Multi-Threshold Algorithm Based on Havrda and Charvat Entropy for Edge Detection in Satellite Grayscale Images

Mohamed A. El-Sayed, Hamida A. M. Sennari

Department of Mathematics, Faculty of Science, Aswan University, Aswan, Egypt.
Department of Mathematics, Faculty of Science, Fayoum University, Al Fayoum, Egypt.

DOI: 10.4236/jsea.2014.71005                

Abstract

Automatic edge detection of an image is considered a type of crucial information that can be extracted by applying detectors with different techniques. It is a main tool in pattern recognition, image segmentation, and scene analysis. This paper introduces an edge-detection algorithm, which generates multi-threshold values. It is based on non-Shannon measures such as Havrda & Charvat’s entropy, which is commonly used in gray level image analysis in many types of images such as satellite grayscale images. The proposed edge detection performance is compared to the previous classic methods, such as Roberts, Prewitt, and Sobel methods. Numerical results underline the robustness of the presented approach and different applications are shown.

Keywords

Multi-Threshold; Edge Detection; Measure Entropy; Havrda & Charvat’s Entropy

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	S. S. Alamri, N. V. Kalyankar and S. D. Khamitkar, “Image Segmentation By Using Edge Detection,” International Journal on Computer Science and Engineering (IJCSE), Vol. 2, No. 3, 2010, pp. 804-807.
[2]	J. Lzaro, J. L. Martn, J. Arias, A. Astarloa and C. Cuadrado, “Neuro Semantic Thresholding Using OCR Software for High Precision OCR Applications,” Image Vision Computing, Vol. 28, No. 4, 2010, pp. 571-578. http://dx.doi.org/10.1016/j.imavis.2009.09.011
[3]	Z. Xue, D. Ming, W. Song, B. Wan and S. Jin, “Infrared Gait Recognition Based on Wavelet Transform and Support Vector Machine,” Pattern Recognition, Vol. 43, No. 8, 2010, pp. 2904-2910. http://dx.doi.org/10.1016/j.patcog.2010.03.011
[4]	M. A. El-Sayed, “Edges Detection Based on Renyi Entropy with Split/Merge,” Computer Engineering and Intelligent Systems (CEIS), Vol. 3, No. 9, 2012, pp. 32-41.
[5]	G. C. Anagnostopoulos, “SVM-Based Target Recognition from Synthetic Aperture Radar Images Using Target Region Outline Descriptors,” Nonlinear Analysis: Theory, Methods & Applications, Vol. 71, No. 12, 2009, pp. e2934-e2939. http://dx.doi.org/10.1016/j.na.2009.07.030
[6]	Y.-T. Hsiao, C.-L. Chuang, Y.-L. Lu and J.-A. Jiang, “Robust Multiple Objects Tracking Using Image Segmentation and Trajectory Estimation Scheme in Video Frames,” Image Vision Computing, Vol. 24, No. 10, 2006, pp. 1123-1136. http://dx.doi.org/10.1016/j.imavis.2006.04.002
[7]	M. T. Doelken, H. Stefan, E. Pauli, A. Stadlbauer, T. Struffert, T. Engelhorn, G. Richter, O. Ganslandt, A. Doerfler and T. Hammen, “1H-MRS Profile in MRI Positive versus MRI Negative Patients with Temporal Lobe Epilepsy,” Seizure, Vol. 17, No. 6, 2008, pp. 490-497. http://dx.doi.org/10.1016/j.seizure. 2008.01.008
[8]	S. Kresic-Juric, D. Madej and S. Fadil, “Applications of Hidden Markov Models in Bar Code Decoding,” International Journal of Pattern Recognition Letters, Vol. 27, No. 14, 2006, pp. 1665-1672.
[9]	G. Markus, Essam A. EI-Kwae and R. K. Mansur, “Edge Detection in Medical Images Using a Genetic Algorithm,” IEEE Transactions on Medical Imaging, Vol. 17, No. 3, 1998, pp. 469-474.
[10]	M. Wang and Y. Shuyuan, “A Hybrid Genetic Algorithm Based Edge Detection Method for SAR Image,” IEEE Proceedings of the Radar Conference’05, 9-12 May 2005, pp. 1503-506.
[11]	A. El-Zaart, “A Novel Method for Edge Detection Using 2 Dimensional Gamma Distribution,” Journal of Computing Science, Vol. 6, No. 2, 2010, pp. 199-204.
[12]	M. A. El-Sayed, “A New Algorithm Based Entropic Threshold for Edge Detection in Images,” International Journal of Computer Science Issues (IJCSI), Vol. 8, No. 5, 2011, pp. 71-78.
[13]	V. Aurich and J. Weule, “Nonlinear Gaussian Filters Performing Edge Preserving Diffusion,” Proceeding of the 17th Deutsche Arbeitsgemeinschaft für Mustererkennung (DAGM) Symposium, Bielefeld, 13-15 September 1995, Springer-Verlag, pp. 538-545.
[14]	M. Basu, “A Gaussian Derivative Model for Edge Enhancement,” Pattern Recognition, Vol. 27, No. 11, 1994, pp. 1451-1461.
[15]	G. Deng and L. W. Cahill, “An Adaptive Gaussian Filter for Noise Reduction and Edge Detection,” Proceeding of the IEEE Nuclear Science Symposium and Medical Imaging Conference, San Francisco, 31 October-6 November 1993, IEEE Xplore Press, pp. 1615-1619.
[16]	C. Kang and W. Wang, “A Novel Edge Detection Method Based on the Maximizing Objective Function,” Pattern Recognition, Vol. 40, No. 2, 2007, pp. 609-618.
[17]	Q. Zhu, “Efficient Evaluations of Edge Connectivity and Width Uniformity,” Image Vision Computing, Vol. 14, No. 1, 1996, pp. 21-34.
[18]	B. Mitra, “Gaussian Based Edge Detection Methods—A Survey,” IEEE Transactions on Systems, Man and Cybernetics, Vol. 32, No. 3, 2002, pp. 252-260.
[19]	J. F. Canny, “A Computational Approach to Edge Detection,” IEEE Transactions on Pattern Analysis and Machine Intelligence (IEEE TPAMI), Vol. 8, No. 6, 1986, pp. 769-798.
[20]	N. Senthilkumaran and R. Rajesh, “Edge Detection Techniques for Image Segmentation—A Survey,” Proceedings of the International Conference on Managing Next Generation Software Applications (MNGSA-08), 2008, pp. 749-760.
[21]	K. W. Bowyer, C. Kranenburg and S. Dougherty, “Edge Detector Evaluation Using Empirical ROC Curves,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 1999, pp. 354-359.
[22]	M. Heath, S. Sarkar, T. Sanocki and K. W. Bowyer, “A Robust Visual Method for Assessing the Relative Performance of Edge Detection Algorithms,” IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI), Vol. 19, No. 12, 1997, pp. 1338-1359. http://dx.doi.org/10.1109/34.643893
[23]	M. Shin, D. Goldgof and K. W. Bowyer, “An Objective Comparison Methodology of Edge Detection Algorithms for Structure from Motion Task,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 1998, pp. 190-195.
[24]	R. Deriche, “Using Canny’s Criteria to Derive a Recursively Implemented Optimal Edge Detector,” International Journal of Computer Vision (IJCV), Vol. 1, No. 2, 1987, pp. 167-187. http://dx.doi.org/10.1007/BF00123164
[25]	C. E. Shannon, “A Mathematical Theory of Communication,” Bell System Technical Journal, Vol. 27, No. 3, 1948, pp. 379-423. http://dx.doi.org/10.1002/j.1538-7305.1948.tb01338.x
[26]	A. P. S. Pharwaha and B. Singh, “Shannon and Non-Shannon Measures of Entropy for Statistical Texture Feature Extraction in Digitized Mammograms,” Proceedings of the World Congress on Engineering and Computer Science (WCECS), San Francisco, Vol. II, 20-22 October 2009.
[27]	C. Tsallis, “Possible Generalization of Boltzmann-Gibbs Statistics,” Journal of Statistical Physics, Vol. 52, No. 1-2, 1988, pp. 479-487. http://dx.doi.org/10.1007/BF01016429
[28]	M. P. de Albuquerque, I. A. Esquef and A. R. Gesualdi Mello, “Image Thresholding Using Tsallis Entropy,” Pattern Recognition Letters, Vol. 25, No. 9, 2004, pp. 1059-1065. http://dx.doi.org/10. 1016/j.patrec.2004.03.003
[29]	B. Singh and A. P. Singh, “Edge Detection in Gray Level Images Based on the Shannon Entropy,” Journal of Computing Science, Vol. 4, No. 3, 2008, pp. 186-191. http://dx.doi.org/10.3844/jcssp. 2008.186.191