Concept
DigImage: Particle Tracking
:::: IMAGE CAPTURE
:::: PARTICLE LOCATION
:::: PARTICLE MATCHING
:::: OPERATION
Subsequent Analysis
:::: STRUCTURE OF FILES
:::: BASIC OPERATION OF TRK2DVEL
:::: CONFIGURATION OF TRK2DVEL
:::: FACILITIES
Advanced Features
:::: PARTICLE-TAGGED DATA
:::: IMAGE PREPROCESSING
Experimental Hints
Index
A wide range of techniques have been developed over the years for obtaining qualitative and quantitative measurements of fluid flows. Traditional visualisations are primarily qualitative, yielding the structures present within some finite two or three dimensional domain within the flow. Any quantisation required laborious measurement by hand, typically from photographic film. Hot wire and hot film anemometry (HWA) and laser Doppler anemometry (LDA) yield precise velocity measurements at one or more isolated points within the flow. The inherent Eulerian nature of such measurements does not allow ready access to the Lagrangian character of the flow, nor do they offer much insight into the structures present.
A number of techniques have been developed to overcome the limitations for HWA and LDA. Scanning and multiple probes allows HWA and LDA simultaneous (or nearly so) measurements at a large number of points within a flow. Unfortunately physical limitations mean the number of points remains relatively small and the cost of the equipment required high. An alternative is to base the measurement technique on a multi-dimensional visualisation of the flow. The most successful class of methods to date fall under the heading of particle image velocimetry (PIV). In PIV, the flow is seeded with small, (nearly) neutrally buoyant particles which are assumed to follow fluid elements without affecting the flow itself. The flow is illuminated in some manner such that all the particles in some finite domain are visible. A series of images of the flow are captured on some medium (e.g. film or video tape) to record how the particles move in response to the fluid flow. These images are then analysed in order to determine how the particles, and hence the fluid elements, move in time.
There are two main techniques which may be employed to gain information from successive images containing individually identifiable particles, where the particles may have moved a significant distance (compared with the size of the particles): image cross-correlation (pattern matching PIV) and particle tracking. In the first of these an image of a two-dimensional flow (or a two-dimensional slice of a three-dimensional flow) at time tn is divided into a large number of possibly overlapping cells. The correlation function between each cell at t = tn and a similar cell at t = tn+1, subject to some translation in the plane of the image, is evaluated. This evaluation may be based on either the complete image within the cell or the location of discrete particles. The velocity of a cell is evaluated from the cell translation which optimises the correlation between the two images. In the simplest case, the optimal translation will be that which maximises the correlation function. Prior to this correlation procedure, the image may be enhanced in some manner to remove the effects of background noise. The enhancement procedure may be simply locating the individual particles.
The strengths of the cross-correlation method are that is fairly robust to noise and has excellent velocity resolution (the accuracy with which displacements may be obtained is a function of the cell size and the distribution of features within it rather than the pixel resolution). The spatial resolution is inversely proportional to the cell size: the overall data quality is thus a compromise between velocity and spatial resolution. The main disadvantages are the considerable time required to compute the optimal correlation and the inability to cope with any structure across the illuminated plane (i.e. velocity gradients parallel to the viewing direction). In general the method does not allow individual particles to be tracked, and hence has no immediate access to Lagrangian descriptions. However, it is a relatively simple matter to add some degree of particle tracing once the velocity field is known, and hence access the Lagrangian nature of the flow.
Particle tracking offers a more fundamental approach to PIV. There are two main approaches which are exactly equivalent to the manual methods of analysing streak (or multiple exposure) photographs and multiple (time series) photographs. In the streak photograph method, the effective camera shutter is opened for a long time during which the particles move many particle diameters. This long exposure may be produced directly with a suitably slow shutter speed, or synthesised by combining multiple exposures (e.g. ORing a sequence of video frames using a digital frame grabber with a shutter speed equal to the field rate - the DigImage option [;UP Particle streaks - bright particles] and macro STREAK.CMD both perform such an operation). Once the streaks have been produced, image processing techniques may be applied to locate them and analyse their shape, orientation etc.
The alternative of utilising a time series of images offers a greater volume of information on the particle positions as a function of time, especially in the context of digital image processing where quantisation yields a relatively low spatial and intensity resolution. Knowing the approximate location of a particle at a relatively large number of times enables a much more accurate estimation of the position of a particle at a given time, and of its velocity, provided the sampling frequency is much higher than the highest frequency in the particle motion. To make use of this information some method must be developed for tracking particles from one image to the next. In the limit of particles moving only a small fraction of their diameter between each sample, the process of matching particles in one image with their position in the next image is straight forward - the particle images closest together in two adjacent samples will correspond to the same physical particle. However, if the particles may move many diameters between samples, more sophisticated algorithms must be employed.
The algorithm used in the matching process may utilise spatial and temporal information in addition to particle characteristics and prior knowledge of the flow. Generally, only some of these features will be needed to determine which particle image is which particle. For example, if spatial correlation is not utilised, then two-dimensional projections of three-dimensional flows with significant velocity gradients parallel to the direction of viewing, may be analysed (recall that cross-correlation techniques are unable to cope with such images). Moreover, the basic approach is not limited to a two-dimensional projection of a three-dimensional flow but is capable of full three-dimensional analysis. By applying the matching process repeatedly, time-series for individual particles may be obtained to describe some of the Lagrangian nature of the flow.
The accuracy with which the velocities may be measured is limited by the accuracy with which the individual particle images may be located and the time period over which the velocity may reasonably be evaluated (this must be shorter than the period corresponding to the maximum frequency in which you are interested). The accuracy of location depends in turn on the particle size and the method used to determine their positions. In general, the velocity resolution will be less than that for the cross-correlation approach, but is nevertheless adequate in most situations. The spatial resolution is limited primarily by the number of particles in the flow: the more particles, the higher the resolution. In practice the resolution of video technology and the frame grabber imposes the most stringent limitation on the number of particles able to be tracked. Eulerian as well as Lagrangian descriptions may be obtained, utilising a suitable interpolation method, if the particle seeding density is sufficiently high.
This document outlines and describes the two-dimensional
particle tracking technique utilised by DigImage. This method
represents an efficient, reliable approach to tracking particles
from a two-dimensional projection of a flow. The computation required
to analyse each frame pair increases only slightly faster than
linearly with the number of particles, allowing between 5 and
30 frame pairs per minute to be analysed. A step by step tutorial
is also provided in the file DigImage\Macros\Track.CMD.
This macro may be used either with the sample tracking movie available
from http://tiki.damtp.cam.ac.uk/digimage/examples/tracking/ ,
or by printing it out as step by step instructions on how to set
up DigImage for particle tracking.
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