58 citations · 110 across the 31 of their papers we have counts for
33 papers
A Fast Minimization Algorithm for the Euler Elastica Model Based on a Bilinear Decomposition
Zhifang Liu, Baochen Sun, Xue-Cheng Tai +2
The Euler Elastica (EE) model with surface curvature can generate artifact-free results compared with the traditional total variation regularization model in image processing. Howe…
Connections between Operator-splitting Methods and Deep Neural Networks with Applications in Image Segmentation
Hao Liu, Xue-Cheng Tai, Raymond Chan
Deep neural network is a powerful tool for many tasks. Understanding why it is so successful and providing a mathematical explanation is an important problem and has been one popul…
PottsMGNet: A Mathematical Explanation of Encoder-Decoder Based Neural Networks
Xue-Cheng Tai, Hao Liu, Raymond Chan
For problems in image processing and many other fields, a large class of effective neural networks has encoder-decoder-based architectures. Although these networks have made impres…
Preconditioned Algorithm for Difference of Convex Functions with applications to Graph Ginzburg-Landau Model
Xinhua Shen, Hongpeng Sun, Xuecheng Tai
In this work, we propose and study a preconditioned framework with a graphic Ginzburg-Landau functional for image segmentation and data clustering by parallel computing. Solving no…
A uniform preconditioner for a Newton algorithm for total-variation minimization and minimum-surface problems
Xue-Cheng Tai, Ragnar Winther, Xiaodi Zhang +1
Solution methods for the nonlinear partial differential equation of the Rudin-Osher-Fatemi (ROF) and minimum-surface models are fundamental for many modern applications. Many effic…
Priori Error Estimate of Deep Mixed Residual Method for Elliptic PDEs
Lingfeng Li, Xue-cheng Tai, Jiang Yang +1
In this work, we derive a priori error estimate of the mixed residual method when solving some elliptic PDEs. Our work is the first theoretical study of this method. We prove that…
A Binary Characterization Method for Shape Convexity and Applications
Shousheng Luo, Jinfeng Chen, Yunhai Xiao +1
Convexity prior is one of the main cue for human vision and shape completion with important applications in image processing, computer vision. This paper focuses on characterizatio…
Elastica Models for Color Image Regularization
Hao Liu, Xue-Cheng Tai, Ron Kimmel +1
One classical approach to regularize color is to tream them as two dimensional surfaces embedded in a five dimensional spatial-chromatic space. In this case, a natural regularizati…
Geodesic Models with Convexity Shape Prior
Da Chen, Jean-Marie Mirebeau, Minglei Shu +2
The minimal geodesic models based on the Eikonal equations are capable of finding suitable solutions in various image segmentation scenarios. Existing geodesic-based segmentation a…
An Operator-Splitting Method for the Gaussian Curvature Regularization Model with Applications to Surface Smoothing and Imaging
Hao Liu, Xue-Cheng Tai, Roland Glowinski
Gaussian curvature is an important geometric property of surfaces, which has been used broadly in mathematical modeling. Due to the full nonlinearity of the Gaussian curvature, eff…
Generalization Error Analysis of Neural networks with Gradient Based Regularization
Lingfeng Li, Xue-Cheng Tai, Jiang Yang
We study gradient-based regularization methods for neural networks. We mainly focus on two regularization methods: the total variation and the Tikhonov regularization. Applying the…
Variational Image Motion Estimation by Accelerated Dual Optimization
Hongpeng Sun, Xue-Cheng Tai, Jing Yuan
Estimating optical flows is one of the most interesting problems in computer vision, which estimates the essential information about pixel-wise displacements between two consecutiv…
Overlapping Domain Decomposition Methods for Ptychographic Imaging
Huibin Chang, Roland Glowinski, Stefano Marchesini +3
In ptychography experiments, redundant scanning is usually required to guarantee the stable recovery, such that a huge amount of frames are generated, and thus it poses a great dem…
Alternating minimization for a single step TV-Stokes model for image denoising
Bin Wu, Xue-Cheng Tai, Talal Rahman
The paper presents a fully coupled TV-Stokes model, and propose an algorithm based on alternating minimization of the objective functional whose first iteration is exactly the modi…
Sparse-data based 3D surface reconstruction with vector matching
Bin Wu, Xue-Cheng Tai, Talal Rahman
Three dimensional surface reconstruction based on two dimensional sparse information in the form of only a small number of level lines of the surface with moderately complex struct…
Multidimensional TV-Stokes for image processing
Bin Wu, Xue-Cheng Tai, Talal Rahman
A complete multidimential TV-Stokes model is proposed based on smoothing a gradient field in the first step and reconstruction of the multidimensional image from the gradient field…
Iterative regularization algorithms for image denoising with the TV-Stokes model
Bin Wu, Leszek Marcinkowski, Xue-Cheng Tai +1
We propose a set of iterative regularization algorithms for the TV-Stokes model to restore images from noisy images with Gaussian noise. These are some extensions of the iterative…
A Color Elastica Model for Vector-Valued Image Regularization
Hao Liu, Xue-Cheng Tai, Ron Kimmel +1
Models related to the Euler's elastica energy have proven to be useful for many applications including image processing. Extending elastica models to color images and multi-channel…
Convex Shape Prior for Deep Neural Convolution Network based Eye Fundus Images Segmentation
Jun Liu, Xue-Cheng Tai, Shousheng Luo
Convex Shapes (CS) are common priors for optic disc and cup segmentation in eye fundus images. It is important to design proper techniques to represent convex shapes. So far, it is…
Efficient ADMM and Splitting Methods for Continuous Min-cut and Max-flow Problems
Hongpeng Sun, Xuecheng Tai, Jing Yuan
The Potts model has many applications. It is equivalent to some min-cut and max-flow models. Primal-dual algorithms have been used to solve these problems. Due to the special struc…
A level set representation method for N-dimensional convex shape and applications
Lingfeng li, Shousheng Luo, Xue-Cheng Tai +1
In this work, we present a new efficient method for convex shape representation, which is regardless of the dimension of the concerned objects, using level-set approaches. Convexit…
Convex Shape Representation with Binary Labels for Image Segmentation: Models and Fast Algorithms
Shousheng Luo, Xue-Cheng Tai, Yang Wang
We present a novel and effective binary representation for convex shapes. We show the equivalence between the shape convexity and some properties of the associated indicator functi…
Deep Convolutional Neural Networks with Spatial Regularization, Volume and Star-shape Priori for Image Segmentation
Jun Liu, Xiangyue Wang, Xue-cheng Tai
We use Deep Convolutional Neural Networks (DCNNs) for image segmentation problems. DCNNs can well extract the features from natural images. However, the classification functions in…
Data-driven Method for 3D Axis-symmetric Object Reconstruction from Single Cone-beam Projection Data
Shousheng Luo, Ruyue Meng, Suhua Wei +3
In this paper we consider 3D axis-symmetric (AS) object reconstruction from single cone-beam x-ray projection data. Traditional x-ray CT fails to capture fleeting state of material…