Scaling in GPA

[ethancohen123]

Is it possible to remove the scalling in the gpa function ? The size of the shapes I want to analyse matter for the analysis Thanks

[vaipatel]

Hi,

I'm wondering if you just need to make sure that the aligned landmark sets have their original scales. If so I can offer a slightly un-pretty albeit one-line workaround.

First, ensure that you run gpa with do_scaling=False which is the default. This will make it so that

• all the scaling factors at gpa_result['b'] are the exact inverses of the scales of the centered landmark sets
• all the aligned landmark sets in gpa_result['aligned'] will have scale 1

Now if you just execute the line remove_scale(gpa_result['aligned'], gpa_result['b']), you will be dividing the unitized and aligned landmark sets by the inverses of their scales, which will effectively multiply these aligned landmark sets by their original scales. This should scale them back to their original scales.

Here's a short snippet:

import numpy as np
import morphops as mops

# Make a dataset
A = [[0,0],[2,0],[2,2],[1,3],[0,2]]
B = [[0.1,-0.1],[2,0],[2.3,1.8],[1,3],[0.4,2]]
C = [[-0.1,-0.1],[2.1,0],[2,1.8],[0.9,3.1],[-0.4,2.1]]

# Get the scale of the centered dataset - only needed for later np.allclose verification
centered_ABC = mops.remove_position([A,B,C])
orig_scales = mops.get_scale(centered_ABC)

# Do GPA on the dataset with `do_scaling=False`
gpa_result = mops.gpa([A,B,C])

# One line workaround
aligned_and_rescaled = mops.remove_scale(gpa_result['aligned'], gpa_result['b']))

# Check that the orig_scales and aligned_and_rescaled scales are the same
print(np.allclose(orig_scales, mops.get_scale(aligned_and_rescaled)))

And if you need the new sum of squared differences you can run lmk_util.ssqd(aligned_and_rescaled).

Would something like this work for your application?

[ethancohen123]

Yes that works perfectly , thanks ! 👍