Separating and extracting data using edge detection

I want to use edge detection to separate my data and put the “pieces” into separate matrices.

I begin with a large matrix (~1000x1000). Within it, I have data points that are clustered together and several cells of "NaN" that separate the clusters from each other. After changing the NaN values to a very big negative number and using the "mat2gray" function, I run the "edge" function. Viewing this shows that the clusters are well outlined.

What I would like to do now, knowing where the edges of the clusters are, is create matrices containing the original data of a single cluster for each cluster.

My problem is that I do not know how to use the output of the edge function to accomplish that. I would appreciate any advice, including if this is an inefficient/impossible/dumb way to get what I want. My motivation for using edge detection is that the cluster placement and spacing is not constant and the "pattern" of the clusters change from data set to data set.