Synthesis and Comparison of Improved Edge Detection Technique Based on Metaheuristic and Intelligent Algorithm Optimization

In the recent years, edge detection and the ant colony algorithm are the methods used in many computer vision applications such as segmentation [1], binarization [2], feature extraction [3], face recognition [4] and edge detection [5]. Intelligent approaches, based on the swarming behavior of animal colonies in nature, has been used widely and successfully in image processing tools, especially when it comes to edge detection, which is the most difficult task because of the complexity of images. Traditional methods were used for detecting cracks brightened up in bridges by Abdel-Qader et al. [6]. Other studies of edge detection presented for measuring the crack width and detecting cracks on surfaces respectively by Adhikari et al. [7] and Dorafshan et al. [8] and Dorafshan et al. [9]. These studies proved that the common edge detector operator achieved the most accurate crack detection.

Thresholding is one of the most used methods in computer vision applications, but a weak compactness of various distribution representing clusters leads to false detection of edge pixels. This approach suffers from the spatial correlation of images and there are different images having the same histograms that give the same threshold value. however, the running time and the location of the various clusters which delimit the full and continuous edge, present the common and crucial problems in this topic. A lot of studies have been done that remedy to these gaps, Otsu [10], Kittler and Illingworth [11], potential difference [12], max entropy [13, 14], and multilevel threshold [15]. Two ways separate the foreground from the background. The first one is bi-level thresholds in Grayscale Images (GIs) and medical images. The second is based on thresholding and clustering an image into various classes. There are two categories of thresholding technique: parametric and non-parametric [16], (1) determines the optimal thresholds by optimizing inter-class and intra-class variances [17] and (2) requires assuming, for each segmented area, the probability density model and estimating the relevant parameters. Recent studies [18] have proved that the Artificial Bee colony (ABC) can be a suitable tool to find optimum thresholds and edge detection, it's an easy algorithm and has a limited parameters and offering very high robustness [19]. Moreover, metaheuristic algorithms can be the best choice of problem optimization to improve edge detectors. The automatic threshold selection was evaluated by Ye et al. [20] based on the ABC algorithm. Zhang et al. optimize running time using global thresholding based on ABC algorithm [21], in addition Ma et al. operate with the GI to select threshold for image segmentation [22].

In this paper we have proposed many edge detection techniques based on intelligent, statistique, and metaheuristic tools. Therefore, color is the more significant information that ameliorate the compactness of various distribution allowing a high quality thresholding. The metaheuristic algorithms are used on clusters center optimization to obtain more significant color image segmentation. The ABC algorithm is incorporated with the Otsu multi-level thresholding approach which operates with color image converted in Lab, YCbCr, HSL color space. Also ACO algorithm was used with the Graph Cut approach that consists of dividing the image into many regions and minimizing an energy function F(λ) which leads to assign an index to each optimal region. As for the PSO algorithm optimizes the clusters center and provides segmented image in the output. And also we have introduced different type of signal energy like joint and conditional entropy for edge detection. Finally, Fuzzy logic technique have done for the same raison and the robustness was tested by salt & pepper noise. This paper is organized as follows. Section 2 describes edge detection based on the metaheuristic optimization algorithm. Section 3 describes edge detection based on the fuzzy logic and various Shannon entropies. Section 4 discusses the experimental results and shows the robustness of our suggested techniques.

3.1 ACO

According to Dorigo’s ACO website, "Ant colony optimization studies artificial systems that take inspiration from the behavior of the real ant colonies and which are used to solve discrete optimization problems [29]". Thus, by observing ants during the foraging activity, and then discovering the strategy of these ants to find the shortest track to reach food sources. Then, he imitated and modeled its behavior in searching of the best path in a graph.

The strategy goes like this [30]: When ants are looking for food, going from their nest to food sources, they have decided where to go and which path to take. At first, they find themselves in front of several paths lead to the food source, so they explore it all randomly. During their movements, ants are capable of producing chemicals, known as pheromones, deposited to mark the path on the ground that others can follow. The more they use the shorter selected trail, the most optimal line will become increasingly attractive and the pheromone trail concentration will grow stronger, while decreased by the evaporation phenomenon on the other paths. This is because of some natural factors (temperature and wind). Accordingly, the ants will more likely choose to follow the path with higher pheromone levels.

3.2 ACO Algorithm for optimum clusters selection

First of all, we have to say that the ant system algorithm is improved to solve the Traveling Salesmen Problem (TSP) [31], which is all about finding the least costing path verifying two conditions: Starting from one point, the salesmen have to go to all other cities just once and come back to the original. Each artificial ant has to find the best solution by moving step by step on the search space states. Figure 2 describes ACO algorithm and summarize the different steps [32]:

• Step 1: The k ants are randomly distributed on the n nodes of the graph.
• Step 2: Each ant k has its own memory that contains its starting node and the initial rate of pheromone τ₀.
• Step 3: Initialize the pheromone paths: τ_ij(0)= τ₀.
• Step 4: Each k^th ant, at the moment t, sitting at the state i will choose its next suitable state j from the set of the unvisited state J_i^k according to the state transition probability function given by Eq. (1):

$P_{i j}^{k}(t)= \begin{cases}\frac{{\tau_{i j(t)^{\alpha}} \quad \times \eta_{i j}(t)^{\beta}}}{\sum l \in J_{i}^{k} \times {\tau_{i j(t)^{\alpha}} \quad \times \eta_{i j}(t)^{\beta}}} & \text { if } j \in J_{i}^{k} \\ 0 & \text { Otherwise }\end{cases}$    (1)

where, τ_ij(t) is the pheromone trail intensity between the two states i and j, η_il(t) is the heuristic function (visibility), and α and β are two adjustable parameters used to regulate the influence of the pheromone and the visibility. For the TSP, the visibility is inversely proportional to the Euclidean distance between two nodes $\frac{1}{d(i, j)}$.

• Step 5: Each k^th ant calculates the length of its tour L_k(t).
• Step 6: Each k^th ant calculates the pheromone amount it has been deposit on the edge (i, j) at iteration t by Eq. (2) [33]:

$\Delta \tau_{i j}^{k}(t)=\left\{\begin{array}{cl}\frac{\mathrm{Q}}{L_{k}(t)} & \text { if }(i, j) \in L_{k}(t) \\ 0 & \text { otherwise }\end{array}\right.$    (2)

• Step 7: The pheromones are updated in such a way that the shortest path gets more pheromone than the longest path. The pheromone update formula is giving by Eq. (3):

$\tau_{i j}(t+n)=(1-\rho) \times \tau_{i j}(t)+\rho \times \Delta \tau_{i j}(t)$    (3)

where, $\rho \in[0,1]$ is the evaporation factor, and it regulates the pheromone reduction.

• Step 8: Repeat from step 4 until all ants do a step.
• Step 9: Save the best path that it has been found so far (list of nodes visited by an ant).

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Figure 2. Flowchart of ACO algorithm organization

• Step 10: After each ant completes n iterations, the complete tour is obtained. Then, a global update rule presented by Eq. (4) will be applied:

$\tau_{i j}(t+n)=(1-\rho) \times \tau_{i j}(t)+\rho \times \tau_{0}$    (4)

• Step 11: Re-iterate from step 4 until we reach the termination condition (the maximum number of iterations).

Exit: The solution of the algorithm: The best path that it has been found.

3.3 Image segmentation by graph cut

Graph cut methods treat the image segmentation as a label assignment problem. Image I will be divided into homogeneous Nreg regions [34, 35] that respect some of the image characteristics (intensity, color…). Each region R_l is represented by a group of pixels, whose have a similar border and one label l. In this case, the segmentation is performed via minimizing an energy function [36] expressed by Eq. (5):

$F(\lambda)=D(\lambda)+\gamma R(\lambda)$    (5)

where, λ is an indexing function that assigns each pixel of image I to a region. Eq. (6) and (7) respectively represent the D measure that calculates the disagreement between the intensity of pixels in each segment and the segment representative intensity, and R measures the difference between the intensity of pixels from each other in each segment, and γ is a positive constant regularizing coefficient that controls the relative importance of first and second terms.

$D(\lambda)=\sum_{l \in L} \sum_{p \in R_{l}}\left(\mu_{l}-I_{p}\right)^{2}$    (6)

where, R_l [37] is the average of intensity values of the pixels in segment l, and μ_l is the intensity representative of R_l.

$R(\lambda)=\sum_{p, q \in N} r(\lambda(p), \lambda(q))$    (7)

where, N a neighborhood group that contains all pairs of neighboring pixels, and $r(\lambda(p), \lambda(q))$ is a smoothness regularization function given by the truncated squared absolute difference. Let $G=\{V, E\}$  be a weighted graph, where V is a group of vertices and edges link between them, and $G^{\prime}=\left\{V^{\prime}, E^{\prime}\right\}$  be a cut, where $E^{\prime} \subset E$  is a partition of vertices into two subsets (source and the sink) in the induced graph with separate terminals [38].

3.4 Determination of optimum cluster centers using ACO

Now let us incorporate the ACO algorithm with the graph cut approach for image segmentation. Firstly, we have to define the states of the environment in which the ant colony lives. Hence, the discrete space, where the artificial ants move and try to find a solution, is defined by the pixels of the image with a size of M×N, and the food is the edge pixels.

3.4.1 Initialization process

Aydin and Uğur [39] created the three histograms of the three-dimensional color spaces, and then they gathered the center points of bins. x, y and z are the bin center sets:

$x=\left\{x_{1}, x_{2}, \ldots, x_{n}\right\} \quad y=\{y 1, y 2, \ldots, y n\} \quad z=\{z 1, z 2, \ldots, z n\}$

where, n is the number of bins in histograms x_i, and y_i and z_i are the centers of each bin. The combination of these three bin center sets defines the candidate cluster center point set. Moreover, the search space is defined by the following expression: $S=\{(x 1, y 1, z 1),(x 1, y 1, z 2), \ldots,(x n, y n, z n)\}$.

3.4.2 Heuristic function

The visibility of pixels at position (i, j) is defined by Eq. (8):

$\mu_{i j}=V_{c}\left(I_{i, j}\right) / Z$    (8)

where, $Z=\sum_{i=1}^{m} \sum_{j=1}^{n} \operatorname{Vc}(I i, j)$  is a normalization factor and I(i, j) is the pixel value at position (i, j), and V_c(I_i, j) (Figure 3) is the function of a window of pixels with a size of 3×3 which can be measured with Eq. (9):

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Figure 3. Computation of variation V_c(I_i, j) at I(i, j) pixel position defined in Eq. (9)

$V_{c}\left(I_{i, j}\right)=f\left(\left|\mathrm{I}_{-1}-1, \mathrm{j}-1-\mathrm{I}_{\mathrm{i}}+1, \mathrm{j}+1\right|\right.$

$\left.+\left|\mathrm{I}_{\mathrm{i}-1, \mathrm{j}+1}-\mathrm{I}_{\mathrm{i}+1, \mathrm{j}-1}\right|+\ldots+\left|\mathrm{I}_{\mathrm{i}-1, \mathrm{j}}-\mathrm{I}_{\mathrm{i}+1, \mathrm{j}}\right|\right)$    (9)

The f() function is determined by Eq. (10):

$f(x)= \begin{cases}\sin \left(\frac{\pi x}{2 \lambda}\right) \lambda x i f j \in J_{i}^{k} \\ 0 & \text { else }\end{cases}$    (10)

where, λ adjusts the function shape, as shown in Figure 3.

3.4.3 Ants’ solution construction process

Unlike the original ACO, this approach has some differences:

• Pheromone update rule: Only the best ant deposits an amount of pheromone on the cluster centers according to formula 4, instead of just deposing it between states.
• Memory: Each ant has a different solution length at each iteration.
• Pixel transition rule: The selection of the next suitable state will be done according to formula 1. However, when it comes to selecting the next cluster centers, we will use its pheromone levels and its heuristic value, without using any knowledge about previously visited states or the current positioned state.
• Fitness function: The fitness function assures to select optimum cluster center sets and to determine a minimum number of suitable cluster centers for clustering. The fitness is determined by Eq. (11):

$f=\frac{\sum_{i=1}^{m} \sum_{j=1}^{n} \min \left(\operatorname{dist}\left(p_{i}, C_{j}\right)\right)}{N}$

$+\frac{M \times \max (M) \times \ln (M)}{n}$    (11)

where, N represents the number of bins in a histogram, M represents the number of cluster centers in an ant solution, p_i is a pixel, C_j is the cluster center in the ant solution, and max(M) is the maximum number of cluster centers that can be in a solution. After determining the cluster centers by the ACO method, the labels are fixed. Then we apply the graph cut method.

3.4.4 Graph cut method and edge detection

Our objective here is to find the cut with the smallest cost. Based on the pixels’ information of the image, we set the weight of the graph. Then we measure the minimum cost cuts which are the minimum of the energy function, i.e. the sum of the image edge weights. This method can simply identify multiple regions simultaneously, unlike other methods where we have to segment the image into a foreground and a background, repeatable until reaching a stop criterion (no further segment). Finally, in each iteration, the graph cut method directly improves the boundary of identified segments.

Our technique is built on these steps: A 3×3 mask is designed to extract the values of neighbor pixels in each treated image. The inputs of our fuzzy system are based on pixel values and the variation between all pixel against the center pixel. These values are divided under fuzzy subsets. Fuzzy inference rules are defined to decide the partnership of this pixel if it is a boundary or not. The defuzzification step is made by Mamdani’s system, when the resulting output of the fuzzy system is calculated by the centroid method.

We have used trapezoidal and triangular membership function respectively for fuzzy inputs and outputs. Two fuzzy linguistic variables for inputs (black and white), as well as two fuzzy linguistic variables for outputs (black and edge), are utilized. In our edge detection technique, the inference rules are used to calculate the value of the center pixel based on neighboring pixels. We have used Mamdani fuzzy system which contains 13 rules defining S as an edge pixel, like depicted in Figure 4; i.e., all represented cases confirm the partnership of S to the edge pixels.

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Figure 4. Graphical evaluation of rules

This section describes, presents, evaluates and discusses the results elaborated by the developed technique based on Shannon's entropy information (Figure 5 and Figure 6), metaheuristic approach (Figure 13, Figure 14 and Figure 15) and by the fuzzy logic technique (Figures 10, 11 and 12). Furthermore, we have checked and confirmed the robustness and effectiveness of our approaches by introducing different levels of salt-and pepper noise, as illustrated in Figure 10. Our contributions use various color level. The results of the conditional entropy (Figures 7 and 9) show the impact and the relationship between color levels, and the higher quality results compared to the joint entropy (Figure 8). The RGB color space are excellent: They are accurate to original images and offer a good quality of discrimination. All the image details are also directly identifiable. The edge detection results of these images on the Lab color space are acceptable but not so accuracy.

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Figure 5. Results by thresholding method based on Shannon entropy

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Figure 6. Edge detection results based on Shannon entropy

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Figure 7. Edge detection results based on conditional entropy

The following parameters are used in all experiments: number of bees = 5, number of iterations =50, limit=100. Figure 13, shows that image represented in YCbCr color space have crucial edge detection than other systems. The edge detection in the HSL color space does not give promising results: many details are missed in treated images or indiscernible, and have a blurred quality. Tables 1, 2 and 3 present the performance metrics of our approach and other algorithms. Our processing method has operated with these parameters: number of ants = 5, number of iterations = 20, α=1, β=0.1, ρ=0.1, number of bins = 15 and max(k)=15. Compared to the Canny method and the ACO technique with gray level, the obtained results are better and have a relevant quality. The PSNR and PR values of our new approach prove this amelioration. After analyzing all the results. we can say that an edge detection image (Figure 10) is improved by our new approach and is better than results using gray-scale images. It gives also good results compared to Canny method, even with various levels of noise and while having reduced running time.

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Figure 8. Edge detection results based on joint entropy.

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Figure 9. Edge detection results based on conditional entropy

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Figure 10. Results of fuzzy method based on pixel value with Salt & pepper noise

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Figure 11. Results of fuzzy method based on pixel difference

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Figure 12. Edge detection based on pixel difference with Salt & pepper noise

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(Image 1)

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(Image 2)

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(Image 3)

Figure 13. Results by ABC algorithm

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Figure 14. Results by PSO algorithm

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Figure 15. Results by ACO algorithm

Table 1. Segmentation quality evaluation of first image in various color space

Table 2. Segmentation quality evaluation of second image in various color space

Table 3. Segmentation quality evaluation of third image in various color space