How can I use scipy.ndimage.interpolation.affine_transform to rotate an image about its centre?

Question

I am perplexed by the API to scipy.ndimage.interpolation.affine_transform. And judging by this issue I\'m not the only one. I\'m actually wanting to do more interesting th

Answer 1

Once treddy's answer got me a working baseline, I managed to get a better working model of affine_transform. It's not actually as odd as the issue linked in the original question hints.

Basically, each point (coordinate) p in the output image is transformed to pT+s where T and s are the matrix and offset passed to the function. So if we want point c_out in the output to be mapped to and sampled from c_in from the input image, with rotation R and (possibly anisotropic) scaling S we need pT+s = (p-c_out)RS+c_in which can be rearranged to yield s = (c_int-c_out)T (with T=RS).

For some reason I then need to pass transform.T to affine_transform but I'm not going to worry about that too much; probably something to do with row-coordinates with transforms on the right (assumed above) vs column-coordinates with transforms on the left.

So here's a simple test rotating a centred image:

src=scipy.misc.lena()
c_in=0.5*array(src.shape)
c_out=array((256.0,256.0))
for i in xrange(0,7):
    a=i*15.0*pi/180.0
    transform=array([[cos(a),-sin(a)],[sin(a),cos(a)]])
    offset=c_in-c_out.dot(transform)
    dst=scipy.ndimage.interpolation.affine_transform(
        src,transform.T,order=2,offset=offset,output_shape=(512,512),cval=0.0,output=float32
    )
    subplot(1,7,i+1);axis('off');imshow(dst,cmap=cm.gray)
show()

Here's it modified for different image sizes

src=scipy.misc.lena()[::2,::2]
c_in=0.5*array(src.shape)
c_out=array((256.0,256.0))
for i in xrange(0,7):
    a=i*15.0*pi/180.0
    transform=array([[cos(a),-sin(a)],[sin(a),cos(a)]])
    offset=c_in-c_out.dot(transform)
    dst=scipy.ndimage.interpolation.affine_transform(
        src,transform.T,order=2,offset=offset,output_shape=(512,512),cval=0.0,output=float32
    )
    subplot(1,7,i+1);axis('off');imshow(dst,cmap=cm.gray)
show()

And here's a version with anisotropic scaling to compensate for the anisotropic resolution of the source image.

src=scipy.misc.lena()[::2,::4]
c_in=0.5*array(src.shape)
c_out=array((256.0,256.0))
for i in xrange(0,7):
    a=i*15.0*pi/180.0
    transform=array([[cos(a),-sin(a)],[sin(a),cos(a)]]).dot(diag(([0.5,0.25])))
    offset=c_in-c_out.dot(transform)
    dst=scipy.ndimage.interpolation.affine_transform(
        src,transform.T,order=2,offset=offset,output_shape=(512,512),cval=0.0,output=float32
    )
    subplot(1,7,i+1);axis('off');imshow(dst,cmap=cm.gray)
show()