Spatial segregation from a raster of racial distribution in the USA

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I am trying to measure the degree of racial segregation at some geographic level (let's say the county level, for simplicity) in the USA. I have a shapefile with these geographic units.

To do so, I've downloaded this map in which there are dots of different colors (4 colors) and each color represents a different race. Each dot is a person. I have georeferenced the map so I have a properly georeferenced raster.

What would be the best way of computing a segregation index at the level of my geographic units? Given that:

-In each pixel, there can be different colored dots, so that the resulting pixel is a mixture of colors. It is then not trivial for me to infer the % of each race in each pixel/grid- I am not that familiar with research on spatial segregation, so I could use some help on the measure I have to choose.

I can do it using: QGIS, GDAL, Python or R



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