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08/25/2023
A Fast Minimization Algorithm for the Euler Elastica Model Based on a Bilinear Decomposition
The Euler Elastica (EE) model with surface curvature can generate artifa...
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07/18/2023
Connections between Operator-splitting Methods and Deep Neural Networks with Applications in Image Segmentation
Deep neural network is a powerful tool for many tasks. Understanding why...
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07/18/2023
PottsMGNet: A Mathematical Explanation of Encoder-Decoder Based Neural Networks
For problems in image processing and many other fields, a large class of...
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08/02/2022
A uniform preconditioner for a Newton algorithm for total-variation minimization and minimum-surface problems
Solution methods for the nonlinear partial differential equation of the ...
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06/15/2022
Priori Error Estimate of Deep Mixed Residual Method for Elliptic PDEs
In this work, we derive a priori error estimate of the mixed residual me...
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03/22/2022
Multiple Convex Objects Image Segmentation via Proximal Alternating Direction Method of Multipliers
This paper focuses on the issue of image segmentation with convex shape ...
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03/18/2022
Elastica Models for Color Image Regularization
One classical approach to regularize color is to tream them as two dimen...
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03/05/2022
IDmUNet: A new image decomposition induced network for sparse feature segmentation
UNet and its variants are among the most popular methods for medical ima...
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08/04/2021
An Operator-Splitting Method for the Gaussian Curvature Regularization Model with Applications in Surface Smoothing and Imaging
Gaussian curvature is an important geometric property of surfaces, which...
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07/06/2021
Generalization Error Analysis of Neural networks with Gradient Based Regularization
We study gradient-based regularization methods for neural networks. We m...
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10/31/2020
Overlapping Domain Decomposition Methods for Ptychographic Imaging
In ptychography experiments, redundant scanning is usually required to g...
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09/28/2020
Sparse-data based 3D surface reconstruction with vector matching
Three dimensional surface reconstruction based on two dimensional sparse...
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09/24/2020
Iterative regularization algorithms for image denoising with the TV-Stokes model
We propose a set of iterative regularization algorithms for the TV-Stoke...
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09/24/2020
Alternating minimization for a single step TV-Stokes model for image denoising
The paper presents a fully coupled TV-Stokes model, and propose an algor...
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09/24/2020
Multidimensional TV-Stokes for image processing
A complete multidimential TV-Stokes model is proposed based on smoothing...
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08/19/2020
A Color Elastica Model for Vector-Valued Image Regularization
Models related to the Euler's Elastica energy have proven to be very use...
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05/15/2020
Convex Shape Prior for Deep Neural Convolution Network based Eye Fundus Images Segmentation
Convex Shapes (CS) are common priors for optic disc and cup segmentation...
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03/21/2020
A level set representation method for N-dimensional convex shape and applications
In this work, we present a new efficient method for convex shape represe...
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02/22/2020
Convex Shape Representation with Binary Labels for Image Segmentation: Models and Fast Algorithms
We present a novel and effective binary representation for convex shapes...
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02/10/2020
Deep Convolutional Neural Networks with Spatial Regularization, Volume and Star-shape Priori for Image Segmentation
We use Deep Convolutional Neural Networks (DCNNs) for image segmentation...
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09/22/2019
Volume Preserving Image Segmentation with Entropic Regularization Optimal Transport and Its Applications in Deep Learning
Image segmentation with a volume constraint is an important prior for ma...
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08/09/2019
Convex hull algorithms based on some variational models
Seeking the convex hull of an object is a very fundamental problem arisi...
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05/22/2018
Convexity Shape Prior for Level Set based Image Segmentation Method
We propose a geometric convexity shape prior preservation method for var...
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07/28/2017