Hi Tony

typically you don't measure distortion by total displacement as if you rotate the sphere the displacement would be large but you would not incur any distortion.

There are a bunch of measures that try to summarize distortion, but basically there is areal and angular distortion that can be combined in different summary measures. Areal you can measure by first normalizing the two surfaces to have the same total area (not needed in the sphere comparison, but if you want to compare to e.g. white you would need to), then look at the ratio of the area of each triangle. Angular you can compare directly. There are other measures like harmonic energy you can also look at.

cheers Bruce

On Fri, 10 Nov 2017, tony han wrote:

Hi Bruce,

Thanks for your quick response! So I have several follow-up questions:

1. As I load the two files (.sphere and .sphere.reg), there are two variables for each file, i.e.

coordinates and facets. If I want to measure the distortion during registration, I will only need to look at coordinates? If so, the most appropriate way is simply calculating the Euclidean distance for each vertex between the two files (i.e., compute the distance between the first row of coordinates in .sphere file and the first row of coordinates in .sphere.reg, and so forth)?

2. What file I can use to get the distortion by the sphere inflation, as you mentioned?

3. The measure of vertex-wise distortion is basically how far each vertex has been warped from its

original coordinate (native space) to the new coordinate (fsaverage space)? Thanks!

Best,

Tony

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From: freesurfer-bounces@nmr.mgh.harvard.edu freesurfer-bounces@nmr.mgh.harvard.edu on behalf of Bruce Fischl fischl@nmr.mgh.harvard.edu Sent: Thursday, November 9, 2017 12:28:13 PM To: Freesurfer support list Subject: Re: [Freesurfer] comparing sphere and sphere.reg   Hi Tony

you can do that but it won't measure the distortion induced by the sphere mapping itself.

cheers Bruce

On Thu, 9 Nov 2017, tony han wrote:

...

Hi,

I'm trying evaluating the distortion for each subject from their native space to fsaverage atlas space. Is it a appropriate measure to compare ?h.sphere and ?h.sphere.reg? I assume that by comparison, I may get the how each vertex warped during the registration? Thanks!

Best,

Tony