I want to calculate the number of points that overlap a raster with different areas (the areas have different numerical values).
How can I determine how many points fall within each area of the raster?
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This is one way to do it:
Create a count field and a spatial join between the point shapefile and the polygon shapefile.
Alternatively, you can use extract multivalue to point in order to get the value of the raster under each point. Then you open the attribute table of your point layer and you click on the raster_value column to summarize the number of points for each of the values.