arXiv subjects

Shoujun Huang

Publications and source records attributed to Shoujun Huang.

7 recordsLinked to original sources

arXiv2026

LHMCF-Net: A Learned Hyperbolic Mean Curvature Flow Network for Medical Images Segmentation

Motivated by the classical Chan-Vese model and the ability of deep priors to capture complex spatial structures, we develop a segmentation model that leverages learned hyperbolic mean curvature flow (LHMCF) as a mathematical foundation for integrating feature space data fidelity and deep structural priors within a unified high-dimensional framework. The proposed LHMCF model is governed by a second-order dissipative hyperbolic PDE, where the introduction of a velocity field provides inertia and momentum to the evolving interface. This hyperbolic mechanism enables the contour to bypass noise-induced local minima and propagate coherently through low-contrast or ambiguous regions, addressing limitations inherent to first-order parabolic flows. To solve the continuous LHMCF model, we construct a deep unfolding network, named LHMCF-Net, which maps the iterative numerical procedure of the PDE into a sequence of discrete evolution stages. Each stage corresponds to one physically interpretable update of the underlying dynamical system, allowing the network to inherit the stability and geometric consistency of the PDE while supporting end-to-end optimization. Comprehensive experiments on three publicly available medical segmentation datasets demonstrate that LHMCF-Net achieves superior performance, particularly in challenging scenarios with low contrast and unclear boundaries. These results highlight the effectiveness of embedding hyperbolic geometric evolution into deep unfolding architectures and underscore the potential of physically inspired models for robust medical image segmentation.

cs.CV↗

arXiv2026

Hyperbolic mean curvature flow computed by physics-informed neural networks

In this paper, we explore the evolution of plane curves and surfaces governed by the hyperbolic mean curvature flow. We propose a mesh-free approach based on the physics-informed neural networks (PINNs), which eliminates the need for discretization and meshing of computational domains, and is efficient in solving partial differential equations involving high dimensions. To the best of our knowledge, this is the first result on the numerical analysis by employing the PINNs for the hyperbolic geometric evolution equations in the literature. The effectiveness of this method is demonstrated through several numerical simulations by selecting diverse initial curves and surfaces, as well as both constant and non-constant initial velocities.

math-ph↗

arXiv2025

Information Entropy-Based Framework for Quantifying Tortuosity in Meibomian Gland Uneven Atrophy

In the medical image analysis field, precise quantification of curve tortuosity plays a critical role in the auxiliary diagnosis and pathological assessment of various diseases. In this study, we propose a novel framework for tortuosity quantification and demonstrate its effectiveness through the evaluation of meibomian gland atrophy uniformity,serving as a representative application scenario. We introduce an information entropy-based tortuosity quantification framework that integrates probability modeling with entropy theory and incorporates domain transformation of curve data. Unlike traditional methods such as curvature or arc-chord ratio, this approach evaluates the tortuosity of a target curve by comparing it to a designated reference curve. Consequently, it is more suitable for tortuosity assessment tasks in medical data where biologically plausible reference curves are available, providing a more robust and objective evaluation metric without relying on idealized straight-line comparisons. First, we conducted numerical simulation experiments to preliminarily assess the stability and validity of the method. Subsequently, the framework was applied to quantify the spatial uniformity of meibomian gland atrophy and to analyze the difference in this uniformity between \textit{Demodex}-negative and \textit{Demodex}-positive patient groups. The results demonstrated a significant difference in tortuosity-based uniformity between the two groups, with an area under the curve of 0.8768, sensitivity of 0.75, and specificity of 0.93. These findings highlight the clinical utility of the proposed framework in curve tortuosity analysis and its potential as a generalizable tool for quantitative morphological evaluation in medical diagnostics.

cs.CV↗

arXiv2025

Active Contour Models Driven by Hyperbolic Mean Curvature Flow for Image Segmentation

Parabolic mean curvature flow-driven active contour models (PMCF-ACMs) are widely used for image segmentation, yet they suffer severe degradation under high-intensity noise because gradient-descent evolutions exhibit the well-known zig-zag phenomenon. To overcome this drawback, we propose hyperbolic mean curvature flow-driven ACMs (HMCF-ACMs). This novel framework incorporates an adjustable acceleration field to autonomously regulate curve evolution smoothness, providing dual degrees of freedom for adaptive selection of both initial contours and velocity fields. We rigorously prove that HMCF-ACMs are normal flows and establish their numerical equivalence to wave equations through a level set formulation with signed distance functions. An efficient numerical scheme combining spectral discretization and optimized temporal integration is developed to solve the governing equations, and its stability condition is derived through Fourier analysis. Extensive experiments on natural and medical images validate that HMCF-ACMs achieve superior performance under high-noise conditions, demonstrating reduced parameter sensitivity, enhanced noise robustness, and improved segmentation accuracy compared to PMCF-ACMs.

cs.CV↗

arXiv2024

The Initial Stages of a Generic Singularity for a 2D Pressureless Gas

We consider the Cauchy problem for the equations of pressureless gases in two space dimensions. For a generic set of smooth initial data (density and velocity), it is known that the solution loses regularity at a finite time $t_0$, where both the the density and the velocity gradient become unbounded. Aim of this paper is to provide an asymptotic description of the solution beyond the time of singularity formation. For $t>t_0$ we show that a singular curve is formed, where the mass has positive density w.r.t.1-dimensional Hausdorff measure. The system of equations describing the behavior of the singular curve is not hyperbolic. Working within a class of analytic data, local solutions can be constructed using a version of the Cauchy-Kovalevskaya theorem. For this purpose, by a suitable change of variables we rewrite the evolution equations as a first order system of Briot-Bouquet type, to which a general existence-uniqueness theorem can then be applied.

math.AP↗

arXiv2024

An edge detection-based deep learning approach for tear meniscus height measurement

Automatic measurements of tear meniscus height (TMH) have been achieved by using deep learning techniques; however, annotation is significantly influenced by subjective factors and is both time-consuming and labor-intensive. In this paper, we introduce an automatic TMH measurement technique based on edge detection-assisted annotation within a deep learning framework. This method generates mask labels less affected by subjective factors with enhanced efficiency compared to previous annotation approaches. For improved segmentation of the pupil and tear meniscus areas, the convolutional neural network Inceptionv3 was first implemented as an image quality assessment model, effectively identifying higher-quality images with an accuracy of 98.224%. Subsequently, by using the generated labels, various algorithms, including Unet, ResUnet, Deeplabv3+FcnResnet101, Deeplabv3+FcnResnet50, FcnResnet50, and FcnResnet101 were trained, with Unet demonstrating the best performance. Finally, Unet was used for automatic pupil and tear meniscus segmentation to locate the center of the pupil and calculate TMH,respectively. An evaluation of the mask quality predicted by Unet indicated a Mean Intersection over Union of 0.9362, a recall of 0.9261, a precision of 0.9423, and an F1-Score of 0.9326. Additionally, the TMH predicted by the model was assessed, with the fitting curve represented as y= 0.982x-0.862, an overall correlation coefficient of r^2=0.961 , and an accuracy of 94.80% (237/250). In summary, the algorithm can automatically screen images based on their quality,segment the pupil and tear meniscus areas, and automatically measure TMH. Measurement results using the AI algorithm demonstrate a high level of consistency with manual measurements, offering significant support to clinical doctors in diagnosing dry eye disease.

eess.IV↗

arXiv2023

Generic Singularities for 2D Pressureless Flow

In this paper, we consider the Cauchy problem for pressureless gases in two space dimensions with generic smooth initial data (density and velocity). These equations give rise to singular curves, where the mass has positive density w.r.t.~1-dimensional Hausdorff measure. We observe that the system of equations describing these singular curves is not hyperbolic. For analytic data, local solutions are constructed using a version of the Cauchy-Kovalevskaya theorem. We then study the interaction of two singular curves, in generic position. Finally, for a generic initial velocity field, we investigate the asymptotic structure of the smooth solution up to the first time when a singularity is formed.

math.AP↗