Related papers: Optical Flow on Moving Manifolds

We introduce a general framework for training flow matching models on Riemannian symmetric spaces, a large class of manifolds that includes the sphere, hyperbolic space and Grassmannians. We exploit their algebraic structure to reformulate…

A recent paper by Gatys et al. describes a method for rendering an image in the style of another image. First, they use convolutional neural network features to build a statistical model for the style of an image. Then they create a new…

Occlusion is an inevitable and critical problem in unsupervised optical flow learning. Existing methods either treat occlusions equally as non-occluded regions or simply remove them to avoid incorrectness. However, the occlusion regions can…

Optical methods are most convenient to analyze spatially periodic patterns with wavevector $\bm q$ in a thin layer of a nematic liquid crystal. In the standard experimental setup a beam of parallel light with a 'short' wavelength $\lambda…

Let M be an even dimensional compact Riemannian manifold with boundary and let D be a Dirac operator acting on the sections of the Clifford module E over M. We impose certain local elliptic boundary conditions for D obtaining a selfadjoint…

Scene flow describes 3D motion in a 3D scene. It can either be modeled as a single task, or it can be reconstructed from the auxiliary tasks of stereo depth and optical flow estimation. While the second method can achieve real-time…

In this paper we give a geometric interpretation of the renormalization algorithm and of the continued fraction map that we introduced in arxiv:0905.0871 to give a characterization of symbolic sequences for linear flows in the regular…

Learning-based optical flow estimation has been dominated with the pipeline of cost volume with convolutions for flow regression, which is inherently limited to local correlations and thus is hard to address the long-standing challenge of…

A major challenge for video semantic segmentation is the lack of labeled data. In most benchmark datasets, only one frame of a video clip is annotated, which makes most supervised methods fail to utilize information from the rest of the…

A stochastic flow is constructed on a frame bundle adapted to a Riemannian foliation on a compact manifold. The generator A of the resulting transition semigroup is shown to preserve the basic functions and forms, and there is an…

We present rectified flow, a surprisingly simple approach to learning (neural) ordinary differential equation (ODE) models to transport between two empirically observed distributions \pi_0 and \pi_1, hence providing a unified solution to…

We propose a novel method for learning convolutional neural image representations without manual supervision. We use motion cues in the form of optical flow, to supervise representations of static images. The obvious approach of training a…

Recent learning-based methods for event-based optical flow estimation utilize cost volumes for pixel matching but suffer from redundant computations and limited scalability to higher resolutions for flow refinement. In this work, we take…

The field of mathematical morphology offers well-studied techniques for image processing. In this work, we view morphological operations through the lens of persistent homology, a tool at the heart of the field of topological data analysis.…

Given two consecutive RGB-D images, we propose a model that estimates a dense 3D motion field, also known as scene flow. We take advantage of the fact that in robot manipulation scenarios, scenes often consist of a set of rigidly moving…

To date, top-performing optical flow estimation methods only take pairs of consecutive frames into account. While elegant and appealing, the idea of using more than two frames has not yet produced state-of-the-art results. We present a…

Michor and Mumford showed that the mean curvature flow is a gradient flow on a Riemannian structure with a degenerate geodesic distance. It is also known to destroy the uniform density of gridpoints on the evolving surfaces. We introduce a…

This paper deals with the scarcity of data for training optical flow networks, highlighting the limitations of existing sources such as labeled synthetic datasets or unlabeled real videos. Specifically, we introduce a framework to generate…

In this paper we study the reconstruction of moving object densities from undersampled dynamic X-ray tomography in two dimensions. A particular motivation of this study is to use realistic measurement protocols for practical applications,…

Hamilton's equations of motion form a fundamental framework in various branches of physics, including astronomy, quantum mechanics, particle physics, and climate science. Classical numerical solvers are typically employed to compute the…