Related papers: Optical Flow on Evolving Sphere-Like Surfaces
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…
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…
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…
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…
Optical flow is a powerful tool for the study and analysis of motion in a sequence of images. In this article we study a Horn-Schunck type spatio-temporal regularization functional for image sequences that have a non-Euclidean, time varying…
We propose a novel optical flow based approach to enhance the axial resolution of anisotropic 3D EM volumes to achieve isotropic 3D reconstruction. Assuming spatial continuity of 3D biological structures in well aligned EM volumes, we…
We study the formation of images in a reflective sphere in three configurations using caustics of the field of light rays. The optical wavefront emerging from a source point reaching a subject following passage through the optical system…
We investigate cell trajectories during zebrafish early embryogenesis based on 3D+time photonic microscopy imaging data. To remove the collective flow motion and focus on fluctuations, we analyze the deviations of pairs of neighboring…
Existing optical flow methods make generic, spatially homogeneous, assumptions about the spatial structure of the flow. In reality, optical flow varies across an image depending on object class. Simply put, different objects move…
The shape of liquid surface in a rotating frame depends on the angular velocity. In this experiment, a fluid in a rectangular container with a small width is placed on a rotating table. A smartphone fixed to the rotating frame…
Slow flow of a single fluid through a porous medium is well understood on a macroscopic level through Darcy's law, a linear relation between flow rate and a combination of pressure differences, viscosity, and gravitational forces. Two-phase…
We introduce variational approximations for curve evolutions in two-dimensional Riemannian manifolds that are conformally flat, i.e.\ conformally equivalent to the Euclidean space. Examples include the hyperbolic plane, the hyperbolic disk,…
A very simple model for cell swelling by osmosis is introduced, resulting in a parabolic free boundary problem. In case of radially symmetric initial conditions, it is shown that the model can be viewed as a gradient flow involving entropy,…
Borrowing terminology from fluid mechanics, the concepts of {\em Eulerian} and {\em Lagrangian optical flow sensing} are introduced. Eulerian optical flow sensing assumes that each photoreceptor in the camera or eye can instantaneously…
Recent experiments have shown that when a near-hemispherical lipid vesicle attached to a solid surface is subjected to a simple shear flow it exhibits a pattern of membrane circulation much like a dipole vortex. This is in marked contrast…
We formulate hydrodynamic equations and spectrally accurate numerical methods for investigating the role of geometry in flows within two-dimensional fluid interfaces. To achieve numerical approximations having high precision and level of…
A theoretical and experimental study of the spin-over mode induced by the elliptical instability of a flow contained in a slightly deformed rotating spherical shell is presented. This geometrical configuration mimics the liquid rotating…
Experimental and numerical investigations are performed to provide an assessment of the transport behavior of an ultrasonic oscillatory two-phase flow in a microchannel. The work is inspired by the flow observed in an innovative ultrasonic…
During the upstroke of a normal eye blink, the upper lid moves and paints a thin tear film over the exposed corneal and conjunctival surfaces. This thin tear film may be modeled by a nonlinear fourth-order PDE derived from lubrication…
Many vesicles have a spherical resting shape and exposure to fluid flows induces an exchange between sub-optical area and visible (systematic) deformation, while the total area is conserved. The dynamics which controls the exchange between…