Automated visual tracking for studying the ontogeny of zebrafish swimming

The zebrafish Danio rerio is a widely used model organism in studies of genetics, developmental biology, and recently, biomechanics. In order to quantify changes in swimming during all stages of development, we have developed a visual tracking system that estimates the posture of fish. Our current approach assumes planar motion of the fish, given image sequences taken from a top view. An accurate geometric fish model is automatically designed and fit to the images at each time frame. Our approach works across a range of fish shapes and sizes and is therefore well suited for studying the ontogeny of fish swimming, while also being robust to common environmental occlusions. Our current analysis focuses on measuring the influence of vertebra development on the swimming capabilities of zebrafish. We examine wild-type zebrafish and mutants with stiff vertebrae (stocksteif) and quantify their body kinematics as a function of their development from larvae to adult (mutants made available by the Hubrecht laboratory, The Netherlands). By tracking the fish, we are able to measure the curvature and net acceleration along the body that result from the fish's body wave. Here, we demonstrate the capabilities of the tracking system for the escape response of wild-type zebrafish and stocksteif mutant zebrafish. The response was filmed with a digital high-speed camera at 1500 frames s–1. Our approach enables biomechanists and ethologists to process much larger datasets than possible at present. Our automated tracking scheme can therefore accelerate insight in the swimming behavior of many species of (developing) fish

Global axis shape of magnetic clouds deduced from the distribution of their local axis orientation

Coronal mass ejections (CMEs) are routinely tracked with imagers in the interplanetary space while magnetic clouds (MCs) properties are measured locally by spacecraft. However, both imager and insitu data do not provide direct estimation on the global flux rope properties. The main aim of this study is to constrain the global shape of the flux rope axis from local measurements, and to compare the results from in-situ data with imager observations. We perform a statistical analysis of the set of MCs observed by WIND spacecraft over 15 years in the vicinity of Earth. With the hypothesis of having a sample of MCs with a uniform distribution of spacecraft crossing along their axis, we show that a mean axis shape can be derived from the distribution of the axis orientation. In complement, while heliospheric imagers do not typically observe MCs but only their sheath region, we analyze one event where the flux-rope axis can be estimated from the STEREO imagers. From the analysis of a set of theoretical models, we show that the distribution of the local axis orientation is strongly affected by the global axis shape. Next, we derive the mean axis shape from the integration of the observed orientation distribution. This shape is robust as it is mostly determined from the global shape of the distribution. Moreover, we find no dependence on the flux-rope inclination on the ecliptic. Finally, the derived shape is fully consistent with the one derived from heliospheric imager observations of the June 2008 event. We have derived a mean shape of MC axis which only depends on one free parameter, the angular separation of the legs (as viewed from the Sun). This mean shape can be used in various contexts such as the study of high energy particles or space weather forecast.Comment: 13 pages, 12 figure

Identification of geometrical models of interface evolution for dendritic crystal growth

This paper introduces a method for identifying geometrical models of interface evolution, directly from experimental imaging data. These local growth models relate normal growth velocity to curvature and its derivatives estimated along the growing interface. Such models can reproduce many qualitative features of dendritic crystal growth as well as predict quantitatively its early stages of evolution. Numerical simulations and experimental crystal growth data are used to demonstrate the applicability of this approach

Locally Adaptive Frames in the Roto-Translation Group and their Applications in Medical Imaging

Locally adaptive differential frames (gauge frames) are a well-known effective tool in image analysis, used in differential invariants and PDE-flows. However, at complex structures such as crossings or junctions, these frames are not well-defined. Therefore, we generalize the notion of gauge frames on images to gauge frames on data representations $U:\mathbb{R}^{d} \rtimes S^{d-1} \to \mathbb{R}$ defined on the extended space of positions and orientations, which we relate to data on the roto-translation group $SE(d)$, $d=2,3$. This allows to define multiple frames per position, one per orientation. We compute these frames via exponential curve fits in the extended data representations in $SE(d)$. These curve fits minimize first or second order variational problems which are solved by spectral decomposition of, respectively, a structure tensor or Hessian of data on $SE(d)$. We include these gauge frames in differential invariants and crossing preserving PDE-flows acting on extended data representation $U$ and we show their advantage compared to the standard left-invariant frame on $SE(d)$. Applications include crossing-preserving filtering and improved segmentations of the vascular tree in retinal images, and new 3D extensions of coherence-enhancing diffusion via invertible orientation scores