Hough transformation for an automated band detection in electron backscatter diffraction (EBSD) patterns is a commonly used. As two-dimensional coordinates the tilt and the distance from a circular region of interest is used. The resolution of this Hough space is described by a single number. Does anybody know how this number is calculated? Are they identical for the different EBSD systems, or are there differences known? Since one dimension is an angle the other is a distance, for what the number stands for?
Dear Gert,
here at page 40 you can see Hough options from EDAX TEAM software (we use it):
https://rsc.aux.eng.ufl.edu/_files/documents/964.pdf .
so there is theta step size (1 degree) and binned pattern size (96) so I think that Hough size is 96 (distance) x 180 (angle).
Yes, in that example it is 1 ° and can be changed as well as binned pattern size.
Possibly there is some ambiguity here. In an automated system, one resolution is an input - this is the angle step size as mentioned by Grzegorz. The number that we get as an output is the resolution of the distance. I feel you are asking about the second one.
Coming to why it is so, the simple Hough transform (HT) has two parameters - angle and distance. The resolution of both these can be changed and the corresponding transform will change. However, in an automated system, the user only specifies the resolution of the angle, and the system accordingly calculates the resolution of the distance. This is done to aid the image processing - if the Hough peaks have a particular geometry (peak height=peak width), they can be easily extracted by using a mask. (The 3x3, 7x7 etc settings during HT that may be available correspond to the size of this mask). The result is that band detection becomes easier (for the algorithm)and maybe faster. I'm not sure if there is an associated drawback - would be very interested to hear your opinion on this.
The formula to calculate distance resolution from angle resolution is not specified (to best of my knowledge) in commercial systems, but it should be traceable back to the original papers on automating HT.
My question is really related to the Hough resolution. As Grezegor pointed out, you can change in TSL several options. I agree with him. Slide 19 shows at least the angular resolution. 3° is shown....and I hope this described Hough resolution 60. Slide 18 shows a few combinations which are derived from a spherical screen and a circular ROI. That the shown rectangular Hough space suggest a higher angular resolution should not disturb us. I assume that default settings select someting like h 60x60. From HKL I actually do not know this. I believe that I've heard the number given there is only half the sizhe hh z,owever I h e. Is this reasonable? There you can only select ONE number, like 65.
Ideally, one would like to be able to set both parameters of Hough resolution, i.e. distance and angle. In HKL, we set the distance resolution (what they call the Hough resolution and has values like 50, 60 etc), and it determines the angle resolution by itself (possibly uses a default value, or uses the input value using something like http://www.ebsd-image.org/documentation/reference/ops/hough/op/autohoughtransform.html)
In TSL, we set the angle resolution (theta step size) explicitly and the distance resolution is determined by the system. We have an indirect input, though, the binned pattern size (eg. 60x60), which corresponds to the image space, not the Hough space. As shown on slide 18, this is distinct from Hough resolution, though there is some relation ("...can have some independence")
So while neither gives total (or transparent) control over the HT, TSL does give atleast 1 explicit and 1 implicit parameter.
To clarify, in the above answer " (possibly uses a default value, or uses the input value ..." is a hypothesis only, I don't find a description anywhere. :)
For high-binned patterns the vertical Hough resolution can be certainly the image resolution, but for low or un-binned patterns it is (from my point of view) not. Did you ever try to Hough-transform a non-binned pattern? It takes seconds, and not a fraction of a second as required for the mapping.Therefore it seems to by the case that patterns are binned down software-internally (S. Wright wrote this as well in one of his nice papers). I guess that all patterns are binned to a lower size...but not lower than..., e.g. lower than 200 but not lower than 40 pixels. I also do not know what you will do with the butterfly filter since his dimension is related to the resolution. From my point of view it should not be very beneficial to play with the free settings of Hough space (except you are adapting the filter in the same way). I guess, the indexing is optimized for a regular resolution, and so the butterfly filter. Nevertheless, the question is still open, what HKL is doing? Is this the same "real" resolution or some proportional factor? And since they enable to change the resolution in steps of 1...do they resize the images for the selected resolution?
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