58 citations · 110 across the 31 of their papers we have counts for
15 papers · 1 filter
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…
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…
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…
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…
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…
Volume Preserving Image Segmentation with Entropic Regularization Optimal Transport and Its Applications in Deep Learning
Haifeng Li, Jun Liu, Li Cui +2
Image segmentation with a volume constraint is an important prior for many real applications. In this work, we present a novel volume preserving image segmentation algorithm, which…
Convex hull algorithms based on some variational models
Lingfeng Li, Shousheng Luo, Xue-Cheng Tai +1
Seeking the convex hull of an object is a very fundamental problem arising from various tasks. In this work, we propose two variational convex hull models using level set represent…
A Regularized Convolutional Neural Network for Semantic Image Segmentation
Fan Jia, Jun Liu, Xue-cheng Tai
Convolutional neural networks (CNNs) show outstanding performance in many image processing problems, such as image recognition, object detection and image segmentation. Semantic se…
Convexity Shape Prior for Level Set based Image Segmentation Method
Shi Yan, Xue-cheng Tai, Jun Liu +1
We propose a geometric convexity shape prior preservation method for variational level set based image segmentation methods. Our method is built upon the fact that the level set of…
New region force for variational models in image segmentation and high dimensional data clustering
Ke Wei, Ke Yin, Xue-Cheng Tai +1
We propose an effective framework for multi-phase image segmentation and semi-supervised data clustering by introducing a novel region force term into the Potts model. Assume the p…