# Moments of inertia in image processing

1. Aug 20, 2008

### psycovic23

Hi,

I'm currently working on an imaging problem that oddly requires some physics. Basically, I'm given a set of gray scale pixels and I have to determine whether they're a fiber or just random noise. My question is, how do I calculate the moment of inertia of the pixels while considering their gray scale value? I know how to calculate a uniform moment of inertia ($$\sum r^{2}$$), but not when I have to consider discrete, non uniform weights to each pixel.

A continuation of that part is, how might I quantize the "blob-iness" of the pixels? A professor suggested finding the eigenvalues of the inertial matrix [m_x m_xy; m_xy m_y], but I'm not entirely sure what the eigenvalues end up representing. Any ideas?

Thanks!

2. Aug 21, 2008

### pallidin

I found this to be a very confusing question with regards to the moment of inertia and imaging until I pondered "grey scale"

Are you referring to an electron microscope?

3. Aug 21, 2008

### Andy Resnick

What you are trying to do is a fairly standard analysis, and many programs out there (MatLab, ImageJ, etc) have routines for this already. Essentially, you are weighting the calculation by intensity rather than mass, but the idea is the same, and the eigenvalues are the "principal axes", if you like, of the blob.

http://en.wikipedia.org/wiki/Image_moments

4. Aug 21, 2008

### psycovic23

I'm using Matlab, but have been unable to find any functions to do it. Are there functions in the Image Processing kit that I'm missing?

5. Aug 21, 2008

### Andy Resnick

I'm surprised there's not an obvious choice... the 'regionprops' tool has a few things that may work for you.