Related papers: Ordinary Differential Equation and Complex Matrix …
Implicit computational complexity is a lively area of theoretical computer science, which aims to provide machine-independent characterizations of relevant complexity classes. % for uniformity with subsequent uses >> 1960s (but feel free to…
We introduce a combinatorial topological framework for characterizing the global dynamics of ordinary differential equations (ODEs). The approach is motivated by the study of gene regulatory networks, which are often modeled by ODEs that…
Deformation field estimation is an important and challenging issue in many medical image registration applications. In recent years, deep learning technique has become a promising approach for simplifying registration problems, and has been…
This work explores the effectiveness of masked image modelling for learning representations of retinal OCT images. To this end, we leverage Masked Autoencoders (MAE), a simple and scalable method for self-supervised learning, to obtain a…
Binary embedding of high-dimensional data requires long codes to preserve the discriminative power of the input space. Traditional binary coding methods often suffer from very high computation and storage costs in such a scenario. To…
With the increasing application of robots, stable and efficient Visual Odometry (VO) algorithms are becoming more and more important. Based on the Fourier Mellin Transformation (FMT) algorithm, the extended Fourier Mellin Transformation…
Image registration has played an important role in image processing problems, especially in medical imaging applications. It is well known that when the deformation is large, many variational models cannot ensure diffeomorphism. In this…
Matrix exponentiation (ME) is widely used in various fields of science and engineering. For example, the unitary dynamics of quantum systems is described by exponentiation of Hamiltonian operators. However, despite a significant attention,…
PDE-constrained optimization problems find many applications in medical image analysis, for example, neuroimaging, cardiovascular imaging, and oncological imaging. We review related literature and give examples on the formulation,…
This paper proposes a new framework and algorithms to address the problem of diffeomorphic registration on a general class of geometric objects that can be described as discrete distributions of local direction vectors. It builds on both…
Purpose: To develop a neural ordinary differential equation (ODE) model for visualizing deep neural network (DNN) behavior during multi-parametric MRI (mp-MRI) based glioma segmentation as a method to enhance deep learning explainability.…
In this work, we conducted a survey on different registration algorithms and investigated their suitability for hyperspectral historical image registration applications. After the evaluation of different algorithms, we choose an intensity…
The free-form deformation model can represent a wide range of non-rigid deformations by manipulating a control point lattice over the image. However, due to a large number of parameters, it is challenging to fit the free-form deformation…
We are interested in the numerical solution of coupled nonlinear partial differential equations (PDEs) in two and three dimensions. Under certain assumptions on the domain, we take advantage of the Kronecker structure arising in standard…
Prevalent Computational Aberration Correction (CAC) methods are typically tailored to specific optical systems, leading to poor generalization and labor-intensive re-training for new lenses. Developing CAC paradigms capable of generalizing…
Deformable medical image registration plays an important role in clinical diagnosis and treatment. Recently, the deep learning (DL) based image registration methods have been widely investigated and showed excellent performance in…
Deformable image registration (alignment) is highly sought after in numerous clinical applications, such as computer aided diagnosis and disease progression analysis. Deep Convolutional Neural Network (DCNN)-based image registration methods…
Definite integrals with parameters of holonomic functions satisfy holonomic systems of linear partial differential equations. When we restrict parameters to a one dimensional curve, the system becomes a linear ordinary differential equation…
Time series alignment methods call for highly expressive, differentiable and invertible warping functions which preserve temporal topology, i.e diffeomorphisms. Diffeomorphic warping functions can be generated from the integration of…
Differential equations in general and neural ODEs in particular are an essential technique in continuous-time system identification. While many deterministic learning algorithms have been designed based on numerical integration via the…