Optical Flow on Evolving Sphere-Like Surfaces

A Numerical Framework for Efficient Motion Estimation on Evolving Sphere-Like Surfaces based on Brightness and Mass Conservation Laws

In this work we consider brightness and mass conservation laws for motion estimation on evolving Riemannian 2-manifolds that allow for a radial parametrisation from the 2-sphere. While conservation of brightness constitutes the foundation for optical flow methods and has been generalised to said scenario, we formulate in this article the principle of mass conservation for time-varying surfaces which are embedded in Euclidean 3-space and derive a generalised continuity equation. The main motivation for this work is efficient cell motion estimation in time-lapse (4D) volumetric fluorescence micr…

Optical Flow on Evolving Surfaces with an Application to the Analysis of 4D Microscopy Data

We extend the concept of optical flow to a dynamic non-Euclidean setting. Optical flow is traditionally computed from a sequence of flat images. It is the purpose of this paper to introduce variational motion estimation for images that are defined on an evolving surface. Volumetric microscopy images depicting a live zebrafish embryo serve as both biological motivation and test data.

Optical Flow on Evolving Surfaces with Space and Time Regularisation

We extend the concept of optical flow with spatiotemporal regularisation to a dynamic non-Euclidean setting. Optical flow is traditionally computed from a sequence of flat images. The purpose of this paper is to introduce variational motion estimation for images that are defined on an evolving surface. Volumetric microscopy images depicting a live zebrafish embryo serve as both biological motivation and test data.

Decomposition of Optical Flow on the Sphere

We propose a number of variational regularisation methods for the estimation and decomposition of motion fields on the $2$-sphere. While motion estimation is based on the optical flow equation, the presented decomposition models are motivated by recent trends in image analysis. In particular we treat $u+v$ decomposition as well as hierarchical decomposition. Helmholtz decomposition of motion fields is obtained as a natural by-product of the chosen numerical method based on vector spherical harmonics. All models are tested on time-lapse microscopy data depicting fluorescently labelled endoderma…

n球面上的动态约束稳定化

Dynamic Constrained Stabilization on the n-sphere (Extended version)

本文提出了一种基于约束接近度的动态阻尼机制，用于第二类系统在n球面上的约束稳定化，实现了目标点的几乎全局渐近稳定，并展示了其在刚体姿态稳定中的应用。

利用光学光束测量估计湍流介质的时间演化折射率：一种数据同化方法

Estimating the time-evolving refractivity of a turbulent medium using optical beam measurements: a data assimilation approach

本研究提出利用数据同化技术，结合近轴波动方程和扩展卡尔曼滤波，从光束强度测量中估计湍流介质随时间演化的折射率，并验证了其恢复空间与时间变化的有效性。