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Found 27 papers, 0 papers with code
BP-DeepONet: A new method for cuffless blood pressure estimation using the physcis-informed DeepONet
Unlike previous methods, our approach requires the predicted ABP waveforms to satisfy the Navier-Stokes equation with a time-periodic condition and a Windkessel boundary condition.
Double-well Net for Image Segmentation
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 Double-well Nets.
A Fast Minimization Algorithm for the Euler Elastica Model Based on a Bilinear Decomposition
A host of numerical experiments are conducted to show that the new algorithm produces good results with much-improved efficiency compared to other state-of-the-art algorithms for the EE model.
Connections between Operator-splitting Methods and Deep Neural Networks with Applications in Image Segmentation
In this paper, we give an algorithmic explanation for deep neural networks, especially in their connections with operator splitting.
PottsMGNet: A Mathematical Explanation of Encoder-Decoder Based Neural Networks
We use the two-phase Potts model for image segmentation as an example for our explanations.
A Binary Characterization Method for Shape Convexity and Applications
This paper focuses on characterization methods for convex objects and applications in image processing.
Elastica Models for Color Image Regularization
Recently, the authors proposed a color elastica model, which minimizes both the surface area and elastica of the image manifold.
IDmUNet: A new image decomposition induced network for sparse feature segmentation
Because of the sparsity prior and deep unfolding method in the structure design, this IDmUNet combines the advantages of mathematical modeling and data-driven approaches.
An Operator-Splitting Method for the Gaussian Curvature Regularization Model with Applications to Surface Smoothing and Imaging
In our method, we decouple the full nonlinearity of Gaussian curvature from differential operators by introducing two matrix- and vector-valued functions.
Generalization Error Analysis of Neural networks with Gradient Based Regularization
We mainly focus on two regularization methods: the total variation and the Tikhonov regularization.
An Elastica Geodesic Approach With Convexity Shape Prior
The minimal geodesic models based on the Eikonal equations are capable of finding suitable solutions in various image segmentation scenarios.
Sparse-data based 3D surface reconstruction with vector matching
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 structures, containing both structured and unstructured geometries, is considered in this paper.
Iterative regularization algorithms for image denoising with the TV-Stokes model
We propose a set of iterative regularization algorithms for the TV-Stokes model to restore images from noisy images with Gaussian noise.
Alternating minimization for a single step TV-Stokes model for image denoising
A convergence analysis is given.
Multidimensional TV-Stokes for image processing
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.
A Color Elastica Model for Vector-Valued Image Regularization
Here, we introduce an addition to the Polyakov action for color images that minimizes the color manifold curvature.
Convex Shape Prior for Deep Neural Convolution Network based Eye Fundus Images Segmentation
This method is flexible and it can handle multiple objects and allow some of the objects to be convex.
A level set representation method for N-dimensional convex shape and applications
We apply this new method to two applications: object segmentation with convexity prior and convex hull problem (especially with outliers).
Convex Shape Representation with Binary Labels for Image Segmentation: Models and Fast Algorithms
We present a novel and effective binary representation for convex shapes.
Deep Convolutional Neural Networks with Spatial Regularization, Volume and Star-shape Priori for Image Segmentation
The novelty of our method is to interpret the softmax activation function as a dual variable in a variational problem, and thus many spatial priors can be imposed in the dual space.
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 many real applications.
Convex hull algorithms based on some variational models
In this model, the convex hull is characterized by the zero sublevel-set of a convex level set function, which is non-positive at every given point.
A Regularized Convolutional Neural Network for Semantic Image Segmentation
That is, spatial regularity of the segmented objects is still a problem for CNNs.
Convexity Shape Prior for Level Set based Image Segmentation Method
We apply our method to region and edge based level set segmentation models including Chan-Vese (CV) model with guarantee that the segmented region will be convex.
Simplified Energy Landscape for Modularity Using Total Variation
We show that modularity optimization is equivalent to minimizing a convex TV-based functional over a discrete domain, again, assuming the number of communities is known.
New region force for variational models in image segmentation and high dimensional data clustering
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.
Efficient 3D Endfiring TRUS Prostate Segmentation with Globally Optimized Rotational Symmetry
Segmenting 3D endfiring transrectal ultrasound (TRUS) prostate images efficiently and accurately is of utmost importance for the planning and guiding 3D TRUS guided prostate biopsy.
