Yuping Duan

Wenxiao Li, Faqiang Wang, Yuping Duan et al.

Topological features play an essential role in ensuring geometric plausibility and structural consistency in image analysis tasks such as segmentation and skeletonization. However, integrating topology-preserving learning based on simple points into deep learning tasks remains challenging, as existing simple point detection methods are confined to binary images and are non-differentiable, rendering them incompatible with gradient-based optimization in modern deep learning. Moreover, morphological and purely data-driven approaches often fail to guaranty topological consistency. To address these limitations, we propose a novel method that directly computes simple points on continuous-valued images, enabling differentiable topological inference. Building on this theory, we develop an efficient skeleton extraction algorithm that preserves topological structures in binary and continuous-valued images. Furthermore, we design a variational model that enforces topological constraints by preserving topologically non-removable (i.e., non-simple) points, which can be seamlessly integrated into any deep neural network segmentation with softmax or sigmoid outputs. Experimental results demonstrate that the proposed approach effectively improves topological integrity and structural accuracy across multiple benchmarks. The codes are available in https://github.com/levnsio/CSP.

Hongkun Sun, Jing Xu, Yuping Duan

The convolutional neural network-based methods have become more and more popular for medical image segmentation due to their outstanding performance. However, they struggle with capturing long-range dependencies, which are essential for accurately modeling global contextual correlations. Thanks to the ability to model long-range dependencies by expanding the receptive field, the transformer-based methods have gained prominence. Inspired by this, we propose an advanced 2D feature extraction method by combining the convolutional neural network and Transformer architectures. More specifically, we introduce a parallelized encoder structure, where one branch uses ResNet to extract local information from images, while the other branch uses Transformer to extract global information. Furthermore, we integrate pyramid structures into the Transformer to extract global information at varying resolutions, especially in intensive prediction tasks. To efficiently utilize the different information in the parallelized encoder at the decoder stage, we use a channel attention module to merge the features of the encoder and propagate them through skip connections and bottlenecks. Intensive numerical experiments are performed on both aortic vessel tree, cardiac, and multi-organ datasets. By comparing with state-of-the-art medical image segmentation methods, our method is shown with better segmentation accuracy, especially on small organs. The code is publicly available on https://github.com/HongkunSun/ParaTransCNN.

Tianle Lu, Ke Chen, Yuping Duan

We introduce a novel formulation for curvature regularization by penalizing normal curvatures from multiple directions. This total normal curvature regularization is capable of producing solutions with sharp edges and precise isotropic properties. To tackle the resulting high-order nonlinear optimization problem, we reformulate it as the task of finding the steady-state solution of a time-dependent partial differential equation (PDE) system. Time discretization is achieved through operator splitting, where each subproblem at the fractional steps either has a closed-form solution or can be efficiently solved using advanced algorithms. Our method circumvents the need for complex parameter tuning and demonstrates robustness to parameter choices. The efficiency and effectiveness of our approach have been rigorously validated in the context of surface and image smoothing problems.

Jingyu Kong, Yuan Guo, Yu Wang et al.

Real-world data often has a long-tailed distribution, where the scarcity of tail samples significantly limits the model's generalization ability. Denoising Diffusion Probabilistic Models (DDPM) are generative models based on stochastic differential equation theory and have demonstrated impressive performance in image classification tasks. However, existing diffusion probabilistic models do not perform satisfactorily in classifying tail classes. In this work, we propose the Anisotropic Diffusion Probabilistic Model (ADPM) for imbalanced image classification problems. We utilize the data distribution to control the diffusion speed of different class samples during the forward process, effectively improving the classification accuracy of the denoiser in the reverse process. Specifically, we provide a theoretical strategy for selecting noise levels for different categories in the diffusion process based on error analysis theory to address the imbalanced classification problem. Furthermore, we integrate global and local image prior in the forward process to enhance the model's discriminative ability in the spatial dimension, while incorporate semantic-level contextual information in the reverse process to boost the model's discriminative power and robustness. Through comparisons with state-of-the-art methods on four medical benchmark datasets, we validate the effectiveness of the proposed method in handling long-tail data. Our results confirm that the anisotropic diffusion model significantly improves the classification accuracy of rare classes while maintaining the accuracy of head classes. On the skin lesion datasets, PAD-UFES and HAM10000, the F1-scores of our method improved by 4% and 3%, respectively compared to the original diffusion probabilistic model.

Bin Li, Li Li, Zhenwei Zhang et al.

Underwater optical images inevitably suffer from various degradation factors such as blurring, low contrast, and color distortion, which hinder the accuracy of object detection tasks. Due to the lack of paired underwater/clean images, most research methods adopt a strategy of first enhancing and then detecting, resulting in a lack of feature communication between the two learning tasks. On the other hand, due to the contradiction between the diverse degradation factors of underwater images and the limited number of samples, existing underwater enhancement methods are difficult to effectively enhance degraded images of unknown water bodies, thereby limiting the improvement of object detection accuracy. Therefore, most underwater target detection results are still displayed on degraded images, making it difficult to visually judge the correctness of the detection results. To address the above issues, this paper proposes a multi-task learning method that simultaneously enhances underwater images and improves detection accuracy. Compared with single-task learning, the integrated model allows for the dynamic adjustment of information communication and sharing between different tasks. Due to the fact that real underwater images can only provide annotated object labels, this paper introduces physical constraints to ensure that object detection tasks do not interfere with image enhancement tasks. Therefore, this article introduces a physical module to decompose underwater images into clean images, background light, and transmission images and uses a physical model to calculate underwater images for self-supervision. Numerical experiments demonstrate that the proposed model achieves satisfactory results in visual performance, object detection accuracy, and detection efficiency compared to state-of-the-art comparative methods.

Xinyu Zhao, Jun Liu, Faqiang Wang et al.

The elliptical shape prior information plays a vital role in improving the accuracy of image segmentation for specific tasks in medical and natural images. Existing deep learning-based segmentation methods, including the Segment Anything Model (SAM), often struggle to produce segmentation results with elliptical shapes efficiently. This paper proposes a new approach to integrate the prior of elliptical shapes into the deep learning-based SAM image segmentation techniques using variational methods. The proposed method establishes a parameterized elliptical contour field, which constrains the segmentation results to align with predefined elliptical contours. Utilizing the dual algorithm, the model seamlessly integrates image features with elliptical priors and spatial regularization priors, thereby greatly enhancing segmentation accuracy. By decomposing SAM into four mathematical sub-problems, we integrate the variational ellipse prior to design a new SAM network structure, ensuring that the segmentation output of SAM consists of elliptical regions. Experimental results on some specific image datasets demonstrate an improvement over the original SAM.

Yijie Yang, Qifeng Gao, Yuping Duan

The unrolling method has been investigated for learning variational models in X-ray computed tomography. However, it has been observed that directly unrolling the regularization model through gradient descent does not produce satisfactory results. In this paper, we present a novel deep learning-based CT reconstruction model, where the low-resolution image is introduced to obtain an effective regularization term for improving the network`s robustness. Our approach involves constructing the backbone network architecture by algorithm unrolling that is realized using the deep equilibrium architecture. We theoretically discuss the convergence of the proposed low-resolution prior equilibrium model and provide the conditions to guarantee convergence. Experimental results on both sparse-view and limited-angle reconstruction problems are provided, demonstrating that our end-to-end low-resolution prior equilibrium model outperforms other state-of-the-art methods in terms of noise reduction, contrast-to-noise ratio, and preservation of edge details.

Jie Zhang, Yuping Duan, Yue Lu et al.

In this paper, we propose new operator-splitting algorithms for the total variation regularized infimal convolution (TV-IC) model [4] in order to remove mixed Poisson-Gaussian(MPG) noise. In the existing splitting algorithm for TV-IC, an inner loop by Newton method had to be adopted for one nonlinear optimization subproblem, which increased the computation cost per outer loop. By introducing a new bilinear constraint and applying the alternating direction method of multipliers (ADMM), all subproblems of the proposed algorithms named as BCA (short for Bilinear Constraint based ADMM algorithm) and BCAf(short for a variant of BCA with fully splitting form) can be very efficiently solved; especially for the proposed BCAf, they can be calculated without any inner iterations. Under mild conditions, the convergence of the proposed BCA is investigated. Numerically, compared to existing primal-dual algorithms for the TV-IC model, the proposed algorithms, with fewer tunable parameters, converge much faster and produce comparable results meanwhile.