Math Forum Discussions

Peter Lundh

Posts: 11
Registered: 1/25/05

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

Plain Text

Hi-

I have an image processing problem that I need help with. I am looking
at cell-size and morphology in a cell-structure 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 cell-structure is imaged with a fluorescent Microscope at 40x. To
determine the individual cell size I look at a region-of-interest
(ROI) in the Frequency domain where the peak spatial frequency can
easily be converted into the average cell-size (top-right corner of
image 4 and 5). The tissue sample is around 5 cm square and it is
quite a delicate process to prepare and flat-mount it (image 1). To
get the
Fourier transform to register a distinct peak frequency I use the
following pre-processing steps (results can be seen on the left of
image 4 and 5):
1) Blind deconvolution - to improve image resolution and compensate
for out-of-focus areas of the flat-mounted tissue.
2) Uniform local histogram equalisation (CLAHE) - to optimally enhance
image contrast.
3) Gaussian low-pass filtering - to eliminate low-frequency 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 cell-size. Finally, I plot the mean
cell-size and the standard deviation against the distance from the
centre of the tissue (the cell-size 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 none-RPE 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 (top-right of image 5).

These are my two questions:
1) How can I improve on the pre-processing of the microscopic images
to enhance the cell-walls, or edges and eliminate other non-continues
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?