Spatial transformations

Biomedical Image Analysis in Python

Stephen Bailey

Instructor

OASIS Database

OASIS logo

Significant variability

multi-brain-array

Registration

Align images to template
Minimize spatial variability
Templates:
- may represent multiple subjects
- may be an "average" image
Entails many spatial transformations

three-images-registering

Affine transformations preserve points, lines, and planes

trasformation-example

Translation

shifted-head

import imageio
import scipy.ndimage as ndi

im=imageio.imread('OAS1036-2d.dcm')
im.shape

(256, 256)

com = ndi.center_of_mass(im)

d0 = 128 - com[0]
d1 = 128 - com[1]

xfm = ndi.shift(im, 
          shift=[d0, d1])

Rotation

ndi.rotate(im,
           angle=25,
           axes=(0,1))

rotated-head

Image rotation

xfm = ndi.rotate(im, angle=25)

xfm.shape

(297, 297)

reshaped-rotation

xfm = ndi.rotate(im, angle=25, 
              reshape=False)
xfm.shape

(256, 256)

normal-rotation

Transformation matrix

Transformation matrix: applied to one image for registration.

Elements of the matrix encode "instructions" for different affine transformations.

image-with-four-transforms

Applying a transformation matrix

# Identity matrix
mat = [[1, 0, 0],
       [0, 1, 0],
       [0, 0, 1]]

xfm = ndi.affine_transform(im, 
                           mat)

original-image

# Translate and rescale
mat = [[0.8, 0,   -20],
       [0,   0.8, -10],
       [0,   0,   1]]
xfm = ndi.affine_transform(im,
                           mat)

transformed-image

Let's practice!

Biomedical Image Analysis in Python