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Using Fourier analysis to measure cell size and shape
Posted:
Nov 26, 2004 11:00 AM


Hi
I have an image processing problem that I need help with. I am looking at cellsize and morphology in a cellstructure and although my problem does not directly concern any particular MatLab functions, it relates to methods that are easily implemented in MatLab (which is the software that I use) and probably someone here can give me some useful and general, or specific advice. To help illustrate my problem I have put some images on this webpage <<a href="http://www.homepages.ucl.ac.uk/~smgxro1/page1.html">http://www.homepages.ucl.ac.uk/~smgxro1/page1.html</a>> and I will be referring to those images below.
The cellstructure is imaged with a fluorescent Microscope at 40x. To determine the individual cell size I look at a regionofinterest (ROI) in the Frequency domain where the peak spatial frequency can easily be converted into the average cellsize (topright corner of image 4 and 5). The tissue sample is around 5 cm square and it is quite a delicate process to prepare and flatmount it (image 1). To get the Fourier transform to register a distinct peak frequency I use the following preprocessing steps (results can be seen on the left of image 4 and 5): 1) Blind deconvolution  to improve image resolution and compensate for outoffocus areas of the flatmounted tissue. 2) Uniform local histogram equalisation (CLAHE)  to optimally enhance image contrast. 3) Gaussian lowpass filtering  to eliminate lowfrequency changes (due to uneven illumination, tissue thickness etc.).
Once I have the peak frequency of a given ROI and I know the image px/µm ratio I can derive the mean cellsize. Finally, I plot the mean cellsize and the standard deviation against the distance from the centre of the tissue (the cellsize increases with distance from centre). In the centre of the tissue the cells are tightly packed in a hexagonal lattice, which makes it ideal for an isotropic Fourier analysis (image 2 and 4). However, towards the extreme periphery several morphological changes take place: The cell shapes becomes severely deformed, the cell contents change (and hence, the pixel brightness, edge gradients etc.) and noneRPE cells are mixed into the lattice. Image 3 illustrates but one of countless and random cell configurations and as a consequence the frequency spectra becomes even harder to evaluate (topright of image 5).
These are my two questions: 1) How can I improve on the preprocessing of the microscopic images to enhance the cellwalls, or edges and eliminate other noncontinues cell artefacts? 2) The mean cell size and it's standard deviation give a very accurate measurement of the central and highly regular lattice, but when the cell structure becomes more irregular, it is less meaningful. Are there better spatial descriptors  and methods to measure them  for the random cell shapes that I encounter at the periphery of the tissue?



