Thanks for the response. I will attempt to implement this workaround to eliminate the improper fits/angles, but I have couple ideas that I wanted to get your opinion about. When I first begain working on this problem I thought to fit vectors to the perimeter points close to the corners and then use the VectorAngle operation to calculate the angle between them. However, I didn't yet find a good way to tell Mathematica to estimate the vector most closely aligned to the perimeter tangent.

All things considered, it seems to me that your algorithm does a reasonably accurate job of measureing angles where one of the line fits does not approach verticle and the graient infinity, so a simple solution might be to test for these condition and drop the results from each measurement where it is true. In the case of the microstructure I'm working with eliminating all those measurements should not bias the results since the orientations of particle contacts should be completely random (after all, they were processed in the absence of gravity). Of course the algorithm would not be as robust, but would still provide a good basis for further work in the field. Let me know what you think. Phill

Hello David G., I was able to adjust the code to accept a full-sized digital image and ran the calculation with some initial success. Overall I believe that this code estimates each angle in fundamental sound method, with a few exceptions. The biggest problem seems to appear with angles where points along the perimeter adnacent to the corner appear to be nearly verticle with respect to the y-axis of the plot. The fitted line shown in some of these plots (I have shown the first 25) don't seem to fit well with the data points. I suspect there may be a problem related to the lack of a defined slope with lines are verticle. Do you have any thoughts?

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I haven't developed a particularly interesting angle analysis algorithm, however I've done a lot of implementation work that may be of interest to you.

Whilst Mathematica's image processing and morphological tools are fantastic, I felt one could only go so far with image based analysis. Ideally one would calculate an ordered perimeter so that the position of used data relative to each corner is well understood.

To this end I split the perimeter into closed cycles to order the data:

Then I manually detected corners by traversing these cycles with a rolling average and logging high angular change.

This lets one directly look at the pixel data either side of a corner point. Ideally one might fit a curve to each meeting edge, allowing a low radius angle to be calculated from high radius data. I just use linear fits, fifteen pixels either side of the corners, and this is fairly ok.

The whole procedure is fairly clean and commented in the attached notebook.

I have to agree with David on this one, this is an interesting problem!

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This is an interesting problem. I have been thinking of an approach based disks of successive radii. Looking at the top image, begin at a vertex and define a disk region of a small radius. Count the black pixels within the disk. Do the same for successively greater radii. At each step, the rate at which the black pixel count grows is a function of the arc subtended by the black region at that radius. For any given radius, this may be a noisy number. But if the curve could be fit, perhaps from the fit could be determined an estimate of the angle of separation at the start. It would help if some assumption could be made regarding the form of the function to be fit.

Hi Phillip,

Would you mind posting some source data, for example one of your input images at max resolution.

My immediate commentary regards data cleanliness. The sample image you're working from contains four areas that are aligned with varied precision. You are examining corners along these boundaries, along with corners at the edges of the image (notably some noise in the top right has created at least one erroneous corner.)

I would suggest partitioning your input into each separate image, and then extracting the shapes entirely contained in each image. If you're expecting high variance this suggestion may be inappropriate, as it may skew your corner data towards that of smaller 'blobs'.

Finally, all of these corners feature highly curved edges, thus the higher resolution we examine the smaller the output angles will be. Will all the input data be at a consistent resolution? Is there a specific pixel radius you want to specify measuring at?

David