Hello everyone!
I have a pair of images (A and B) of the same object, and these images were taken at different time moments. Some parts of the object shifted, deformed or even disappeared; moreover, the images were acquired from slightly different angles. I want to quantify the spatial similarity of the two images.
This procedure is sometimes called image registration. The result of image registration is a pair of deformation fields for the A->B transformtaion and the reverse B->A transformtation. I use the bUnwarpJ plug-in of Fiji to build the two transformtations.
How could I quantify the typical deformation in the two transformtations? Are there any standard measures for it?
Dear Dmitry Bagrov ,
A heuristic for computing similarity in unstructured image data.
https://towardsdatascience.com/image-similarity-theory-and-code-2b7bcce96d0a
Regards,
Shafagat
The difficulty with deformations is that they are usually not homogeneous throughout an image (except e.g. your camera is fixed and your object is moving horizontally across your image).
If you're interested in pixel similarities, you could use the structural similarity index (SSIM). However, this is not a metric, since it is perception-based (But there are variants that could be used as a metric).
Another method would be to run some optical flow algorithms and look at the resulting vector fields.
Gebhard Stopper, thanks!
Let's say I have a vector field - I obtained it as the output of the bUnwarpJ plug-n. It is presented as a set of B-splines, but it can be easily converted to the X and Y components of shifts for individual pixels.
Which meaninful quantities should I calculate based on this vector field? Are there any standards?
For example, I think that prior to any calculations I should remove the overall shift and rotation components from the vector field, because the shift and the rotation retain the interpixel distances and do not characterize the deformation. After that, I can calculate the average modulus of the residual? Or the standard deviation? or anything else?
It of course depends on what you want to achieve. For example, when we do cell tracking, a large number of cells move on a mostly linear path from A to B. Some move in curves, some have more complex motion patterns.
So, what we often do is we get the overall motion vector of our cells (we do some segmentation beforehand) i.e. endPos - startPos. This way we get the overall direction of motion. For this you could use the mean vector or the larges vector of your segmented object.
What we also do is normalizing the motion vectors and put them in a (polar) histogram e.g. divided into 30° steps. This lets you immediately see if there is a dominant direction of motion.
Alternatively you can of course use the per-pixel vectors to get local deformation fields. Computing the vector magnitude per-pixel can show you where more or less deformation or motion takes place.
Removing the overall shift is definitely a good idea. I would probably try to detect it in the background first (e.g. average background shift). After that you can go crazy with statistics and maybe Shannon/Kolmogorov Entropy to get the metric you need.
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