A fast and efficient numerical algorithm for image segmentation and denoising

Yuzi Jin; Soobin Kwak; Seokjun Ham; Junseok Kim; Yuzi Jin; Soobin Kwak; Seokjun Ham; Junseok Kim

doi:10.3934/math.2024243

AIMS Mathematics

2024, Volume 9, Issue 2: 5015-5027. doi: 10.3934/math.2024243

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A fast and efficient numerical algorithm for image segmentation and denoising

1.
Department of Mathematics, Jilin Institute of Chemical Technology, Jilin, 132022, China
2.
Department of Mathematics, Korea University, Seoul, 02841, Republic of Korea

Received: 08 December 2023 Revised: 05 January 2024 Accepted: 18 January 2024 Published: 24 January 2024
MSC : 65M06, 68U10

Image segmentation is the process of partitioning an image into homogenous regions, and represents one of the most fundamental and important procedures in image processing. Image denoising is a process to remove unwanted noise from a digital image, enhancing its visual quality. Various algorithms, like non-local means and deep learning-based approaches, have been developed to remove noise while preserving important image details. Currently, the prevalent application of pattern recognition technology is achieved through the implementation of image segmentation algorithms. In this study, we present a new, highly efficient, and fast computational scheme specifically developed for a phase-field mathematical model of image segmentation. The numerical methodology is based on an operator splitting method (OSM). The split operators are solved by using closed-form analytic solutions and a finite difference method (FDM) with an alternating direction explicit (ADE) method. To show the notable efficiency and rapid computational performance of the proposed computational algorithm, we conduct a series of numerical experiments. Through these computational tests, we confirm a significant contribution to the advancement of methodologies employed in the critical domain of image processing.
- alternating direction explicit method,
- phase-field model,
- image segmentation
Citation: Yuzi Jin, Soobin Kwak, Seokjun Ham, Junseok Kim. A fast and efficient numerical algorithm for image segmentation and denoising[J]. AIMS Mathematics, 2024, 9(2): 5015-5027. doi: 10.3934/math.2024243

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Abstract

Image segmentation is the process of partitioning an image into homogenous regions, and represents one of the most fundamental and important procedures in image processing. Image denoising is a process to remove unwanted noise from a digital image, enhancing its visual quality. Various algorithms, like non-local means and deep learning-based approaches, have been developed to remove noise while preserving important image details. Currently, the prevalent application of pattern recognition technology is achieved through the implementation of image segmentation algorithms. In this study, we present a new, highly efficient, and fast computational scheme specifically developed for a phase-field mathematical model of image segmentation. The numerical methodology is based on an operator splitting method (OSM). The split operators are solved by using closed-form analytic solutions and a finite difference method (FDM) with an alternating direction explicit (ADE) method. To show the notable efficiency and rapid computational performance of the proposed computational algorithm, we conduct a series of numerical experiments. Through these computational tests, we confirm a significant contribution to the advancement of methodologies employed in the critical domain of image processing.

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