Scatter plot or 2D histogram for mixture of Gaussian fitting?

Question

I am ust a little bit confused about whether I should use a scatter plot or a 2D histogram to fit a mixture of Gaussians.

The problem is I have intensities from one image with 2 channels. For example, a RGB image but using just Red and Green channels. Then I plot the scatter plot and try to do a mixture of Gaussian fitting for the data points in the scatter plot.

However, thinking about the problem again, I am not sure if I should do a Mixture of Gaussian for the 2D histogram. Essentially, a 2D histogram is different from a 2D scatter plot, am I right?

Sorry about my confusion and thanks for your help.

Answer 1

A scatterplot and a 2d-histogram are two ways of presenting the same information. The second is basically taking the first and binning it to get an idea of the local density.

As such, you could fit a mixture to either kind of information (you don't fit it directly to the display, but to the data); if you fit to binned data rather than raw data obviously you'd lose some information, but it would still be quite possible to do so.

Since you ask which you should do, it appears you have the ability to choose. Where feasible, unbinned data would give you more information than binned data, but other considerations can impact the choice.