Is there a way to convert an image to gridded raster data?

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I've been doing some research exploring different types of mapping data analysis. I've hand drawn a map of some areas using GIMP, which simply divides an area into regions on a blank, geographic map. Then I figured it would be nice to have some kind of data to qualify each of these regions, which would be things like population, total area, agriculture, etc. Of course, there are some applications online that can calculate area and population of a given region, but that would be pretty painstaking to do one-by-one. Then I found out that places online like NASA has a plethora of datasets already, in the form of gridded data.

Unfortunately, the maps I drew are raw images, like PNG or similar image types, not gridded or raster data. I imagine there should be some way to convert the image to a raster of cells, where each cell is assigned an ID number corresponding to which region on the map it belongs to (unless its a edge case, literally). Knowing the kind of magic that image processing or feature detection can do nowadays, I would really expect this sort of algorithm would be trivial by comparison (as my map is completely featureless except the borders of regions and the coast of continents). Of course, I could try to work it out myself, but I don't want to reinvent the wheel. (Also the map projection isn't any issue, because I know the projection of the map I used, and changing from one projection to another is pretty straight forward).

So is there a way to convert an image type to a dataset of raster cells? Worse comes to worst, I could redraw the whole thing in a different application that is able to to generate a gridded dataset, but I have no idea what software would do that. Also, I apologize if this question is too broad at all, I am not sure if there is a more specific forum that I can ask for help on.

Thanks, Nathan

Edit Here is a sample of my map that gives an idea what kind of image I'm talking about. You can visual see that the map is divided into four regions. My goal would be to convert this into a raster, where reach cell is given some ID number (like a number 0-3 for example) depending on which region it falls into.

enter image description here

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