Adaptive sparse regularized fuzzy clustering noise image segmentation algorithm based on complementary spatial information

The Fuzzy C-means clustering (FCM) algorithm has gained prominence as a widely utilized technique for data partitioning and image segmentation in various applications. Nevertheless, it exhibits certain limitations in its current form, primarily in its inability to effectively incorporate spatial information from images and its diminished robustness and accuracy when confronted with noisy image data. This paper proposes an adaptive sparse regularization FCM algorithm for noisy image segmentation based on complementary spatial information. Firstly, a novel local spatial operation based on the non-averaging idea and a novel non-local spatial operation based on wavelet transform are proposed. Combining these two kinds of spatial information, we construct the FCM objective function incorporating the complementary spatial information. Secondly, the absolute pixel difference between the original image and the local and non-local information is computed, using the absolute difference and its inverse to achieve adaptation computation of critical parameters. Finally, the sparse regularization term is introduced into the objective function of FCM, which reduces the number of iterations of the algorithm. In addition, we also designed a three-step iterative algorithm to solve the sparse regularization-based FCM model, which consists of a Lagrange multiplier method, a hard threshold operator, and a normalization operator, respectively. Numerous experiments on synthetic images and authentic images on the BSDS500 dataset show that the proposed algorithm is superior to state-of-the-art algorithms. Furthermore, extensive experiments on different types of authentic images on different databases show that the proposed algorithm has good generalization performance and may be applied in most image segmentation situations.