I used the edge (canny) function to retain the edge-line (black and white TIFF image, so not a vector graphic) of a wiggled cell wall in a microscope image. I want to analyse the exact shape and distribution of the wiggles, however the cell walls are also curved across the picture (not just round). Does someone have experience in Matlab on how to straighten a curvature (perhaps convolution with another image that I could make of the cell wall shape without wiggles - but how can I do that with images)? How would you then analyze the final staightend but still wiggled line? (Locally fit to function/polynomail and derive?) I found the options Hough Transform (lines only) and bwtraceboundary (closed boundaries only), which both don't quite seem to fit.
Generally, the polynomial fit as well as FFT/DCT approach is doable. But, both of the methods have some assumptions. Data for FFT/DCT must be function-like. It means that for one x-value there must be only one y-value. In addition a common variant requires equidistant x values. You should modify your pre-processing stage to meed these requirements. The polynomial fit assumption are not so strict, only the polynomial output must be (will be) function (see the "definition" above) - so be sure and do not switch axes before the fit. From these reasons, I suggest the polynomial fit. If you are not sure, that all images are function-like (horizontal left-to-right), I recommended some appropriate rotation pre-step.
I have written down a matlab-function example (attached). Using is simple:
img = imread('BWimage.tif');
xy = staightData(img);
perhaps you should add some code to let us see what "format" the input data has. Would help me / us helping you ;)
Hallo Tobias, see my publication, the method is very close to what you need, however it is in c++ and it is part of a rather lager API, nevertheless the algorithms will help you:
Conference Proceeding: Eccentricity edge-graphs from HDR images for object recognition by humanoid robots... please do not hesitate to contact me :)
I would suggest you to look at two separate sets of work:
1) segmentation tools in the spirit of geodesic active contours/geodesic active regions/snakes/level sets. They may regularize the wiggling contours, see for instance the pictures in http://www.iacl.ece.jhu.edu/static/gvf/ and a GUI at http://www.iacl.ece.jhu.edu/static/gvf/snakedemo/
2) tools form mathematical morphology, i.e. erosion, dilation, opening, closing, with illustration here http://www.inf.ufsc.br/~visao/khoros/html-dip/c9/s4/front-page.html
Generally, the polynomial fit as well as FFT/DCT approach is doable. But, both of the methods have some assumptions. Data for FFT/DCT must be function-like. It means that for one x-value there must be only one y-value. In addition a common variant requires equidistant x values. You should modify your pre-processing stage to meed these requirements. The polynomial fit assumption are not so strict, only the polynomial output must be (will be) function (see the "definition" above) - so be sure and do not switch axes before the fit. From these reasons, I suggest the polynomial fit. If you are not sure, that all images are function-like (horizontal left-to-right), I recommended some appropriate rotation pre-step.
I have written down a matlab-function example (attached). Using is simple:
img = imread('BWimage.tif');
xy = staightData(img);
Thank you for your advice! This is exactly what I was looking for.
@Jan Vanek: Thank you in particular for the efford you put into helping/ explaining solutions to me! The code is a very good guide! Your rotation is a lot more elegant than what I implemented by then and the polynomial fit works really well. I appreaciate that greatly. It is an answer to all the posed questions for this implementation.
@Laurent Duval: Both very usefull. 1) My edge detection already works very well but for potentially more complex images in the future, the snake finding algorithm might be great value. 2) Nice demonstration. It seems to be a nice solution im malab to use bwmorph 'dilate', and then bwmorph 'skel' instead of 'close' in order to close the line.
@David Gonzalez-Aguirre: Fascinating material! However a bit more complex to read into for the "side problem" that I am trying to solve.
Actually, there is still one problem with substracting the polynomal fit to remove the curved cell shape: The "wiggles" have a normal orientation to the polynomial fit/cell surface. By only substracting the fit, they appear tilted depending on their original position on the curve. Also the sizes decrease. The structures should idealy keep the orientation relative to the fit and then be "stretched" into a linear shape. This is possiby closer to David Gonzalez-Aguirre's work. But I haven't quite gotten through it yet. I will keep thinking about it.
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