Mathematics driven methods with fractional calculus and topological data analysis in image segmentation

Jain, Tarun; Joshi, Aditya; Keswani, Arul; Kumar, Ajay; Dadheech, Pankaj

doi:10.47974/JIM-2107

Open Access Research Article

Mathematics driven methods with fractional calculus and topological data analysis in image segmentation

Tarun Jaintarunjainjain02@gmail.comDepartment of Computer Science EngineeringManipal University JaipurJaipur, Rajasthan, IndiaView full profile → , Aditya Joshiajoshi2002@gmail.comDepartment of Computer Science EngineeringManipal University JaipurJaipur, Rajasthan, IndiaView full profile → , Arul Keswaniarulkeswani1905@gmail.comDepartment of Computer Science EngineeringManipal University JaipurJaipur, Rajasthan, IndiaView full profile → , ^*Ajay KumarCorresponding authordr.ajaykr0088@gmail.comDepartment of Computer Science EngineeringManipal University JaipurJaipur, Rajasthan, IndiaView full profile → , Pankaj Dadheechpankajdadheech777@gmail.comDepartment of Computer Science and EngineeringSwami Keshvanand Institute of Technology, Management and GramothanJaipur, Rajasthan, IndiaView full profile →

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pp. 637–646Vol. 28Issue 2March 2025DOI: 10.47974/JIM-2107XML

Received:: 08 Feb 2024
Published Online:: 15 Mar 2025
Article type:: Research Article
Language:: EN
Article no.:: JIM-2107
Pages:: 637–646

Abstract

This research paper introduces a novel mathematical model that integrates fractional calculus with topological data analysis (TDA) for image segmentation. Fractional calculus, which extends the concept of derivatives and integrals to arbitrary orders, effectively addresses the non-local and hereditary properties of images, capturing textures and patterns across various scales and complexities. TDA, utilizing robust tools for identifying shape and connectivity features, complements this by capturing intricate topological characteristics often overlooked by traditional segmentation methods. Leveraging persistent homology, a core concept in TDA, the model classifies, and segments image regions based on their topological features, which remain invariant under deformations such as bending and stretching. This integrated approach aims to enhance the accuracy and reliability of image segmentation, offering a significant advancement over existing methods.

Keywords

Fractional calculus Topological data analysis Image segmentation Persistent homology Mathematical modeling in image processing Advanced edge detection

Subject Classifications

Primary 65A05Secondary 26C10

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