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Edge detection using ACO and F ratio

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Abstract

Edge detection is an important step for finding the discontinuities of images and detecting the boundaries of objects. This work presents a novel algorithm for image edge detection using ant colony optimization and Fisher ratio (F ratio)-based techniques. Ants generally search the food from the nest to the food source in the way that maximizes the intensity of pheromone (a chemical secretion). The proposed technique considers that the movements of the artificial ants are steered by the local intensity variation in the image pixel. The directions of ants movements in the image are determined using a direction probability matrix, computed by pheromone and heuristic information of possible directions. In this work, F ratio technique is utilized to determine the optimum threshold value from updated pheromone matrix. This threshold value is further used to extract binary edge map from pheromone matrix. The experiment is conducted on the different test images, i.e., Cameraman, Lena, Coins, Peppers, House and Pillsetc image. The proposed edge detection algorithm is evaluated on the basis of statistical parameters such as kappa, figure of merit, Baddeley’s delta metric and Hausdorff distance, and the experimental results show that the proposed method performs better as compared to earlier reported techniques in most of the cases.

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Abbreviations

\(p_{ij}^{(n)}\) :

The probability of the ant movement from node \(i\) to \(j\) at \(n\)th construction step

\({\tau _{ij}^{(n - 1)}}\) :

The pheromone information value at edge \((i,j)\) within \(n\)th construction step

\(\Omega _i\) :

The neighborhood nodes of node \(i\)

\({{\eta }_{ij}}\) :

The heuristic information at edge \((i,j)\)

\(\alpha ,\beta \) :

The weighing factors for pheromone and heuristic information

\({\tau _{ij}^{(n)}}\) :

The pheromone information value at edge \((i,j)\) after completing the \(n\)th construction step of all ants

\(\varphi \) :

The pheromone decay coefficient

\({\tau _{0}}\) :

The initial value of the pheromone

\(\rho \) :

The evaporation rate

\(\Delta _{ij}^{(k)}\) :

The amount of pheromone laid on edge \((i,j)\) by \(k\)th ant

\(I\) :

The image whose edge to be detected

\(K\) :

Number of ants

\(N\) :

Number of construction steps

\(M1\times M2\) :

The dimension of input image \(I\)

\(\tau ^{(0)}\) :

The initial pheromone matrix

\(\tau _\mathrm{init}\) :

The initial value of each component of the pheromone matrix

\(\tau _\mathrm{min}\) :

The minimum value of pheromone information

\(\eta _{i,j}\) :

The heuristic matrix information at pixel \((i,j)\)

\(c\) :

The clique matrix

\(I_{i,j}\) :

The image pixel intensity at pixel coordinate \((i,j)\)

\(V_c (I_{i,j})\) :

The functional value of local group of pixels \(c\) at pixel \((i,j)\)

\(Z\) :

The normalization factor

\(L\) :

The number of ants movement steps within each construction step

\(p_{(l,m),(i,j)}^{(n)}\) :

The probability of the ant movement from the pixel \((l,m)\) to pixel \((i,j)\) at \(n\)th construction step

\(\tau _{i,j}^{(n - 1)}\) :

The value of pheromone matrix at pixel \((i,j)\) within \(n\)th construction step

\(\Omega _{(l,m)}\) :

The neighborhood of pixel \((l,m)\)

\(\Delta _{i,j}^{(k)}\) :

The amount of pheromone laid at pixel \((i,j)\), visited by \(k\)th ant

\({\tau _{i,j}^{(n)}}\) :

The value of pheromone matrix at pixel \((i,j)\) after completing \(n\)th construction step of all ants

\({\tau _{i,j}^{(0)} }\) :

The initial pheromone value at pixel \((i,j)\)

\(T\) :

The threshold value between cluster 1 and cluster 2

\(F\text {ratio}_{\,T}\) :

The value of Fisher ratio for threshold value \(T\)

\(\mu _{1T},\mu _{2T}\) :

The means of cluster 1 and cluster 2

\(v_{1T},v_{2T}\) :

The variances of cluster 1 and cluster 2

\(C_1,C_2\) :

The clusters of pheromone matrix consist of all data points having intensity level below and above \(T\)

\(T^*\) :

The optimum threshold value between \(C_1\) and \(C_2\)

\(k(I_1,I_2)\) :

The kappa parameter for images \(I_1\) and \(I_2\)

\(F\) :

Figure of merit

\(I_I,I_A\) :

The number of ideal and actual edge points of image \(I\)

\(d(i)\) :

The pixel miss distance of the \(i\)th edge detected

\(\alpha _f\) :

Scaling constant

\(H(A,B)\) :

The Hausdorff distance between set \(A\) and set \(B\)

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Authors and Affiliations

  1. Department of Electronics and Communication Engineering, National Institute of Technology, Rourkela, 769008, India

    Samit Ari, Dipak Kumar Ghosh & Prashant Kumar Mohanty

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  1. Samit Ari
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Correspondence to Dipak Kumar Ghosh.

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Ari, S., Ghosh, D.K. & Mohanty, P.K. Edge detection using ACO and F ratio. SIViP 8, 625–634 (2014). https://doi.org/10.1007/s11760-013-0569-4

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