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A new gravitational image edge detection method using edge explorer agents

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Abstract

In this paper, a new algorithm for image edge detection based on the theory of universal gravity is proposed. The problem is represented by a discrete space in which each image pixel is considered as a celestial body and its mass is considered to be corresponding to the pixel’s grayscale intensity. To find the edgy pixels a number of moving agents are randomly generated and initialized through the image space. Artificial agents move through the space via the forces of celestial bodies that are located in their neighborhood and in this way they can find the promising edge pixels. A large number of experiments are employed to determine suitable algorithm parameters and confirm the legitimacy of the proposed algorithm. Also, the results are compared with conventional and soft computing based methods like Sobel, Canny and ant-based edge detector. As compared to other standard techniques, our algorithm provides more accurate results over 11 test images via Baddeley’s error metric. The visual and quantitative comparisons reveal the effectiveness and robustness of the proposed algorithm.

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Acknowledgments

The authors would like to give special thanks to the anonymous reviewers and Miss Esmat Rashedi for her useful advices. Furthermore, the authors would like to express their gratitude towards Mr. Carlos Lopez-Molina for giving us his BDM programs and for providing valuable help.

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Authors and Affiliations

  1. Department of Electrical Engineering, Shahid Bahonar University of Kerman, P.O. Box 76169-133, Kerman, Iran

    Fatemeh Deregeh & Hossein Nezamabadi-pour

Authors
  1. Fatemeh Deregeh
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  2. Hossein Nezamabadi-pour
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Corresponding author

Correspondence to Hossein Nezamabadi-pour.

Appendix

Appendix

For more enlightening mind, consider the following example. Figure 12 shows a typical 3 × 3 window of an image. The intensity value for each pixel is shown in the figure. Suppose that the fun(.) is an identity function, thus the velocity vector for the explorer body in the center of the window is calculated as follows.

Fig. 12
figure 12

a 3 × 3 window of an image that shows the pixel’s intensity values and the explorer body (yellow circle), the red vector is direction of \( \vec{v}^{ \bot } \) and the blue vector is direction of \( \vec{v} \)

Full size image
$$ f_{r,s}^{x} = \mathop \sum \nolimits I\left( {k,l} \right)\frac{k}{{\left( {\sqrt {k^{2} + l^{2} } } \right)^{3} }} = 6*\left(\frac{ - 1}{2\sqrt 2 } - 1 - \frac{ - 1}{2\sqrt 2 }\right) + \frac{1}{2\sqrt 2 } + 1 + \frac{1}{2\sqrt 2 } = - 5 - \frac{5}{\sqrt 2 } $$
(28)
$$ f_{r,s}^{y} = \mathop \sum \nolimits I\left( {k,l} \right)\frac{l}{{\left( {\sqrt {k^{2} + l^{2} } } \right)^{3} }} = 6*\left(\frac{1}{2\sqrt 2 } - \frac{1}{2\sqrt 2 }\right) + \frac{1}{2\sqrt 2 } - \frac{1}{2\sqrt 2 } = 0 $$
(29)

and hence:

$$ \vec{v} = \left[ {\begin{array}{*{20}c} { - 5 - \frac{5}{\sqrt 2 }} \\ 0 \\ \end{array} } \right]. $$
(30)
$$ \vec{v}^{ \bot } = \left[ {\begin{array}{*{20}c} 0 \\ { - 5 - \frac{5}{\sqrt 2 }} \\ \end{array} } \right] $$
(31)

From the result it could be seen that the direction for the explorer body in not toward brighter pixels.

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Deregeh, F., Nezamabadi-pour, H. A new gravitational image edge detection method using edge explorer agents. Nat Comput 13, 65–78 (2014). https://doi.org/10.1007/s11047-013-9382-9

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