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Article

A New Class of Edge Filter Based on a Cross-correlation-like Equation Derived from Fractional Calculus Principles

by
Mario Gonzalez-Lee
1,*,
Hector Vazquez-Leal
2,
Jose R. Garcia-Martinez
1,
Eli G. Pale-Ramon
3,
Luis J. Morales-Mendoza
1,
Mariko Nakano-Miyatake
4 and
Hector Perez-Meana
4
1
Facultad de Ingeniería en Electrónica y Comunicaciones, Universidad Veracruzana, Av. Venustiano Carranza S/N, Poza Rica Veracruz 93390, Mexico
2
Facultad de Instrumentacion Electronica, Universidad Veracruzana, Cto. Gonzalo Aguirre Beltrán S/N, Xalapa 91000, Mexico
3
Department of Electronics Engineering, Universidad de Guanajuato, Salamanca 36885, Mexico
4
Seccion de Estudios de Posgrado e Investigacion, Instituto Politécnico Nacional, Av. Santa Ana No. 1000, Del. Coyoacan, Ciudad de Mexico 04440, Mexico
*
Author to whom correspondence should be addressed.
Appl. Sci. 2024, 14(13), 5428; https://doi.org/10.3390/app14135428
Submission received: 23 May 2024 / Revised: 14 June 2024 / Accepted: 17 June 2024 / Published: 22 June 2024
(This article belongs to the Special Issue Digital Image Processing: Technologies and Applications)

Abstract

In this paper, we propose a new sliding window edge-oriented filter that computes the output pixels using a cross-correlation-like equation derived from the principles of fractional calculus (FC); thus, we call it the “fractional cross-correlation filter” (FCCF). We assessed the performance of this filter utilizing exclusively edge-preservation-oriented metrics such as the gradient conduction mean square error (GCMSE), the edge-based structural similarity (EBSSIM), and the multi-scale structural similarity (MS-SSIM); we conducted a statistical assessment of the performance of the filter based on those metrics by using the Berkeley segmentation dataset benchmark as a test corpus. Experimental data reveal that our approach achieves higher performance compared to conventional edge filters for all the metrics considered in this study. This is supported by the statistical analysis we carried out; specifically, the FCCF demonstrates a consistent enhancement in edge detection. We also conducted additional experiments for determining the main filter parameters, which we found to be optimal for a broad spectrum of images. The results underscore the FCCF’s potential to make significant contributions to the advancement of image processing techniques since many practical applications such as medical imaging, image enhancement, and computer vision rely heavily on edge detection filters.
Keywords: edge filter; fractional calculus; filtering model edge filter; fractional calculus; filtering model

Share and Cite

MDPI and ACS Style

Gonzalez-Lee, M.; Vazquez-Leal, H.; Garcia-Martinez, J.R.; Pale-Ramon, E.G.; Morales-Mendoza, L.J.; Nakano-Miyatake, M.; Perez-Meana, H. A New Class of Edge Filter Based on a Cross-correlation-like Equation Derived from Fractional Calculus Principles. Appl. Sci. 2024, 14, 5428. https://doi.org/10.3390/app14135428

AMA Style

Gonzalez-Lee M, Vazquez-Leal H, Garcia-Martinez JR, Pale-Ramon EG, Morales-Mendoza LJ, Nakano-Miyatake M, Perez-Meana H. A New Class of Edge Filter Based on a Cross-correlation-like Equation Derived from Fractional Calculus Principles. Applied Sciences. 2024; 14(13):5428. https://doi.org/10.3390/app14135428

Chicago/Turabian Style

Gonzalez-Lee, Mario, Hector Vazquez-Leal, Jose R. Garcia-Martinez, Eli G. Pale-Ramon, Luis J. Morales-Mendoza, Mariko Nakano-Miyatake, and Hector Perez-Meana. 2024. "A New Class of Edge Filter Based on a Cross-correlation-like Equation Derived from Fractional Calculus Principles" Applied Sciences 14, no. 13: 5428. https://doi.org/10.3390/app14135428

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