2D distribution/histogram's center of mass

I have a bunch of 2D histograms showing the relative dependency of two variables X and Y, under several conditions. Each histogram is 7x7, is produced with imagesc(), and looks something like this:

I would like to compute a single (scalar) measure of central tendency for each of these distributions. Something like a center of mass, although I havent found anything like this in the Matlab documentation, and I don't know anything about the field of image analysis.

Also, ideally, I could show this graphically as well by perhaps highlighting the cell of each distribution that contains this center of mass, or better still, a region within a certain radius of the center of mass that contains 68.2% (one standard deviation) of the volume of the distribution.

Any help much appreciated.

[José-Luis]

If by center of mass you mean the median of a multivariate distribution, then there are very many ways of doing that. The simplest one would be to compute the median along x and the median along y. Depending on the nature of your data, it might give you terrible results.

[z8080]

Thanks, I realise this was a very vague and open-ended question :) My data represent subjective ratings from participants on X and Y, two perceptual measures. The different conditions represent different genres of music, and they all have very different-looking histograms, suggesting at a qualitative level that music from each genre is very different in terms of how X and Y relate to each other. I just want a quantitative measure of this difference.

Which measure do you think would the most appropriate/relevant? Let me know if I should give more details. Many thanks indeed!

[José-Luis]

You could fit it to a multivariate normal distribution, see mvregress(), see how well it fits, and the statistics of the distribution could give some insight into the problem.

[z8080]

I'll try that, thank you very much for your help