public class PIV_analyser
extends Object
implements ij.plugin.filter.PlugInFilter

PIV analysis

This plugin calculates the optic flow for each pair of images made with the given stack. It does using the PIV method, which is the most basic technique for optic flow, and is a block-based method. This a technique, mainly used in acoustics or in fluids mechanics, that enables the measurements of a velocity field in one plane, using imaging and image analysis. It can be seen as one of the most simple pattern matching problem implementation.

See the book Raffael, M.; Willert, C. & Kompenhans, J. (2007), Particle Image Velocimetry: A Practical Guide (2nd ed.), Berlin: Springer-Verlag, ISBN 978-3-540-72307-3

PIV analysis is based on inferring in what direction and in what amount a part of an image has moved between two successive instant. In the aforementioned domains, a flow is visualized by seeding it with light-reflecting particle (smoke in air, bubbles, glass beads in water, ...) and imaged at two very close instant. The cross-correlation between parts of the two images where pattern generated by particles can be seen is then used to compute the velocity field.

The PIV algorithm is made of the following steps:

1. two images are acquired of the same object are acquired at two successive instant;
2. they are spliced in small pieces called interrogation windows;
3. the cross-correlation between the two images is computed for each small window;
4. the peak in the resulting correlation image is searched for. The peak location gives the displacement for which the two image parts look the best alike, that is: the amount by which the second image has to be moved to look like the first image the best;
5. the velocity vector at this point is defined as the peak's position. This assume that between the two successive instants, the image did not change too much in content, but moved or deformed.

Application to Life-science images

Here are two examples of its first applications in Biology:

• comparing flows in a drosophila embryo during gastrulation in control situations and after photo-ablation - Supatto, W.; Débarre, D. & Moulia, B. et al. (2005), "In vivo modulation of morphogenetic movements in Drosophila embryos with femtosecond laser pulses", PNAS 102: 1047-1052, PMID 15657140
• quantifying blood flow during cardiogenesis in zebrafish embryo - Hove, J.R. (2003), "Intracardiac fluid forces are an essential epigenetic factor for embryonic cardiogenesis", Nature 421: 172-177, PMID 12520305

For us, the main interest of this technique is that it allows the computation of a velocity field without having to segment objects out of an image and track them, which makes it particularly interesting when dealing with brightfield or DIC images. The trade off is loss of precision, but also the fact that you might get completely irrelevant vectors.

Algorithm

As stated before, this plugin implements a very naive and promotive algorithm, without a sense of subtlety. It has a very pedestrian approach, that make it slow. For each pixel away from the border of the image, a block is extracted for the front image and the back image. The correlation matrix is then calculated from these two blocks, and the result is analyzed to produce a flow vector. This is a highly redundant process, for when the algorithm moves to the next pixel to the right, the blocks content change only a little (only one column is replaced actually, and the rest is shifted left), but the whole correlation matrix is recalculated from scratch (a lot of wasted CPU cycles).

Typically, on a MacBook (grey model, 2009), for an 8-bit stack with a window size of 8x8, the plugin, the plugin can process a stack of 200x200 in approximatively 2 seconds. I recommend downsampling the images, this would diminish the density of results, but make this plugin affordable.

How to use

ROI selection

If you want to restrain the analysis to only a certain portion of the image, select it in a ROI of any shape.

Image features

Tough you don't need to have traceable objects for PIV, there is still some requirements for it.

PIV is based on a very simple pattern matching algorithm. This means that, to be effective, there must be some patterns in your image. Typically, the dotty structures of aggregate in a epi-fluorescence movie or the granularity that can be see on a brightfield image will do. As a rule of thumb if you can see something moving by eye, the PIV might be able to get it quantitatively; otherwise not of course.

Also keep in mind that (so far) it works only for a 2D plane. With optical sections, the algorithm might become puzzled by the appearance of grains moving in the Z direction. Also with thick specimen imaged in brightfield: the image of a dot deforms while moving in Z, which may lead to irrelevant values.

Choice of the interrogation window size

To perform pattern matching, the image is spliced in small pieces. Since you want to have clear patterns to match, it is a good idea to choose you interrogation window size bigger than the image feature whose movement you interested in.

Let us suppose that one one image, some structure can be found in the shape of 'grains' whose size is about 10-15 pixels. To always get at least a full one, a window of 32x32 pixels would be relevant.

Averaging

In fluid dynamics, velocity fields resulting from PIV are generally heavily spatially filtered afterward. In these cases, each of this vector represents velocity in a fluid for which the flow is generally spatially correlated on a large scale, so filtering in the spatial domain makes sense.

One can recommend to filter temporally, that is: for every vector in the field, replace its value by the moving average from a few frames before until a few frames after. If your movie is oversampled temporally, that might be effective in averaging outliers.

Filtering

The plugin returns also a stack made of the peak height and a tentative signal/noise ratio for the analysis.

The peak height is just the value of the correlation peak for each pixels. This can be used to mask irrelevant part of the result image. The algorithm will be typically puzzled where there is no structure to correlate. In these parts of the image, the peak height will be typically low; one can then threshold the peak height image, and use it to mask the result image.

Version history

• 1.0 - 18 April 2009 - First public release.
• 1.1 - 19 April 2009 - is now interruptible
• 1.2 - 20 April 2009 - is now multithreaded

License: GPL

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License 2 as published by the Free Software Foundation.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.