# Image analysis for speckle pattern

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Filippo on 31 Jan 2023
Commented: Image Analyst on 3 Feb 2023
I have a NxN real (double) matrix which contains the information of a speckle pattern like the one shown in figure 1 (see the attachement).
The main goal here is to have a size distribution of the "speckle grains", so we can divide the problem in two different parts:
1. given the image (or the matrix, whatever is the best for the algorithm), try to find the grains of the image;
2. for each grain, apply some sort of analysis (contour? regionprops? edge?) in order to extrapolate the information of its size (i.e.: is it possible to fit a circunference and then extrapolate the diameter/radius?)
The idea is to apply a sort of "pattern recognition" in order to extrapolate both the number of grains and their size information, is it possible?
DGM on 1 Feb 2023
In order to isolate the grains and get information about their properties, you need to first decide what defines a "grain" and how each grain is distinct from the background and its neighbors.
I see a lot of features that are large entangled blobs. If you expect those features to be divided into smaller parts, @Benjamin Thompson's suggestion might be a good place to start.
Filippo on 1 Feb 2023
Thank you for replying. I think that the crux of the problem is to isolate the grains, given the complexity of the pattern. You are right, Benjamin's suggestion is a good place to start, but, unfortunately, it fails in separating all those (very complicated) entangled blobs.

Benjamin Thompson on 31 Jan 2023
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Benjamin Thompson on 1 Feb 2023
We cannot help you define what is a grain in your problem, but once you have done that, these methods will calcalate the grain area and other properties. If you are having problems with this, sometimes changing how the image is captured can help. Try different lighting, a different type of camera, etc.
Filippo on 2 Feb 2023
I agree with you. Indeed, thank you very much for your answer, it helped me by looking at my problem from a different perspective. To answer the last part of your reply: unfortunately I cannot change my image since it is a simulation, so I cannot change lighting, or similar.

Image Analyst on 1 Feb 2023
It's not obvious what a single grain is. What instrument created this? Was it an AFM? Can you zoom in so that the "grains" are bigger than a few pixels? What material is this?
Otherwise I think you'll need to look to other metrics to describe what you are trying to correlate your image analysis measurement to. Like for example you want some image metric to correlate with strength of the material. Well maybe you can measure some bulk metric like the standard deviation of the gray levels and that might be just as good as if you were able to find the grain area distribution.
Filippo on 3 Feb 2023
In a certain way you are right. In fact I need the grain size distribution let's say "for statistical reasons", which might sounds silly. The main reason why I'm struggling in doing this is because I want to compare the value that will come from this "statistical study" to the theoretical value.
I'm already trying to thresholding the image and then calculate the areas of the "binary image" that I obtain in the process. Thank you very much for the suggestion of the "watershed" tool. I appreciate it
Image Analyst on 3 Feb 2023
To do blob detection by thresholding, see my Image Processing Tutorial in my File Exchange:

Bjorn Gustavsson on 3 Feb 2023
A couple of things I'd try would be to determine the size-distribution of the speckles at different intensity-levels. This I'd do by determining the grain-boundaries at some intensity-levels using contour and either of contour-matrix-to-coordinates or getcontourlinecoordinates to get the speckle-boundaries, then find all contours that are closed and calculate their areas using
For each speckle j.
It should be reasonably straightforward to determine which contours are closed - same start and end-point, at least to within double-precision.
Once you have the contour-coordinates and loop over all speckles you might as well calculate the total intensity inside a speckle, for that you should have good use of inpolygon to determine which pixels belong to a speckle (this might not be very efficient, but this should not be a too time-consuming task anyway). You might just as well calculate the centroids (both the area-centroid and the center-of-intensity) of the speckles and look at the distribution of those over the image (nearest-neighbor-distance and whatnot.)
HTH

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