Abstract The variational level set model has been widely used in image segmentation. However, its performance is significantly hindered by bias fields and noise within the images. To address these limitations, we introduce a novel hybrid variational level set model based on dual Gaussian distribution fitting (DGDF) energy in this paper. The DGDF energy integrates both local and global Gaussian distributions. The local energy is derived from the original image, while the global energy employs the corrected image, enabling effective segmentation of images with intensity inhomogeneity. Furthermore, the model demonstrates low sensitivity to weighting parameters and robust performance for noisy images. We develop an alternating iteration algorithm that combines variational methods with gradient descent to efficiently solve the proposed model. Experimental results validate the effectiveness of the model and the algorithm. In addition, the proposed model shows competitiveness on test images and three datasets compared to several state‐of‐the‐art models, including other variational level set models and deep learning‐based techniques.

Abstract Active contour based methods are effective models for image segmentation. However, they always suffer from the limited performance due to the presence of noise and intensity inhomogeneity. To solve this problem, a kernel metric induced local image fitting (KLIF) variational model is proposed in this paper. Firstly, a kernel metric induced local fitting image (KLFI) is introduced by minimising a kernel metric based energy. The combination of the kernel metric and the local fitting image enables the model to be more robust to the noise and intensity inhomogeneity. And then, using the KLFI, a variational level set model that is a squared l 2 distance between the KLFI and the original image is constructed. Two regularisation terms are employed in the model to keep the level set function to be stable during the evolution. At last, an alternating iterative algorithm combining with fixed‐point iteration and gradient descent of three‐step time‐splitting is introduced to solve the proposed model. The experimental results show the effectiveness of the proposed model for image segmentation in the presence of noise and intensity inhomogeneity, and demonstrate the competitive performance over several state‐of‐the‐art variational models in term of accuracy and robustness.

Abstract A non‐convex ternary variational decomposition model is proposed in this study, which decomposes the image into three components including structure, texture and noise. In the model, a non‐convex total variation (NTV) regulariser is utilised to model the structure component, and the weaker G and E spaces are used to model the texture and noise components, respectively. The proposed model provides a very sparse representation of the structure in total variation (TV) transform domain due to the use of non‐convex regularisation and cleanly separates the texture and noise since two different weaker spaces are used to model these two components, respectively. In image denoising application, the proposed model can successfully remove noise while effectively preserving image edges and constructing textures. An alternating direction iteration algorithm combining with iteratively reweighted l 1 algorithm, projection algorithm and wavelet soft threshold algorithm is introduced to effectively solve the proposed model. Numerical results validate the model and the algorithm for both synthetic and real images. Furthermore, compared with several state‐of‐the‐art image variational restoration models, the proposed model yields the best performance in terms of the peak signal to noise ratio (PSNR) and the mean structural similarity index (SSIM).

Belief propagation (BP) algorithm still exists some shortages, such as inaccurate edge preservation and ambiguous detail information in the foreground, while self-adapting dissimilarity measure (SDM) also exists some shortages, such as ill textureless and occluded information in the background. To address these problems, we present a novel stereo matching algorithm fusing BP and SDM with an excellent background and foreground information. Lots of experiments show that BP and SDM can complement each other. BP algorithm can hold the better background information due to message propagation inference, whereas SDM can possess the better foreground information due to detail treatment. Therefore, a piecewise function is proposed, which can combine BP algorithm in an excellent background information and SDM in the foreground information, and greatly improve the disparity effect as a whole. We also expect that this work can attract more attention on combination of local methods and global methods, due to its simplicity, efficiency, and accuracy. Experimental results show that the proposed method can keep the superior performance and hold better background and foreground on the Middlebury datasets, compared to BP and SDM.