# Image Processing Primer

Hi,

I am starting work on a new request to some image processing. Some of the features to identify are straight forward and I have done them many times with particle analysis. This time time in addition the request include analysis of periodic structures, i.e. do stripes appear in the image. My first response is to an FFT on the image and while I can handle the mechanics within Igor, I would like to better understand what the output means.

The objective: The images are taken from a Zygo microscope so height gets mapped to intensity. The question is "are there wave like structures in the image and if so what is there period (how far apart are they), how high are they (amplitude) and what part of the image are they occupying?"

I am using this page http://www.cs.unm.edu/~brayer/vision/fourier.html as a starting point of my education and while I can reproduce some the output within my test images not all. Is there a better reference to understand how to understand and quantify the results of an image fft. Also is there a better way to do this analysis?

Thanks in Advance

Andy
Hello Andy,

When I went to school (back in the Jurassic era) there were two good books on the subject: Bracewell's The Fourier Transform and Its Applications and Goodman's Introduction to Fourier Optics. Bracewell is mostly 1D but is excellent if you want to understand the math. Goodman's is an engineer's book that's pretty elementary.

The web site you listed is interesting but I am not sure how helpful it might be in practice when you actually have to evaluate the transforms and work with complex data.

Returning to the practical problem of the detection of periodic structures I would start by looking at the magnitude of the 2D FT of the images. After accounting for symmetry you can get an idea of what spatial frequencies are present in your data.

Special cases (if you are lucky):

-If there is a small number of predominant frequencies you could extract them from the transform and convert into a fitting problem.

-If the images have a preferred axis you might consider reducing the problem into a 1D array and possibly applying the Lomb Periodogram (happens to be built in operation).

-If you are expecting one or more particular structures you may be able to identify them using match-filtering/correlation approach.

One last note: I assume that you have already tried the various examples in the Image Processing Tutorial.

A.G.
WaveMetrics, Inc.

A.G.

Thank you very much for your input. I am working with a client and if successful they will be buying site licenses for Igor, so wish me luck.

Andy