses three edge points on the image which are randomly selected that represent candidate circles in the edge map of the blood sample image.

First, a validation is done to check if these candidates are really present in the image edge map which is generated in the pre-processing stage that will be discussed later in the paper. This is done by calculating the fitness value of such candidates. The better a candidate circle approximates the actual edge circle, the better will be the fitness function value.

Hence, the edge map should be accurate and precise enough. Further, the segmentation of the image, which will be mentioned in the pre-processing stage later in the paper, plays an important role to accurately measure the similarity of a candidate circle with an actual WBC. Guided by the values of the new objective function, the set of encoded candidate circles are evolved using the PGSA algorithm so that they can fit into the actual WBC on the image. The approach generates a subpixel detector which can effectively identify leukocytes in real images.

PGSA is relatively new, having been introduced in the year and has never been applied to image processing techniques. This paper aims to apply this highly efficient evolutionary technique towards medical image processing, by proposing a new WBC detector algorithm that efficiently recognizes WBC under different complex conditions while considering the whole process as a circle detection problem.

The PGSA is a bionic random algorithm guided by plant phototropism the ability of a plant to bend towards the light source. The light source is the global optimal solution and the PGSA simulates the mechanism of plant phototropism by assessing the morphactin concentration on the growth points of the plant. This morphactin concentration decides the growth of branches and leaves and is dependent on the intensity of light. PGSA regards the feasible region of Integer programming as plant growth environment and evaluates the probability on different growth points according to the changes in the light intensities taken as the corresponding objective function Li and Wang ; Bhattacharjee and Paul Biological experiments state the following plant growth laws: First, the node on the plant with a higher morphactin concentration has a greater probability to grow into a branch.

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Second, the morphactin concentrations on these nodes vary according to the environmental information and the relative positions of these nodes on the plant. If a node has the highest morphactin concentration and hence, if it grows into a branch, the morphactin concentrations of all the remaining plant nodes will be freshly allotted as per the new environment and the just branched node will have a concentration equal to zero. According to the probability model of PGSA, f i is the fitness function for the node i on the plant to grow in the given environment.

The biological laws of plant growth specifies that if the value of f i is smaller, then node i has a better environment for growing into a new branch.

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The mathematical model of PGSA is as follows. Assuming that there are n nodes on the trunk T that might provide a more thriving growth environment than the root, i. The above equation shows that the morphactin concentration of a node in a plant is dependent on the growth environment of all the nodes on the plant. A change in the concentration of one node, therefore effects the rest. The state space can be shown as in Fig. The new state space has greater number of nodes now, i. This growth process stops in the bionic world when the plant has reached its maturity and cannot further branch out.

The PGSA has huge potential to be used in optimization problems. Here, the control parameters are the fitness function [ f i ], the initial solution root , search domain of candidate solutions length of the trunk and branches and candidate solutions plant nodes. Further, it has a well-balanced exploration to exploitation ratio Crepinsek et al. This method keeps exploring the entire search space with random node selection in the search interval [0, 1]. Although, candidate solutions nodes grow in each iteration the search space still remains in the interval [0, 1].

After the exploration, upon the selection of the best candidate solution preferential node , the morphactin concentrations are reassigned by a neighbourhood like search that assesses the nodes in the vicinity of the just grown branch. The morphactin is not only assigned to the nodes on the new branch by exploitation but also to the previous nodes on the trunk by exploration in a given iteration.

This is mainly because the objective function growth environment is dependent on the concentration of all the nodes on the plant. Thus PGSA has a well-balanced exploration to exploitation ratio which is necessary for any search optimization algorithm. There have been many algorithms, both traditional and evolutionary, that have been used for circle detection. As has been stated in the background study, all these methods had some disadvantages. PGSA, being inspired from plant phototropism has many advantages that can be used to solve the circle detection problem.

The steps of the algorithm has been outlined in Fig.

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Our approach is to use the above efficient naturally occurring technique to solve the leukocyte detection problem the overview of which is presented hereunder Figs. To employ the proposed scheme with respect to leukocyte detection, the smear images are pre-processed to obtain two new images. For the segmentation pre-processing part, the WBCs are isolated from other structures including red blood cells and the background pixels.

Information of colour, brightness, and gradients are used with a corresponding threshold to generate classes to classify each pixel. A histogram thresholding has been incorporated to segment the WBCs. Now that the segmentation is done, the corresponding edge map is produced. The edge map maintains the total object structure while being just a simple representation of the original image. There many different methods to detect the edges, but for our work the morphological edge detection procedure has been used Fu and Han ; Chandrasiri and Samarasinghe where erosion followed by inversion of the original image is carried out to ultimately compare it pixel-by-pixel with the original image.

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This results in the detection of pixels which are present in both the images. This gives the calculated edge map.

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For the implementation of the algorithm the set of candidate solutions needs to be initialized. For this purpose, the circle candidates need to be constructed using the three non-collinear points on the edge of the circle, previously stored in the vector P. The centre and radius of the circle C are given by the well-known second degree equation as seen in Eq. Here det.

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Why We Do Not Evolve Software? Analysis of Evolutionary Algorithms

Before defining the fitness function of the proposed scheme in context of the problem at hand, it is necessary to validate whether the circumference coordinates of the candidate circle C exists in the edge image. Upon this validation, the fitness function can be calculated.

Thereafter, the fitness function f C is defined as the pixel by pixel similarity error between the above set of pixels J of the circle candidate C particle and the pixels of the edge map, giving a greater fitness value for a higher resemblance.