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In the realm of digital image applications, image processing technology occupies a pivotal position, with image segmentation serving as a foundational component. As the digital image application domain expands across industries, the conventional segmentation techniques increasingly challenge to cater to modern demands. To address this gap, this paper introduces an MCMC-based image segmentation algorithm based on the Markov Random Field (MRF) model, marking a significant stride in the field. The novelty of this research lies in its method that capitalizes on domain information in pixel space, amplifying the local segmentation precision of image segmentation algorithms. Further innovation is manifested in the development of an adaptive segmentation image denoising algorithm based on MCMC sampling. This algorithm not only elevates image segmentation outcomes, but also proficiently denoises the image. In the experimental results, MRF-MCMC achieves better segmentation performance, with an average segmentation accuracy of 94.26% in Lena images, significantly superior to other common image segmentation algorithms. In addition, the study proposes that the denoising model outperforms other algorithms in peak signal-to-noise ratio and structural similarity in environments with noise standard deviations of 15, 25, and 50. In essence, these experimental findings affirm the efficacy of this study, opening avenues for refining digital image segmentation methodologies. [ABSTRACT FROM AUTHOR]

Kernel fuzzy weighted local information c-means (KWFLICM) algorithm has good segmentation effect in segmenting noisy images, but it can not effectively segment images with low contrast or high noise. The improved algorithm of KWFLICM is a kernel possibilistic fuzzy c-means clustering with local information (KWPFLICM), which has better anti-noise performance. However, this algorithm loses more details of original image when segmenting the image. In this paper, a kernel-based possibilistic fuzzy local information clustering algorithm based on quadratic polynomial is proposed to overcome the shortcomings of KWPFLICM algorithm. At the same time, the local membership information of neighborhood pixels is introduced as the penalty factor to update the local information, so as to further improve the robustness of the algorithm. By optimizing the objective function of modified possibilistic fuzzy local information clustering with quadratic surface centers, the formulas of fuzzy membership, possibilistic typicality, and the coefficients of quadratic polynomial center are derived theoretically, and the convergence of the proposed algorithm is strictly proved by Zangwill theorem and bordered Hessian matrix. Experimental results show that compared with existing state-of-the-art fuzzy clustering-related algorithms, the proposed algorithm has better segmentation performance and stronger anti-noise robustness, and can effectively suppress noise and retain details. It will have far-reaching significance for the development of robust fuzzy clustering segmentation theory. [ABSTRACT FROM AUTHOR]

The possibilistic fuzzy c-means clustering (PFCM) algorithm is a hybridization of possibilistic c-means clustering (PCM) and fuzzy c-means clustering (FCM) algorithms. However, there are two main problems in PFCM. One is that the Euclidean distance employed in PFCM always disregards the imbalance among sample features because it treats all features of data equally, which easily causes misclassification for feature-imbalanced multidimensional data. The other is that PFCM always produces significant center deviations and overlapping centers for multiclass datasets with strong noise injection, due to the difficulty of PFCM in the membership-weight parameter setting and the lack of between-class relationships in possibilistic memberships. Therefore, a feature-weighted suppressed possibilistic fuzzy c-means clustering (FW-S-PFCM) algorithm is presented by introducing a feature-weighted method and "suppressed competitive learning" strategy into the PFCM algorithm in this paper. First, the FW-S-PFCM algorithm introduces a feature-weight matrix into the objective function that can automatically assign feature-weight values to different features and different clusters according to the distribution of samples, thus overcoming the influence of feature imbalance and improving clustering effects for noisy multidimensional datasets. Second, combined with the feature-weight matrix, a "suppressed competitive learning" strategy is designed to resolve the center-overlapping problem in noisy multiclass dataset clustering. Specifically, partial crucial points of each class near the center are selected according to a cluster core generated by a cross-section of a threshold on the possibilistic membership surface. Third, their possibilistic memberships participate in the suppressed learning process to overcome the lack of between-class relationships. Last, a segmentation algorithm for noisy color images based on FW-S-PFCM is proposed combined with the feature-weight method and noise-identification ability of possibilistic memberships. Experiments on synthetic data, UCI data and color image segmentation demonstrate that the proposed FW-S-PFCM algorithm can overcome the partial center-overlapping problem and improve clustering performance on complex datasets with feature imbalance and strong noise injection. The proposed algorithm can also reduce the iteration number, sensitivity to membership weights, and initializations of PFCM. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]