Transforming coordinates with affine matrix from transformation on image.

[jejon]

I want to do the same affine transformation on an image, on a coordinate, which represents a location on the image. I have tried numerous things, but I can't figure out because I still need to grasp how transformations are done precisely under the hood fully. I think it has something to do with how I define my indices (orientation), but I'm unsure.

I have tried to do a simple translation. I checked the values by finding the index pair with the highest value in the image/array.

import numpy as np
from monai.transforms import Affine
points = np.asarray([[100, 108], [60, 88], [120, 88]])
img = np.zeros((3, 300, 256))
img[0, *points[0]] = 1
img[1, *points[1]] = 1
img[2, *points[2]] = 1
transforms = Affine(scale_params=1, rotate_params=0, translate_params=(20, 40))
img_t, affine = transforms(img)
points_t_argmax = np.asarray([ [idx // 256, idx % 256] for idx in np.argmax(img_t.view(img.shape[0], -1), axis=-1)])
points_t = affine @ np.concatenate([points.T, np.zeros((1, img.shape[0])), np.ones((1, img.shape[0]))], 0)
points_t = points_t.T[:, :2]
print("transformed points:\n", points_t)
print("argmax points transformed image:\n", points_t_argmax)
print("Diff:\n", points_t - points_t_argmax)

Results are:

transformed points:
 [[120. 148.]
 [ 80. 128.]
 [140. 128.]]
argmax points transformed image:
 [[ 80  68]
 [ 40  48]
 [100  48]]
Diff:
 [[40. 80.]
 [40. 80.]
 [40. 80.]]

Here is another example with rotation:

points = np.asarray([[100, 108], [60, 88], [120, 88]])
img = np.zeros((3, 300, 256))
img[0, *points[0]] = 1
img[1, *points[1]] = 1
img[2, *points[2]] = 1
transforms = Affine(scale_params=1, rotate_params=np.pi/6)
img_t, affine = transforms(img)
points_t_argmax = np.asarray([ [idx // 256, idx % 256] for idx in np.argmax(img_t.view(img.shape[0], -1), axis=-1)])
points_t = affine @ np.concatenate([points.T, np.zeros((1, img.shape[0])), np.ones((1, img.shape[0]))], 0)
points_t = points_t.T[:, :2]
print("transformed points:\n", points_t)
print("argmax points transformed image:\n", points_t_argmax)
print("Diff:\n", points_t - points_t_argmax)

Results are:

 [[116.38174033  85.86250377]
 [ 91.74072242  48.54199481]
 [143.70224929  78.54199481]]
argmax points transformed image:
 [[ 97 135]
 [ 52 138]
 [104 108]]
Diff:
 [[ 19.38174033 -49.13749623]
 [ 39.74072242 -89.45800519]
 [ 39.70224929 -29.45800519]]

I hope someone can help me with this issue or guide me in the right direction.

I really appreciate any help you can provide.

[wyli]

the affine is defined in the pull direction... perhaps try the inversed affine points_t = inv(affine) @ points

[jejon]

It resolved the issue. The clarification that affine transformation is defined in the pull direction helped me much further; it all makes more sense now. Thanks for the help.