When you convert the polyshape into an image, the result of the centroid would be different due to the resolution of a pixel on an image.
Regarding to the warning message, you may refer to this: https://www.mathworks.com/matlabcentral/answers/606836-why-does-the-polyshape-function-deletes-the-vertices-in-the-input-when-there-are-no-duplicated-poi
Consider the following example with a very simple polyshape:
pgon = polyshape([20 20 17 15],[7 3 2 9]);
[x,y] = centroid(pgon)
Now, convert it to an image:
A = zeros(25,25);
for k = 1:length(pgon.Vertices)
A(pgon.Vertices(k,2),pgon.Vertices(k,1))=1;
end
J = bwconvhull(A);
regionprops(J,'Centroid','Orientation')
If you want to increase the resolution, for example, 100 times. This would give you a closer value.
MagFactor = 100;
A = zeros(25*MagFactor,25*MagFactor);
for k = 1:length(pgon.Vertices)
A(pgon.Vertices(k,2)*MagFactor,pgon.Vertices(k,1)*MagFactor)=1;
end
J = bwconvhull(A);
stat = regionprops(J,'Centroid','Orientation')
cent = stat.Centroid/MagFactor
figure
ax1 = subplot(1,2,1);
plot(pgon);
axis(ax1,'image');
ax1.XLim = [1 25];
ax1.YLim = [1 25];
ax2 = subplot(1,2,2);
imshow(J);
ax2.YDir='normal';
