The Evaluation of Entropy-based Algorithm towards the Production of Closed-Loop Edge

Cahyo Crysdian - Universitas Islam Negeri Maulana Malik Ibrahim Malang, Indonesia

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This research concerns the common problem of edge detection that produces a disjointed and incomplete edge, leading to the misdetection of visual objects. The entropy-based algorithm can potentially solve this problem by classifying the pixel belonging to which objects in an image. Hence, the paper aims to evaluate the performance of entropy-based algorithm to produce the closed-loop edge representing the formation of object boundary. The research utilizes the concept of Entropy to sense the uncertainty of pixel membership to the existing objects to classify pixels as the edge or object. Six entropy-based algorithms are evaluated, i.e., the optimum Entropy based on Shannon formula, the optimum of relative-entropy based on Kullback-Leibler divergence, the maximum of optimum entropy neighbor, the minimum of optimum relative-entropy neighbor, the thinning of optimum entropy neighbor, and the thinning of optimum relative-entropy neighbor. The experiment is held to compare the developed algorithms against Canny as a benchmark by employing five performance parameters, i.e., the average number of detected objects, the average number of detected edge pixels, the average size of detected objects, the ratio of the number of edge pixel per object, and the average of ten biggest sizes. The experiment shows that the entropy-based algorithms significantly improve the production of closed-loop edges, and the optimum of relative-entropy neighbor based on Kullback-Leibler divergence becomes the most desired approach among others due to the production of more considerable closed-loop edge in the average. This finding suggests that the entropy-based algorithm is the best choice for edge-based segmentation. The effectiveness of Entropy in the segmentation task is addressed for further research. 


entropy; relative-entropy; edge detection; optimal edge; closed-loop edge; edge detector evaluation

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G. Papari and N. Petkov, “Edge and line oriented contour detection: State of the art,” Image and Vision Computing, vol. 29, no. 2–3. Elsevier Ltd, pp. 79–103, 2011. doi: 10.1016/j.imavis.2010.08.009.

J. Gimenez, J. Martinez, and A. G. Flesia, “Unsupervised edge map scoring: A statistical complexity approach,” Computer Vision and Image Understanding, vol. 122, pp. 131–142, 2014, doi: 10.1016/j.cviu.2014.02.005.

T. Lelore and F. Bouchara, “FAIR: A fast algorithm for document image restoration,” IEEE Trans Pattern Anal Mach Intell, vol. 35, no. 8, pp. 2039–2048, 2013, doi: 10.1109/TPAMI.2013.63.

A. K. Bharodiya and A. M. Gonsai, “An improved edge detection algorithm for X-Ray images based on the statistical range,” Heliyon, vol. 5, no. 10, Oct. 2019, doi: 10.1016/j.heliyon.2019.e02743.

C. Crysdian, “Performance measurement without ground truth to achieve optimal edge,” Int J Image Data Fusion, vol. 9, no. 2, pp. 170–193, Apr. 2018, doi: 10.1080/19479832.2017.1384764.

M. Mittal et al., “An efficient edge detection approach to provide better edge connectivity for image analysis,” IEEE Access, vol. 7, pp. 33240–33255, 2019, doi: 10.1109/ACCESS.2019.2902579.

I. Tabiai et al., “Hybrid image processing approach for autonomous crack area detection and tracking using local digital image correlation results applied to single-fiber interfacial debonding,” Eng Fract Mech, vol. 216, Jul. 2019, doi: 10.1016/j.engfracmech.2019.106485.

O. Li and P. L. Shui, “Noise-robust color edge detection using anisotropic morphological directional derivative matrix,” Signal Processing, vol. 165, pp. 90–103, Dec. 2019, doi: 10.1016/j.sigpro.2019.06.036.

V. Roth and T. Vetter, Eds., Pattern Recognition, vol. 10496. in Lecture Notes in Computer Science, vol. 10496. Cham: Springer International Publishing, 2017. doi: 10.1007/978-3-319-66709-6.

W. Yang, W. Wu, X. D. Chen, X. Tao, and X. Mao, “How to use extra training data for better edge detection?,” Applied Intelligence, 2023, doi: 10.1007/s10489-023-04587-4.

Y. Lu, C. He, Y. F. Yu, G. Xu, H. Zhu, and L. Deng, “Vector co-occurrence morphological edge detection for colour image,” IET Image Process, vol. 15, no. 13, pp. 3063–3070, Nov. 2021, doi: 10.1049/ipr2.12290.

K. Park, M. Chae, and J. H. Cho, “Image pre-processing method of machine learning for edge detection with image signal processor enhancement,” Micromachines (Basel), vol. 12, no. 1, pp. 1–13, Jan. 2021, doi: 10.3390/mi12010073.

“2020 Cao et al - Learning Crisp Boundaries Using Deep Refinement Network”.

T. Brosch, J. Peters, A. Groth, T. Stehle, and J. Weese, “Deep Learning-Based Boundary Detection for Model-Based Segmentation with Application to MR Prostate Segmentation,” in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Springer Verlag, 2018, pp. 515–522. doi: 10.1007/978-3-030-00937-3_59.

A. Shiozaki, “Edge Extraction Using Entropy Operator,” 1986.

J. Barba, H. Jeanty, P. Fenster, and J. Gil, “The use of local entropy measures in edge detection for cytological image analysis,” J Microsc, vol. 156, no. 1, pp. 125–134, 1989, doi: 10.1111/j.1365-2818.1989.tb02911.x.

F. Hržić, I. Štajduhar, S. Tschauner, E. Sorantin, and J. Lerga, “Local-entropy based approach for X-ray image segmentation and fracture detection,” Entropy, vol. 21, no. 4, Apr. 2019, doi: 10.3390/e21040338.

E. SERT and D. AVCI, “A new edge detection approach via neutrosophy based on maximum norm entropy,” Expert Syst Appl, vol. 115, pp. 499–511, Jan. 2019, doi: 10.1016/j.eswa.2018.08.019.

J. Martínez-Aroza, J. F. Gómez-Lopera, D. Blanco-Navarro, and J. Rodríguez-Camacho, “Clustered entropy for edge detection,” Math Comput Simul, vol. 182, pp. 620–645, Apr. 2021, doi: 10.1016/j.matcom.2020.11.021.

C. E. Shannon, “A Mathematical Theory of Communication.”


S. Kullback and R. A. Leibler, “ON INFORMATION AND SUFFICIENCY,” 1951.

Z. Wang, E. Wang, and Y. Zhu, “Image segmentation evaluation: a survey of methods,” Artif Intell Rev, vol. 53, no. 8, pp. 5637–5674, Dec. 2020, doi: 10.1007/s10462-020-09830-9.

F. Knoll et al., “FastMRI: A publicly available raw k-space and DICOM dataset of knee images for accelerated MR image reconstruction using machine learning,” Radiol Artif Intell, vol. 2, no. 1, Jan. 2020, doi: 10.1148/ryai.2020190007.

Z. Cai, Y. Liang, and H. Huang, “Unsupervised segmentation evaluation: an edge-based method,” Multimed Tools Appl, vol. 76, no. 8, pp. 11097–11110, Apr. 2017, doi: 10.1007/s11042-016-3542-8.

S. J. Mousavirad, H. Ebrahimpour-Komleh, and G. Schaefer, “Automatic clustering using a local search-based human mental search algorithm for image segmentation,” Applied Soft Computing Journal, vol. 96, Nov. 2020, doi: 10.1016/j.asoc.2020.106604.

A. Pemasiri, K. Nguyen, S. Sridharan, and C. Fookes, “Multi-modal semantic image segmentation,” Computer Vision and Image Understanding, vol. 202, Jan. 2021, doi: 10.1016/j.cviu.2020.103085.

H. Abdulrahman, B. Magnier, and P. Montesinos, “From contours to ground truth: How to evaluate edge detectors by filtering,” 2017. [Online]. Available:

B. Magnier, “Edge detection: a review of dissimilarity evaluations and a proposed normalized measure Edge detection: a review of dissimilarity evaluations and a proposed normalized measure: review. Multimedia Tools and Applications Edge Detection: A Review of Dissimilarity Evaluations and a Proposed Normalized Measure,” JOURNAL : MULTIMEDIA TOOLS AND APPLICATIONS, vol. 77, no. 8, pp. 1–45, 2018, doi: 10.1007/s11042-017-5127-6ï.

Nagarjuna College of Engineering and Technology and Institute of Electrical and Electronics Engineers, 2019 Global Conference for Advancement in Technology (GCAT) : Bangalore, India, Oct 18-20, 2019.