For band detection in EBSD (Kikuchi) patterns the Hough transform is used which is applied on binary images exclusively (in commercial software for maximum speed).
If one would apply the Hough transform on the original grayscale images, does the reverse transformation delivers the original EBSD pattern?
Does it also mean, that saving the Hough transforms instead of the EBSD patterns automatically means a loss of information since they are based on binary images?
Moreover, the Hough transform is applied on background corrected images. Does this mean that the storage of the Hough transform, which obviously becomes recently popular, is not as good as it will be represented?
What do you mean by 'EBSD pattern'? The Hough transformation is actually applied to a Kikuchi pattern for a specific location on/in the material. The 'line identification algoritms' are then used to link this to texture. The Hough transform itself is (as far as I know) fully reversible. Of course, if you apply the Hough transform to filtered data (binary and background correction), the Hough data will reproduce the filtered data. Most EBSD softwares also only use and store a limited number of Hough peaks (you can normally choose yourself how many you want) e.g. 5 to 8. This corresponds to 5-8 lines in the Kikuchi pattern. All other lines will be lost. If of course you store the whole Hough image, you should be able the same Kikuchi pattern, but then of course you loose the advantage of only storing the Hough peaks (you trade one image for another).
You can find the answers and details on my website www.ebsd.info under "Pattern Solving". The original Hough transform applies to bitonal rather than gray-tone images and is so a special case of the Radon transform. Patterns are gray-tone images. They are usually in a digital data format due to the use of digital cameras.
The reconstruction of a pattern by backtransformation will not produce a faithful reproduction, simply because the intensity in a Radon cell is equally distributed on the corresponding line in pattern space.
Transformation induces several further artefacts (limited number of pixels and cells, rounding errors due to binarization and pattern coarsening, bands are conic sections rather than straight stripes,...). It is therefore recommended to store the raw patterns. Stored Radon resp. "Hough" peaks are useful for a fast check for "forgotten" phases.
In spite of all these limitations it is quite amazing how well band localization works.
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