Accurate boundary segmentation is critical for high-stakes applications such as disease diagnosis, yet remains challenging due to complex topology, boundary ambiguity, and annotation uncertainty. Diffusion Probabilistic Models (DPMs) generate multiple masks with inherent uncertainty, enhancing boundary delineation compared to deterministic models. However, most existing DPM based segmentation approaches learn discrete binary masks, conflicting with the continuous diffusion process and leading to hard-to-learn degradation during noise addition. Moreover, the prevailing approach of averaging stochastic predictions and applying a fixed threshold disregards structural consistency, often leading to imprecise boundaries, isolated artifacts, and holes. To address these challenges, we propose the $L$ evel $S$ et $R$ epresentation $D$ iffusion model (LSR-Diff), which incorporates a diffusion model with a hybrid mask representation to better capture boundary information, and a novel strategy $E$ nsemble $A$ ggregation via Level $S$ et $E$ volution (EASE) to merge prediction candidates while respecting structural information. The hybrid representation takes advantage of both discrete binary masks and continuous implicit masks, with an intermediate representation to ensure a smooth transition. The EASE module guided by ambiguity estimation and anatomical structure then refines boundary topology, preventing arbitrary mask assembly during the aggregation of stochastic predictions. We conduct extensive experiments across various clinical applications including multiple modalities and tissues, showing that LSR-Diff achieves competitive overall performance and improved edge quality and topology accuracy on the tested tasks.

Multi-organ segmentation in medical image analysis is crucial for diagnosis and treatment planning. However, many factors complicate the task, including variability in different target categories and interference from complex backgrounds. In this paper, we utilize the knowledge of Deformable Convolution V3 (DCNv3) and multi-object segmentation to optimize our Spatially Adaptive Convolution Network (SACNet) in three aspects: feature extraction, model architecture, and loss constraint, simultaneously enhancing the perception of different segmentation targets. Firstly, we propose the Adaptive Receptive Field Module (ARFM), which combines DCNv3 with a series of customized block-level and architecture-level designs similar to transformers. This module can capture the unique features of different organs by adaptively adjusting the receptive field according to various targets. Secondly, we utilize ARFM as building blocks to construct the encoder-decoder of SACNet and partially share parameters between the encoder and decoder, making the network wider rather than deeper. This design achieves a shared lightweight decoder and a more parameter-efficient and effective framework. Lastly, we propose a novel continuity dynamic adjustment loss function, based on t-vMF dice loss and cross-entropy loss, to better balance easy and complex classes in segmentation. Experiments on 3D slice datasets from Synapse demonstrate that SACNet delivers superior segmentation performance in multi-organ segmentation tasks compared to several existing methods.

Various kinds of heart diseases pose a serious threat to human health. To effectively treat and prevent these diseases, accurate segmentation of the entire heart structure is crucial for medical research and application. At present, the solution to this problem still needs to rely on a lot of manpower. Not only is this time-consuming, but accuracy is sometimes difficult to guarantee. In the deep learning methods for medical image segmentation, large labeled images are difficult to obtain. Typically, the large databases have several thousand images, of which only a few hundred have been annotated, and the number of individual patients is even smaller. In this article, we focus on a small part of the dataset to minimize the cost of manual labeling and maximize the accurate segmentation results. The small part of the dataset contains more representative and informative images, avoiding doctors to repeatedly label images with similar information. We proposed a balanced distribution active learning (BDAL) framework for MRI cardiac multistructures segmentation based on reinforcement learning. The deep Q-network framework can learn an effective policy to select some informative and representative images to be labeled from a large number of the unlabeled dataset. We consider the shape features of images and the balance of different class distributions to build new state and action representation, which can help the agent to identify informative and representative images for annotation. Our BDAL method provides an agent to improve the ability of AL to select images to improve the accuracy of segmentation. Moreover, experiments and results show that our BDAL method significantly outperforms all baselines and other AL-based methods under the same amount of annotation budget on MRI cardiac multistructures segmentation in datasets$\mathbf {ACDC}$and$\mathbf {M \& Ms}$.

Medical images often exhibit intricate structures, inhomogeneous intensity, significant noise and blurred edges, presenting challenges for medical image segmentation. Several segmentation algorithms grounded in mathematics, computer science, and medical domains have been proposed to address this matter; nevertheless, there is still considerable scope for improvement. This paper proposes a novel adaptive anatomical structure-based two-layer level set framework (AS2LS) for segmenting organs with concentric structures, such as the left ventricle and the fundus. By adaptive fitting region and edge intensity information, the AS2LS achieves high accuracy in segmenting complex medical images characterized by inhomogeneous intensity, blurred boundaries and interference from surrounding organs. Moreover, we introduce a novel two-layer level set representation based on anatomical structures, coupled with a two-stage level set evolution algorithm. Experimental results demonstrate the superior accuracy of AS2LS in comparison to representative level set methods and deep learning methods.

Although generative models are still being developed, image reconstruction and generation tasks have evolved dramatically. Since the most popular generative models still have some limitations, it is still challenging. For example, while generative adversarial network (GAN) produces clear images, it is hard to train. The hybrid VAE-GAN incorporates the benefits of both, although it is computationally intensive and prone to drawbacks such as overfitting and gradient disappearance. A novel generative model called the Cauchy-Schwarz Divergence-based Introspective Variational Autoencoder (CS-IntroVAE) is based for this challenge. Extensive experiments show that our model has good performance on both tasks by employing mixed Gaussian distributions as prior distributions and Cauchy-Schwarz divergence as a measure of the distance between prior and posterior distributions. The source code is available at https://github.com/CoderSnack/CS-IntroVAE .

Recently, deep learning (DL) is widely used to detect physical phenomena and has obtained encouraging results. Several works have shown that it can learn quantum phenomenon. Subsequently, quantum machine learning (QML) has been paid more attention by academia and industry. Quantum drift-diffusion (QDD) is a commonplace physical phenomenon, which is a macroscopic description of electrons and holes in a semiconductor. They are commonly used to attain an understanding of the property of semiconductor devices in physics and engineering. We are motivated by the relaxation-time limit from the quantum-Navier-Stokes-Poisson system (QNSP) to the QDD equation and the existence of finite energy weak solutions to the QDD equation has been proved. Therefore, in this work, the quantum drift-diffusion learning neural network (QDDLNN) is proposed to investigate the quantum drift phenomena from limited observations. Furthermore, a piece of numerical evidence is found that the NNs can describe quantum transport phenomena by simulating the quantum confinement transport equation-quantum Navier-Stokes equation.

Under the background of the wanton spread of the coronavirus disease (COVID-19), the pandemic is changing and hitting lives all over the world. Fortunately, Spatio-temporal processes bear essential importance in many applied scientific fields. And the disease pandemic can be viewed as Spatio-temporal dynamics processes. Generally, partial differential equations (PDEs) have been widely used to investigate interfacial dynamic processes. In this work, we use a physical-constraint neural network learning the Spatio-temporal mean-field dynamics to control the propagation of epidemics. Also, we use the AI-based algorithm physical-constraint learning (PCL) to solve the minimization problems of the mean-field game (MFG) and control (MFC) problems instead of the traditional computational method. In PCL, the PDEs are encoded into the loss function, where partial derivatives can be obtained through automatic differentiation (AD). We demonstrate how they can be applied in practice by considering the problem of controlling the propagation of epidemics. Numerical experiments on different input data are implemented to demonstrate the effectiveness and superiority of the proposed models compared to the state-of-the-art approach and illustrate how to separate the infected patients in a spatial domain effectively.

Accurate segmentation of medical images plays a very important role in clinical diagnosis so that the segmentation technology for medical images attracts more and more attention. However, most medical images usually suffer from severe intensity inhomogeneity and make accurate segmentation difficult. In this study, the authors propose an efficient and robust active contour model for simultaneous image segmentation and correction. The proposed model not only can accurately segment images with severe intensity inhomogeneity and serious noise but also can eliminate the intensity varying information to get the homogeneous correction images. They first present the level set formulation of the two‐phase model, which is then extended to the multi‐phase formulation. The split Bregman method is applied to efficiently minimise the proposed energy functionals. The proposed model is tested with lots of synthetic images and medical images with promising results. Experimental results demonstrate that the proposed model can accurately segment and correct the inhomogeneous images with serious noise. Quantitative comparison results of the proposed model and other models illustrate the proposed model is more accurate and more efficient. What's more, the proposed model not only is insensitive to the initial contour, but also is robust to the noise.

Magnetic resonance (MR) images have great importance to assist doctors in diagnosing diseases, however, the long MR images scan duration remains the primary obstacle in clinical medicine. Compressed sensing reconstructed technique in MR imaging (CS‐MRI) makes it possible to reconstruct a faithful MR image from very few measurements data, which helps to reduce the scan time. The purpose of this study is to improve the accuracy and efficiency of the CS‐MRI. The authors propose a fast compressed sensing reconstruction model for MR images that can alleviate the aliasing artefacts that come from the reconstruction process by jointly minimising a total variation term, a fitting data term and a median filter term. Moreover, they accelerate the proposed algorithm by applying the split Bregman method to solve the proposed model. Then, the proposed model is applied to reconstruct a large number of MR images. They also compare the performance of the proposed model with another model. It can be observed from the experimental results that the proposed model has shown higher precision in reconstructing image quality and much more efficiency than the other one. Additionally, they also give a discussion on how to choose proper parameters in the proposed model to obtain more satisfactory results.

This study proposes a new method for simultaneous image segmentation and moderate bias correction. Though many methods are proposed to deal with the image intensity inhomogeneity, some problems still exist and have influenced the segmentation results a lot. In this study, a new model is proposed for image segmentation and correction based on the multiplicative intrinsic component optimization (MICO) model. First, the new model in the level set formulation for gray images has been presented and the split Bregman method for fast minimization has been applied. The proposed model is tested with lots of magnetic resonance images and some medical colour images with promising results. Experimental results show that the proposed model can simultaneously segment images and correct bias field moderately. In the experimental part for gray images, a qualitative comparison between the proposed model and the MICO model in both segmentation and bias‐correction results is made. Besides, the proposed model with the Chan‐Vese model and the illumination and reflectance estimation model in the experimental part for colour images are compared. Moreover, the proposed model can segment nature colour images successfully. It is clear that the proposed model has a good performance on many characteristics such as accuracy, efficiency, and robustness.

We present an efficient multi-atlas segmentation and correction model with level set formulation for 3D brain MR images in this paper. We define a new energy functional by combining a weighted label fusion term, a bias field based image information fitting term and a regularization term together. More image information is taken into consideration in the new image data term to substantially improve the segmentation accuracy, especially when serious inhomogeneity and bias field exist in regions of interest in MR images. We introduce a spatially weight function and incorporate it into the label fusion term to increase the robustness of our segmentation algorithm to atlases with different registration accuracy. The new energy functional is in the form of L1 regularization problems, and we minimize it with the split Bregman method to ensure the segmentation efficiency. We apply the proposed model to segment six tissues in 3D brain MR images, including the amygdala, caudate, hippocampus, pallidum, putamen and thalamus. Experimental results have shown that our model can segment regions of interest accurately and eliminate bias field simultaneously. Quantitative comparisons with related methods have demonstrated the superiority of our model in terms of accuracy, efficiency and robustness.

This paper presents an improved active contour model for fast multiphase image segmentation based on the piecewise constant Vese-Chan model and the split Bregman method. We first define a new energy functional by applying the globally convex image segmentation technique to the Vese-Chan energy functional and incorporating the edge information with a non-negative edge detector function. Then we apply the split Bregman method to fast minimize the new energy functional. The efficiency of the improved model compared with the Vese-Chan model is demonstrated by experimental results. This is the main advantage of our improved model over the Vese-Chan model.

In this paper we propose an efficient multi-phase image segmentation for color images based on the piecewise constant multi-phase Vese-Chan model and the split Bregman method. The proposed model is first presented in a four-phase level set formulation and then extended to a multi-phase formulation. The four-phase and multi-phase energy functionals are defined and the corresponding minimization problems of the proposed active contour model are presented. The split Bregman method is applied to minimize the multi-phase energy functional efficiently. The proposed model has been applied to synthetic and real color images with promising results. The advantages of the proposed active contour model have been demonstrated by numerical results.

In this paper, we propose an efficient active contour model for multiphase image segmentation in a variational level set formulation. By incorporating the globally convex segmentation idea and the split Bregman method into the multiphase formulation of the local and global intensity fitting energy model, our new model improved the original local and global intensity fitting energy model in the following aspects. First, we propose a new energy functional using the globally convex segmentation method to guarantee fast convergence. Second, we incorporate information from the edge into the energy functional by using a non-negative edge detector function to detect boundaries more easily. Third, instead of a constant value to control the influence of the local and global intensity fitting terms, we use a weight function varying with the locations of the image to balance the weights between the local and the global fitting terms dynamically. Lastly, the special structure of our energy functional enables us to apply the split Bregman method to minimize the energy much more efficiently. We have applied our model to synthetic images and real brain MR images with promising results. Experimental results demonstrate the efficiency and superiority of our model.