Related papers: Ordinary Differential Equation and Complex Matrix …
Conditioning image generation facilitates seamless editing and the creation of photorealistic images. However, conditioning on noisy or Out-of-Distribution (OoD) images poses significant challenges, particularly in balancing fidelity to the…
Fractional Differential Equations (FDEs) are essential tools for modelling complex systems in science and engineering. They extend the traditional concepts of differentiation and integration to non-integer orders, enabling a more precise…
Accurate registration of medical images is vital for doctor's diagnosis and quantitative analysis. In this paper, we propose a new deformable medical image registration method based on average geometric transformations and VoxelMorph CNN…
Perspective distortion (PD) leads to substantial alterations in the shape, size, orientation, angles, and spatial relationships of visual elements in images. Accurately determining camera intrinsic and extrinsic parameters is challenging,…
We study the Optimal Control Problem (OCP) for regular linear differential-algebraic systems (DAEs). To this end, we introduce the input index, which allows, on the one hand, to characterize the space of consistent initial values in terms…
Low-rank matrix approximation play a ubiquitous role in various applications such as image processing, signal processing, and data analysis. Recently, random algorithms of low-rank matrix approximation have gained widespread adoption due to…
Neural Ordinary Differential Equations (NODEs), a framework of continuous-depth neural networks, have been widely applied, showing exceptional efficacy in coping with representative datasets. Recently, an augmented framework has been…
We present a fast learning-based algorithm for deformable, pairwise 3D medical image registration. Current registration methods optimize an objective function independently for each pair of images, which can be time-consuming for large…
Deep learning hardware achieves high throughput and low power consumption by reducing computing precision and specializing in matrix multiplication. For machine learning inference, fixed-point value computation is commonplace, where the…
Differential-elimination algorithms apply a finite number of differentiations and eliminations to systems of partial differential equations. For systems that are polynomially nonlinear with rational number coefficients, they guarantee the…
We further develop a new framework, called PDE Acceleration, by applying it to calculus of variations problems defined for general functions on $\mathbb{R}^n$, obtaining efficient numerical algorithms to solve the resulting class of…
Dimensionality reduction (DR) plays a crucial role in various fields, including data engineering and visualization, by simplifying complex datasets while retaining essential information. However, achieving both high DR accuracy and strong…
Diffeomorphic deformable image registration is crucial in many medical image studies, as it offers unique, special properties including topology preservation and invertibility of the transformation. Recent deep learning-based deformable…
Binary embeddings provide efficient and powerful ways to perform operations on large scale data. However binary embedding typically requires long codes in order to preserve the discriminative power of the input space. Thus binary coding…
Neural Ordinary Differential Equations (Neural ODEs) represent continuous-time dynamics with neural networks, offering advancements for modeling and control tasks. However, training Neural ODEs requires solving differential equations at…
Recent work in deep learning focuses on solving physical systems in the Ordinary Differential Equation or Partial Differential Equation. This current work proposed a variant of Convolutional Neural Networks (CNNs) that can learn the hidden…
Composite convex optimization models arise in several applications, and are especially prevalent in inverse problems with a sparsity inducing norm and in general convex optimization with simple constraints. The most widely used algorithms…
Image segmentation is a popular area of research in computer vision that has many applications in automated image processing. A recent technique called piecewise flat embeddings (PFE) has been proposed for use in image segmentation; PFE…
It has been found that residual networks are an Euler discretization of solutions to Ordinary Differential Equations (ODEs). In this paper, we explore a deeper relationship between Transformer and numerical methods of ODEs. We show that a…
In this work we propose an adaptive Finite Element Method (FEM) formulation for the Deformable Image Registration problem (DIR) together with a residual-based a posteriori error estimator, whose efficiency and reliability are theoretically…