Hi there, i have a solution,
% in my case i used lon and lat from NetCDF file, you can use the georefence data from your tiff.
%example
lon=-(77:0.05:65); %longitude in WGS84 for example with 0.05 degrees of resolution
lon=-(55:0.05:50); %longitude in WGS84 for example with 0.05 degrees of resolution
%Now do you have to craete a Mesh
[X,Y]=meshgrid(lon,lat);
points=[X(:),Y(:)]; %point of the grid
%Load your polygons
S = shaperead('yourfile.shp');
%Loading polygons (one by one)
for i=1:length(S)
%you can define yours polygons with some variable... or do it directly from Shape
polygons={S(i).X,S(i).Y}; %S(i).X and S(i).Y define the polygon "i" coordenates
%Index of point inside of each a polygon "i"
ind=inpolygon(points(:,1),points(:,2),polygons{:,2},polygons{:,3});
%here the function depends of you, in this example i used mean
mean_variable_polygon(i,:)=mean(your_raster_file(ind));
clear polygons ind
end
In other case, i recomend you use Zonal statistic extraction tool from Qgis.
