- Research
- Open Access
An object localization optimization technique in medical images using plant growth simulation algorithm
- Deblina Bhattacharjee^{1},
- Anand Paul^{1}Email author,
- Jeong Hong Kim^{1} and
- Mucheol Kim^{2}
- Received: 19 May 2016
- Accepted: 29 September 2016
- Published: 13 October 2016
Abstract
The analysis of leukocyte images has drawn interest from fields of both medicine and computer vision for quite some time where different techniques have been applied to automate the process of manual analysis and classification of such images. Manual analysis of blood samples to identify leukocytes is time-consuming and susceptible to error due to the different morphological features of the cells. In this article, the nature-inspired plant growth simulation algorithm has been applied to optimize the image processing technique of object localization of medical images of leukocytes. This paper presents a random bionic algorithm for the automated detection of white blood cells embedded in cluttered smear and stained images of blood samples that uses a fitness function that matches the resemblances of the generated candidate solution to an actual leukocyte. The set of candidate solutions evolves via successive iterations as the proposed algorithm proceeds, guaranteeing their fit with the actual leukocytes outlined in the edge map of the image. The higher precision and sensitivity of the proposed scheme from the existing methods is validated with the experimental results of blood cell images. The proposed method reduces the feasible sets of growth points in each iteration, thereby reducing the required run time of load flow, objective function evaluation, thus reaching the goal state in minimum time and within the desired constraints.
Keywords
- Nature-inspired computing
- Plant growth simulation algorithm
- Medical image segmentation
- Object recognition
Background
Various computing techniques inspired from nature has been extensively used in solving problems spanning from optimization, pattern recognition, machine learning, image detection to computer vision. There is hardly any field that is left uninfluenced by the nature-based computing techniques. Image Processing is one such field where recently biomimicry methods are being used invariably. One such application of nature-inspired computation is in the field of medical image processing, especially focused on object localization. In this paper, the problem of object localization in medical images has been solved with the application of the highly efficient plant growth simulation algorithm (PGSA) (Li and Wang 2008) applied to the analysis of white blood cell (WBC) images. WBCs, also known as leukocytes, play a very important role in the diagnosis of a myriad of diseases. In most haematology labs, such cell differential analyses are performed using manual microscopy but this traditional process is not without its limitations. Such analysis require the availability of highly experienced personnel. Due to the substantial possibility of an inter and intra-observer variability in these manual examinations and due to the highly labour intensive routine procedures, new methods for cell analysis are being developed using digital image processing techniques to form better and reliable systems for disease diagnosis. However, high variability of cell shape, edge, localized features, the contrast between cell boundaries and background, cell size and positions have posed as challenges for the efficient object localization during the analysis of such smear images. In this paper, the process of detecting the white blood cells have been undertaken because as per haematology, the WBC tests are tougher and analysing them manually are more difficult as compared to red blood cells. The WBC detection problem has been solved in this article by viewing it as a circle detection problem because WBCs can be approximated as circular in shape. In medical imaging, detecting circular features holds huge significance (Karkavitsas and Rangoussi 2007). As per the existing conventional method of Hough Transform for circle detection in digital images (Muammar and Nixon 1989), an edge detector is used to first find the two necessary and sufficient parameters for circles i.e. the coordinates and the radius of the circle. Upon finding these, the image is averaged over its pixels, followed by filtration for detecting the image peaks. Finally, the image is transformed using a histogram. However, in order to cover all parameters (x, y, r), a lot of memory is required by this method. 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 1993). To overcome such a problem, some other approaches based on the Hough transform, for instance the probabilistic Hough transform (Fischler and Bolles 1981; Shaked et al. 1996), the randomized Hough transform (RHT) (Xu et al. 1990), the fuzzy Hough transform, Circular Hough transform with local maximization (Yadav et al. 2014), one-dimensional Hough Transform (Zhou et al. 2014), Hough Transform of curves (Campi et al. 2013) and recently scanline-based hybrid Hough Transform (Seo and Kim 2015) have been proposed with better time complexities but having average memory usage and no noise resistance. 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. 2006), WBC identification based on support vector machines (Wang and Chu 2009), and modified transformation methods as proposed in the scientific literatures (Becker et al. 2002; George et al. 2014). These optimization techniques are nature-inspired methods including genetic algorithms (GA) (Ayala-Ramirez et al. 2006), simulated annealing with differential evolution (DE) (Das et al. 2008), harmony search algorithm (Pan et al. 2010, 2011; Cuevas et al. 2012a, b, c), swarm intelligence methods like ant colony optimization based on ant regeneration and recombination to solve the circle detection problem (Chattopadhyay et al. 2008), adaptive bacterial foraging algorithm with adaptive chemotactic step size to facilitate faster convergence (Dasgupta et al. 2008), artificial bee colony algorithm for circle detection (Cuevas et al. 2012a, b, c), clonal selection algorithm for circle detection based on artificial immune system (Isa et al. 2010) and fuzzy cellular neural network (Tong et al. 2005; Wang and Cheng 2007a, b), all of which has been discussed in context of solving the circle detection problem.
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. (2008), simulated annealing and differential evolution has been combined to perform circle detection. 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. 2008), the final circle detection criterion is to threshold the deviation error derived from the detected radius which is the distance between corresponding edge pixels and circle center. This method is essentially a closed loop tracking method, and its performance is questionable when circular shape edges are not enclosed (Chattopadhyay et al. 2008). In Cuevas et al. (2012a, b, c), where the artificial bee colony algorithm has been used, the potential problem is that a lot of memory space would be used if the iteration is set to a large number, but it saves rerun computations. For the fuzzy cellular neural network (Wang and Cheng 2007a, 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. (2008), the method is not inherently capable of detecting multiple circles. In the clonal selection algorithm for circle detection (Isa et al. 2010), both the antigens and antibodies are designed as 10-by-10 images and representations are a binary string which makes it not very practical to process normal resolution images.
In this paper, the detection of WBC has been done by the PGSA. 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 2007a, 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 (2008), Xu et al. (2012), Lu and Yu (2013), Kumar and Thanushkodi (2013), certain improvements have been carried out on PGSA by studying growth characteristics of plants. 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 2005 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.
Circle detection using PGSA
Plant growth simulation algorithm (PGSA)
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 2008; Bhattacharjee and Paul 2016). The algorithm emphasises on a plant system’s method of making decisions which are based on plant’s growth rules and probability models. 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. 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.
Mathematical model for plant growth
After the reallocation of the concentrations to all the nodes on the plant except \(R_{TM}\), the state space of concentrations is again formed with the same interval [0, 1]. Assuming, the newly grown branch b has p nodes, such that \(f(R_{bi}\)) < \(f\left( {R_{0} } \right) \;\left( {i = 1,2, \ldots ,p} \right),\) again a random number β is thrown in the state space and a new node branches out in the next iteration. The new state space has greater number of nodes now, i.e. the nodes previously present (n nodes) and the nodes on the new branch b (p nodes). 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. 2013). 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.
Data pre-processing
To employ the proposed scheme with respect to leukocyte detection, the smear images are pre-processed to obtain two new images. (1) The segmented image and (2) The edge pixel map of the segmented image. 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 2012; Chandrasiri and Samarasinghe 2014) where erosion followed by inversion of the original image is carried out to ultimately compare it pixel-by-pixel with the original image. This results in the detection of pixels which are present in both the images. This gives the calculated edge map.
Thereafter, the (\(x_{i} , y_{i}\)) coordinates for every pixel \(p_{i}\) defining the image edge is stored in the image edge pixel vector P = \(\{ p_{1, } p_{2} , \ldots ,p_{Np} \}\), with \(N_{p}\) being the total number of pixels defining the edge of the analysed image.
Particle representation for candidate solutions
By considering each index as a particle in the search space, the continuous search space is explored by using PGSA for a lookup of circle parameters [\(x_{0} ,y_{0} ,r].\)
Fitness function for the circle detection problem
PGSA implementation
The PGSA has the following steps.
Step 1 The Canny filter finds and stores the edges in the vector P as discussed in the pre-processing step, where P contains the set of all edge pixels of the image. The iteration index is set to 1.
Step 2 k initial particles are generated \((C_{a,iteration = 1} ,a \in [1.{\text{k}}])\) in the plant growth environment state space.
Step 3 The fitness function \(f\left( {C_{a,iteration = i} } \right)\) is evaluated to find the best candidate solution like \(B_{M2}\) as mentioned in the PGSA discussion in the previous section. This best candidate solution is named as \(C^{best} \leftarrow \arg \hbox{min} \{ f(C_{a,iteration = i} )\} .\)
Step 4 As per the PGSA discussed in the previous section, the constraint satisfaction at each of these particles (nodes) is checked, that is their morphactin concentration is calculated as per the Eq. (1). The particle with the higher morphactin concentration has a higher probability to branch out or move to the next iteration as an evolved candidate solution.
Step 5 The new branch position, which is the new particle’s position is stored and the morphactin concentrations of all the particles are calculated again according Eq. (4) and Eq. (5) except for \(C^{best}\) as it has already produced a branch i.e. it is the best solution and hence is the current local optimum solution.
Step 6 For every new particle, a maximum number of q particles are generated as per j = 1, 2,…,q discussed previously and based on the newly calculated morphactin concentration in Step 5, the new best candidate is found on the current generated branch in the previous step. This accounts for a neighbourhood like search for optimal candidate solutions. This process of generating new candidate solutions continues till a better minimized objective function is achieved and stops till there is no improvement in the fitness value of the generated candidate solutions.
Step 7 The set of all nodes that have branched out are the possible candidate solution with the final node \(C^{best}\) being the global best solution and others the local optimal solutions.
Step 8 From the original edge map, the algorithm marks the points corresponding to \(C^{best}\). In case of multi-circle detection it jumps to Step 2.
Step 9 Finally, the best particle \(C_{{N_{c} }}^{best}\) from each circle is used to draw (over the original image) the detected circles, where \(N_{c}\) is the number of circles detected.
Experimental results
Thus, the proposed method can successfully detect damaged, complex and partially hidden leukocytes correctly.
The dataset of smear-blood test images for evaluating the proposed scheme is downloaded from the website Cellavision.com. The dataset includes 80 images from the Cellavision public dataset which were in JPG format of size 360 × 363 pixels, with a resolution of 10 pixels per 1 μm. These images were medically graded and had 463 white blood cells (256 bright leukocytes and 207 dark leukocytes as per the blood smear conditions), all detected by a haematologist—a human medical expert. These numbers were taken as graded standards for all experimentations. For testing the proposed scheme over these images, the true positive rate (known as the number of correctly detected leukocytes over the number of leukocytes detected by the expert) and the false positive rate (known as the number of non-leukocytes that have been wrongly identified as leukocytes over the number of leukocytes which have been actually detected by the medical expert) have been evaluated. The results of the experiments show that the proposed method, achieves 98.28 % leukocyte True Positive Rate with 1.72 % False Positive Rate, and is therefore, arguably better than the other existing methods. To establish this statement, the proposed scheme has been further discussed and compared with other existing methods in context of the leukocyte detection problem as a circle detection problem hereunder.
Discussion
Comparative performance of HT, FCCN, GA+ACO and PGSA for leukocyte detection with respect to true positive rate, false positive rate, false discovery rate and positive predictive value
Leukocyte type | Method | Leukocytes detected (true positives) | Missing leukocytes (false negatives) | Missing leukocytes (false negatives) | True positive rate (%) | False positive rate (%) | False discovery rate (%) | Positive predictive value (%) |
---|---|---|---|---|---|---|---|---|
Bright leukocyte (256) | HT | 135 | 121 | 67 | 46.85 | 30.18 | 59.90 | 66.83 |
FCCN | 206 | 50 | 55 | 78.83 | 24.77 | 19.16 | 78.93 | |
GA + ACO | 217 | 39 | 42 | 83.78 | 18.92 | 15.06 | 83.78 | |
PGSA | 242 | 14 | 10 | 98.01 | 1.99 | 5.56 | 96.03 | |
Dark leukocyte (207) | HT | 100 | 107 | 54 | 48.04 | 26.47 | 69.48 | 64.94 |
FCCN | 168 | 39 | 49 | 81.37 | 24.02 | 17.97 | 77.42 | |
GA + ACO | 183 | 24 | 38 | 88.72 | 18.63 | 10.86 | 82.81 | |
PGSA | 202 | 5 | 6 | 98.55 | 1.45 | 2.40 | 97.12 | |
Overall (463) | HT | 235 | 228 | 121 | 47.42 | 28.40 | 64.04 | 66.01 |
FCCN | 374 | 89 | 104 | 80.05 | 24.41 | 18.62 | 78.24 | |
GA + ACO | 400 | 63 | 80 | 86.15 | 18.78 | 13.13 | 83.33 | |
PGSA | 444 | 19 | 16 | 98.28 | 1.72 | 4.13 | 96.52 |
Under ideal conditions, the precision and sensitivity both are 100 %, thus the circle detection technique under such scenario would be able to find all the circles in the image without any false positives or un-detected circles. But under normal conditions precision and sensitivity is seen to decrease because when detecting such circles from the images the circle detection method has to find both the centre of the circle as well as the radius of the circle.
Precision is a measurement of the rate of correct detection over all detected circles. A perfect situation arrives when there is a straight line all along 100 % of y-axis in Fig. 6 for all the images. It is apparent that Hough Transform based method has the worst results, which is not beyond expectation. A completely extreme case is a 0 % precision, implying no detection at all. Regular Hough Transform suffers a number of false detections with many images. The Modified Genetic Algorithm with Ant Colony Optimization and PGSA are seen to achieve correct detection above 90 % with small standard deviation, which are superior to the Fuzzy Cellular Neural Network (FCCN) and evidently the conventional Hough Transform. The possible problem with the FCCN is that it requires a lot of computational time and memory to train its network and the detection is achieved over a large number of generations. Also, as shown in Cuevas et al. (2012a, b, c), when the number of iterations increases, the possibility to cover other structures increases too. Thus, if the image has a complex background like in smear images, the method gets confused because of which finding the correct contour configuration from the gradient magnitude becomes highly difficult.
Statistics of sensitivity for the four analysed algorithms
Approach | Maximum | Minimum | Mean | SD |
---|---|---|---|---|
Hough transform | 1 | 0 | 0.87 | 0.198 |
FCCN | 1 | 0.56 | 0.93 | 0.104 |
GA + ACO | 1 | 0.5 | 0.97 | 0.075 |
PGSA | 1 | 0.73 | 0.98 | 0.049 |
Comparative performance of leukocyte detection over 80 images contaminated by various levels of gaussian noise
Noise level | Method | Leukocyte detected (true positives) | Missing Leukocyte (false negatives] | Wrongly detected leukocyte (false positives) | True positive rate (%) | False positive rate (%) | False discovery rate (%) | Positive predictive value (%) |
---|---|---|---|---|---|---|---|---|
Gaussian noise 463 leukocytes σ = 10 | HT | 206 | 257 | 77 | 40.37 | 18.07 | 90.81 | 72.79 |
FCCN | 343 | 120 | 71 | 72.53 | 16.67 | 28.99 | 82.85 | |
GA + ACO | 335 | 128 | 65 | 70.66 | 15.26 | 32.00 | 83.75 | |
PGSA | 431 | 32 | 21 | 93.19 | 4.93 | 7.08 | 95.35 | |
Gaussian noise 463 leukocytes σ = 15 | HT | 177 | 285 | 106 | 33.57 | 24.88 | 98.77 | 62.54 |
FCCN | 315 | 148 | 89 | 65.96 | 20.89 | 36.63 | 77.97 | |
GA + ACO | 298 | 165 | 102 | 61.97 | 23.94 | 41.25 | 74.50 | |
PGSA | 414 | 49 | 32 | 89.20 | 7.51 | 10.99 | 92.83 |
Comparative performance of leukocyte detection over 80 images contaminated by various levels of salt and pepper noise
Noise level | Method | Leukocyte detected (true positives) | Missing leukocyte (false negatives) | Wrongly detected leukocyte (false positives) | True positive rate (%) | False positive rate (%) | False discovery rate (%) | Positive predictive value (%) |
---|---|---|---|---|---|---|---|---|
Salt and pepper Noise level 10 % 463 leukocytes | HT | 182 | 281 | 114 | 34.74 | 26.76 | 94.93 | 61.49 |
FCCN | 304 | 159 | 106 | 63.38 | 24.88 | 38.78 | 74.15 | |
GA + ACO | 284 | 179 | 118 | 58.68 | 27.70 | 44.53 | 70.65 | |
PGSA | 424 | 39 | 30 | 91.55 | 7.04 | 8.59 | 93.39 | |
Salt and pepper Noise level 15 % 463 leukocytes | HT | 135 | 328 | 120 | 23.71 | 28.17 | 128.63 | 52.94 |
FCCN | 274 | 189 | 78 | 56.34 | 18.31 | 53.69 | 77.84 | |
GA + ACO | 218 | 245 | 123 | 43.19 | 28.87 | 71.85 | 63.93 | |
PGSA | 408 | 55 | 35 | 87.79 | 8.21 | 12.42 | 92.10 |
Thus, even under noisy conditions the PGSA is the most robust method to detect the leukocytes with the best detection rate, best positive predictive value, least false positive rate and the least false discovery rate.
Conclusion
In this paper, a new bionic random search algorithm has been proposed that makes use of the objective function’s value as an input to the learning model while simulating a plant’s phototropism for the automatic detection of WBCs that are embedded into complicated, obscure and cluttered smear images by considering the WBC detection problem as a circle detection problem. The PGSA has been applied to solve this circle detection problem which gives the location of the WBCs in the images using three non-collinear edge points on the segmented edge map of the image as candidate circles. The resemblance of the encoded candidate circles to the actual WBC is evaluated by the objective function which uses the edge map and segmentation results for calculating the resemblances. Based on the calculated value of the objective function, the set of encoded candidate circles (branch nodes) are evolved by using the PGSA so that they can fit into the actual blood cells that are contained in the edge map. The experimental results and the performance of the PGSA has been compared with other existing WBC detection algorithms which demonstrate the high performance of the proposed method in terms of detection accuracy, precision, and sensitivity and also under noisy conditions. Although, there has been quite some research done to solve the circle detection problem when processing images, it has not been applied in the context of medical image processing. Moreover, PGSA has never been applied to solve such a problem. This evolutionary algorithm is highly efficient and is new to the field of computing intelligence. Thus, it offers a lot of scope for applications, implementations and further extension of this algorithm.
Declarations
Authors’ contributions
Both DB and AP designed the research. DB gathered the data, processed and implemented it while also drafting the manuscript, which was proofread by AP, JHK and MK. All authors read and approved the final manuscript.
Acknowledgements
This study was supported by the Brain Korea 21 Plus project (SW Human Resource Development Program for Supporting Smart Life) funded by Ministry of Education, School of Computer Science and Engineering, Kyungpook National University, Korea (21A20131600005). This work was supported by Institute for Information & communications Technology Promotion (IITP) grant funded by the Korea government (MSIP) [No. 10041145, Self-Organized Software platform (SoSp) for Welfare Devices]. This research was also supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (NRF-2016R1A2A1A05005459).
Competing interests
The authors declare that they have no competing interests.
Ethics approval and consent to participate
No human or animal participant were used in the study, including human tissues. A publicly available database of human blood smear images in digital format has been used.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
References
- Atherton TJ, Kerbyson DJ (1993) Using phase to represent radius in the coherent circle Hough transform. In: Proceedings of the IEEE colloquium on the hough transform. IEEE, LondonGoogle Scholar
- Ayala-Ramirez V, Garcia-Capulin CH, Perez-Garcia A, Sanchez-Yanez RE (2006) Circle detection on images using genetic algorithms. Pattern Recognit Lett 27(6):652–657View ArticleGoogle Scholar
- Becker JM, Grousson S, Coltuc D (2002) From Hough transform to integral geometry. In: Proceedings of IEEE international geoscience and remote sensing symposium (IGARSS’02), vol 3, pp 1444–1446Google Scholar
- Bhattacharjee D, Paul A (2016) A hybrid search optimization technique based on evolutionary learning in plants. In: Proceedings of 2016 7th international conference of swarm intelligence, pp 271–279Google Scholar
- Campi C, Perasso A, Beltrametti MC, Massone AM, Sambuceti G, Piana M (2013) Proceedings of 8th IEEE international symposium on image and signal processing and analysis (ISPA 2013), pp 280–283Google Scholar
- Chandrasiri S, Samarasinghe P (2014) Morphology based automatic disease analysis through evaluation of red blood cells. In: Proceedings of 2014 fifth international conference on intelligent systems, modelling and simulation, pp 318–323Google Scholar
- Chattopadhyay K, Acharya A, Banerjee A, Basu J, Konar A (2008) Fast and efficient circle detection schemes for digital image. In: Proceedings of first international conference on emerging trends in engineering and technology, pp 128–133Google Scholar
- Crepinsek M, Liu S, Mernik M (2013) Exploration and exploitation in evolutionary algorithms: a survey. ACM Comput Surv 45(3):1–33View ArticleMATHGoogle Scholar
- Cuevas E, Ortega-Sanchez N, Zaldivar D, Pérez-Cisneros M (2012a) Circle detection by harmony search optimization. J Intell Robot Syst 66:359–376View ArticleGoogle Scholar
- Cuevas E, Oliva D, Zaldivar D, Perez-Cisneros M, Sossa H (2012b) Circle detection using electro-magnetism optimization. Inf Sci 182(1):40–55MathSciNetView ArticleGoogle Scholar
- Cuevas E, Sención-Echauri F, Zaldivar D, Pérez-Cisneros M (2012c) Multi-circle detection on images using artificial bee colony (ABC) optimization. Soft Comput 16(2):281–296View ArticleGoogle Scholar
- Das S, Dasgupta S, Biswas A, Abraham A (2008) Automatic circle detection on images with annealed differential evolution. In: Proceedings of eighth international conference on hybrid intelligent systems, Sept 2008, pp 684–689Google Scholar
- Dasgupta S, Biswas A, Das S, Abraham A (2008) Automatic circle detection on images with an adaptive bacterial foraging algorithm. In: Proceedings of the 10th annual conference on genetic and evolutionary computation, pp 1695–1696Google Scholar
- Davis J, Goadrich M (2006) The relationship between precision-recall and ROC curves. In: Proceedings of the 23rd international conference on Machine learning, pp 233–240Google Scholar
- Fischler MA, Bolles RC (1981) Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Commun ACM 24(6):381–395MathSciNetView ArticleGoogle Scholar
- Fu Z, Han Y (2012) A circle detection algorithm based on mathematical morphology and chain code. In: Proceedings of 2012 international conference on computing, measurement, control and sensor network, pp 253–256Google Scholar
- George YM, Zayed HH, Roushdy I, Elbagoury BM (2014) Remote computer-aided breast cancer detection and diagnosis system based on cytological images. IEEE Syst J 8(3):949–964ADSView ArticleGoogle Scholar
- Isa N, Sabri NM, Jazahanim KS, Taylor NK (2010) Application of the clonal selection algorithm in artificial immune systems for shape recognition. In: Proceedings of 2010 international conference on information retrieval and knowledge management, pp 223–228Google Scholar
- Karkavitsas G, Rangoussi M (2007) Object localization in medical images using genetic algorithms, vol 2. World Academy of Science, Engineering and Technology, Istanbul, pp 499–502Google Scholar
- Kumar RM, Thanushkodi K (2013) Network reconfiguration and restoration in distribution systems through opposition based differential evolution algorithm and PGSA. In: Proceedings of international conference on current trends in engineering and technology, pp 284–290Google Scholar
- Li T, Wang Z-t (2008) Application of plant growth simulation algorithm on solving facility location problem. Syst Eng Theory Pract 28(12):107–115View ArticleGoogle Scholar
- Lu S, Yu S (2013) A middleware-based model for redundant reader elimination using plant growth simulation algorithm. In: Proceedings of 2013 ninth international conference on computational intelligence and security, pp 36–40Google Scholar
- Luo WQ, Yu JT (2008) Bionic algorithm for solving nonlinear integer programming. Comput Eng Appl 44(7):57–59MathSciNetGoogle Scholar
- Muammar H, Nixon M (1989) Approaches to extending the Hough transform. In: Proceedings of the international conference on acoustics, speech, and signal processing (ICASSP’89), vol 3, pp 1556–1559Google Scholar
- Pan QK, Suganthan PN, Fatih TM, Liang JJ (2010) A self-adaptive global best harmony search algorithm for continuous optimization problems. Appl Math Comput 216:830–848MathSciNetMATHGoogle Scholar
- Pan QK, Suganthan PN, Liang JJ, Fatih Tasgetiren M (2011) A local-best harmony search algorithm with dynamic sub-harmony memories for lot-streaming flow shop scheduling problem. Expert Syst Appl 38:3252–3259View ArticleGoogle Scholar
- Parikh R, Mathai A, Parikh S, Sekhar GC, Thomas R (2008) Understanding and using sensitivity, specificity and predictive values. Indian J Ophthalmol 56(1):45–50View ArticlePubMedPubMed CentralGoogle Scholar
- Seo SW, Kim M (2015) Efficient architecture for circle detection using Hough transform. In: Proceedings of 6th IEEE international conference on information and communication technology convergence, pp 570–572Google Scholar
- Shaked D, Yaron O, Kiryati N (1996) Deriving stopping rules for the probabilistic Hough transform by sequential analysis. Comput Vis Image Underst 63(3):512–526View ArticleGoogle Scholar
- Tong L, Wang C, Wang W, Su W (2005) A global optimization bionics algorithm for solving integer programming—plant growth simulation algorithm. Syst Eng Theory Pract 25:76–85Google Scholar
- Wang C, Cheng HZ (2007a) A plant growth simulation algorithm and its application in power transmission network planning. Autom Electr Power Syst 31(7):24–28Google Scholar
- Wang C, Cheng HZ (2007b) Reconfiguration of distribution network based on plant growth simulation algorithm. Proc CSEE 27(19):50–55Google Scholar
- Wang M, Chu R (2009) A novel white blood cell detection method based on boundary support vectors. In: Proceedings of IEEE international conference on systems, man and cybernetics (SMC’09), pp 2595–2598, San Antonio, TX, USAGoogle Scholar
- Wu J, Zeng P, Zhou Y, Olivier C (2006) A novel color image segmentation method and its application to white blood cell image analysis. In: Proceedings of the 8th international conference on signal processing (ICSP’06), pp 235–239Google Scholar
- Xu L, Oja E, Kultanen P (1990) A new curve detection method: randomized Hough transform (RHT). Pattern Recognit Lett 11(5):331–338View ArticleMATHGoogle Scholar
- Xu L, Tao M, Ming H (2012) A hybrid algorithm based on genetic algorithm and plant growth simulation algorithm. In: Proceedings of 2012 international conference on measurement, information and control, pp 445–448Google Scholar
- Yadav VK, Batham S, Acharya AK, Paul R (2014) Approach to accurate circle detection: circular hough transform and local maxima concept. In: Proceedings of 2014 international conference on electronics and communication systems (ICECS-2014), pp 489–576Google Scholar
- Zhou X, Ito Y, Nakano K (2014) An efficient implementation of the one-dimensional Hough transform algorithm for circle detection on the FPGA. In: Proceedings of 2014 second international symposium on computing and networking, pp 44–452Google Scholar