Related papers: Ordinary Differential Equation and Complex Matrix …

Motivated by the fact that the gradient-based optimization algorithms can be studied from the perspective of limiting ordinary differential equations (ODEs), here we derive an ODE representation of the accelerated triple momentum (TM)…

Ordinary Differential Equations (ODEs) are widely used in physics, chemistry, and biology to model dynamic systems, including reaction kinetics, population dynamics, and biological processes. In this work, we integrate GPU-accelerated ODE…

With the advancement in the digital camera technology, the use of high resolution images and videos has been widespread in the modern society. In particular, image and video frame registration is frequently applied in computer graphics and…

Nonrigid point set registration is widely applied in the tasks of computer vision and pattern recognition. Coherent point drift (CPD) is a classical method for nonrigid point set registration. However, to solve spatial transformation…

Differentiable rendering aims to compute the derivative of the image rendering function with respect to the rendering parameters. This paper presents a novel algorithm for 6-DoF pose estimation through gradient-based optimization using a…

Conventional deformable registration methods aim at solving an optimization model carefully designed on image pairs and their computational costs are exceptionally high. In contrast, recent deep learning based approaches can provide fast…

We present ObjectMatch, a semantic and object-centric camera pose estimator for RGB-D SLAM pipelines. Modern camera pose estimators rely on direct correspondences of overlapping regions between frames; however, they cannot align camera…

Registration is a fundamental task in medical robotics and is often a crucial step for many downstream tasks such as motion analysis, intra-operative tracking and image segmentation. Popular registration methods such as ANTs and NiftyReg…

We propose a reduced-order modeling approach for nonlinear, parameter-dependent ordinary differential equations (ODE). Dimensionality reduction is achieved using nonlinear maps represented by autoencoders. The resulting low-dimensional ODE…

Generating wide-area digital surface models (DSMs) requires registering a large number of individual, and partially overlapped DSMs. This presents a challenging problem for a typical registration algorithm, since when a large number of…

Robustly estimating camera poses from a set of images is a fundamental task which remains challenging for differentiable methods, especially in the case of small and sparse camera pose graphs. To overcome this challenge, we propose…

End-to-end optimization, which simultaneously optimizes optics and algorithms, has emerged as a powerful data-driven method for computational imaging system design. This method achieves joint optimization through backpropagation by…

We propose an adaptive regularization scheme in a variational framework where a convex composite energy functional is optimized. We consider a number of imaging problems including denoising, segmentation and motion estimation, which are…

In this paper, we discuss the solution of certain matrix-valued partial differential equations. Such PDEs arise, for example, when constructing a Riemannian contraction metric for a dynamical system given by an autonomous ODE. We develop…

Semantic image understanding is a challenging topic in computer vision. It requires to detect all objects in an image, but also to identify all the relations between them. Detected objects, their labels and the discovered relations can be…

Deformable image registration plays a critical role in various tasks of medical image analysis. A successful registration algorithm, either derived from conventional energy optimization or deep networks requires tremendous efforts from…

We study the learning of numerical algorithms for scientific computing, which combines mathematically driven, handcrafted design of general algorithm structure with a data-driven adaptation to specific classes of tasks. This represents a…

Deformable image registration is one of the fundamental tasks in medical imaging. Classical registration algorithms usually require a high computational cost for iterative optimizations. Although deep-learning-based methods have been…

The integrability problem of rational first-order ODEs $y^{\prime}=\frac{M(x,y)}{N(x,y)}$, where $M,N \in \mathbb{R}[x,y]$ is a long-term research focus in the area of dynamical systems, physics, etc. Although the computer algebra system…

Multimodal registration is a challenging problem in medical imaging due the high variability of tissue appearance under different imaging modalities. The crucial component here is the choice of the right similarity measure. We make a step…