Comparing images

Biomedical Image Analysis in Python

Stephen Bailey

Instructor

Comparing images

both-images-and-stacked

Summary metrics

Goal: define a metric of similarity between two images.

Cost functions produce metrics to be minimized.

Objective functions produce metrics to be maximized.

Mean absolute error

import imageio
import numpy as np
i1=imageio.imread('OAS1035-v1.dcm')
i2=imageio.imread('OAS1035-v2.dcm')

err = i1 - i2

plt.imshow(err)

mask-error

abs_err = np.abs(err)
plt.imshow(abs_err)

mae = np.mean(abs_err)
mae

29.8570

mask-abs-error

Mean absolute error

Goal: minimize the cost function

# Improve im1 alignment to im2
xfm=ndi.shift(im1, shift=(-8, -8))
xfm=ndi.rotate(xfm, -18,
                 reshape=False)

# Calculate cost
abs_err = np.abs(im1 - im2)
mean_abs_err = np.mean(abs_err)

mean_abs_err

13.0376

adjusted-overlay

Intersection of the union

$$ IOU = \frac{I_1 \cap I_2 }{I_1 \cup I_2}$$

mask1 = im1 > 0
mask2 = im2 > 0

intsxn = mask1 & mask2
plt.imshow(intsxn)

mask-intersection

union = mask1 | mask2
plt.imshow(union)

iou = intsxn.sum() / union.sum()
iou

0.68392

mask-union

Let's practice!

Biomedical Image Analysis in Python