I don't know how you're getting that huge size. EDIT: I know why. I'll mention that at the end.
The code will return a 225x225 image if fed a 512x512 image. That's all down to how imcrop works. It'll often give you an image that's 1px wider than you might expect. The synopsis describes why it behaves that way. You could do something like this
I = imresize(imread('cameraman.tif'),[512 512]);
x_cent = 256;
y_cent = 256;
size_of_cropped_img = 224;
centroide = [x_cent y_cent]; % this isn't used
%I2 = imcrop(I,rect) crops the image I. rect is a four-element position vector of the
%form [xmin ymin width height] that specifies the size and position of the crop rectangle.
%imcrop returns the cropped image, I2.
xmin = x_cent-size_of_cropped_img/2;
ymin = y_cent-size_of_cropped_img/2;
I2 = imcrop(I,[xmin+1 ymin+1 size_of_cropped_img-1 size_of_cropped_img-1]);
size(I2)
Or you could just not use imcrop.
I = imresize(imread('cameraman.tif'),[512 512]);
sz = size(I);
sout = [224 224]; % [y x]
centroide = sz(1:2)/2; % this isn't used
pad = (sz(1:2) - sout)/2;
yrange = max(floor(pad(1))+1,1):min(floor(pad(1))+sout(1),sz(1));
xrange = max(floor(pad(2))+1,1):min(floor(pad(2))+sout(2),sz(2));
I2 = I(yrange,xrange);
size(I2)
The reason you're getting a giant useless image is because you're saving the figure, not the image. Figures are for display only. Saving an image by saving the figure to a raster format is equivalent to taking a screenshot. It's typically destructive, as the image is scaled for display using nearest-neighbor interpolation. So quality is degraded and there's no trivial control over output size (and there's usually a bunch of padding).
If you want to save the image, use imwrite.
imwrite(I2,'myfancyimage.png')
