2 citations · 5 across the 12 of their papers we have counts for
15 papers
Propagate, Then Sharpen: Post-Hoc Refinement of Frozen Node Classifiers
Preben Johnsen Bentdal, Nello Blaser, Xue-Cheng Tai
We study post-hoc refinement of frozen node classifiers: given only the graph and class distributions predicted by a frozen model, can we improve accuracy without access to…
A Unified Variational Framework for Deep Weakly Supervised Image Segmentation
Yin King Chu, Lingfeng Li, Sung Ha Kang +2
We propose a unified variational framework for image segmentation under sparse pixel-level supervision. Our method is based on a simplex-constrained Potts model with a smooth perim…
Computing Smooth Geodesics under Two-Sided Curvature Bounds with Applications to Robotics and Image Analysis
Da Chen, Zhenjiang Li, Jean-Marie Mirebeau +4
Curvature of planar curves serves as a key regularization term for computing second-order minimal paths, due to its tight relevance to desirable geometric properties such as smooth…
Neural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approximations
Shuang Chen, Juncai He, Xue-Cheng Tai
We introduce an abstract neural flow framework for neural networks and neural operators. The framework contains two continuous-depth models, namely neural flows with composition an…
Functional Analysis and Parallel Domain Decomposition for the TV-Stokes Model
Andreas Langer, Marc Runft, Talal Rahman +2
The TV-Stokes model is a two-step variational method for image denoising that combines the estimation of a divergence-free tangent field with total variation regularization in the…
Topology-Guaranteed Image Segmentation: Enforcing Connectivity, Genus, and Width Constraints
Wenxiao Li, Xue-Cheng Tai, Jun Liu
Existing research highlights the crucial role of topological priors in image segmentation, particularly in preserving essential structures such as connectivity and genus. Accuratel…
Mathematical Modeling and Convergence Analysis of Deep Neural Networks with Dense Layer Connectivities in Deep Learning
Jinshu Huang, Haibin Su, Xue-Cheng Tai +1
In deep learning, dense layer connectivity has become a key design principle in deep neural networks (DNNs), enabling efficient information flow and strong performance across a ran…
A Mathematical Explanation of Transformers
Xue-Cheng Tai, Hao Liu, Lingfeng Li +1
The Transformer architecture has revolutionized the field of sequence modeling and underpins the recent breakthroughs in large language models (LLMs). However, a comprehensive math…
A Registration-Based Star-Shape Segmentation Model and Fast Algorithms
Daoping Zhang, Xue-Cheng Tai, Lok Ming Lui
Image segmentation plays a crucial role in extracting objects of interest and identifying their boundaries within an image. However, accurate segmentation becomes challenging when…
Coupled Reconstruction of 2D Blood Flow and Vessel Geometry from Noisy Images via Physics-Informed Neural Networks and Quasi-Conformal Mapping
Han Zhang, Xue-Cheng Tai, Jean-Michel Morel +1
Blood flow imaging provides important information for hemodynamic behavior within the vascular system and plays an essential role in medical diagnosis and treatment planning. Howev…
A Mathematical Explanation of UNet
Xue-Cheng Tai, Hao Liu, Raymond H. Chan +1
The UNet architecture has transformed image segmentation. UNet's versatility and accuracy have driven its widespread adoption, significantly advancing fields reliant on machine lea…
Deep Convolutional Neural Networks Meet Variational Shape Compactness Priors for Image Segmentation
Kehui Zhang, Lingfeng Li, Hao Liu +2
Shape compactness is a key geometrical property to describe interesting regions in many image segmentation tasks. In this paper, we propose two novel algorithms to solve the introd…
BP-DeepONet: A new method for cuffless blood pressure estimation using the physcis-informed DeepONet
Lingfeng Li, Xue-Cheng Tai, Raymond Chan
Cardiovascular diseases (CVDs) are the leading cause of death worldwide, with blood pressure serving as a crucial indicator. Arterial blood pressure (ABP) waveforms provide continu…
Double-well Net for Image Segmentation
Hao Liu, Jun Liu, Raymond H. Chan +1
In this study, our goal is to integrate classical mathematical models with deep neural networks by introducing two novel deep neural network models for image segmentation known as…
A Meshless Solver for Blood Flow Simulations in Elastic Vessels Using Physics-Informed Neural Network
Han Zhang, Raymond Chan, Xue-Cheng Tai
Investigating blood flow in the cardiovascular system is crucial for assessing cardiovascular health. Computational approaches offer some non-invasive alternatives to measure blood…