Update docstring for SimilarityTransform.

[mkcor]

Description

@scott-vsi I've just applied what you suggested back in #7103 (comment).

@lagru this brings up another (minor) question for me: It seems that D (as in "length D") is used to mean n, i.e., the image's number of dimensions. We write "an nD image" so n takes values 2, 3, ... (not D).

Checklist

• A descriptive but concise pull request title
• Docstrings for all functions
• Unit tests
• A gallery example in ./doc/examples for new features
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Summarize the introduced changes in the code block below in one or a few sentences. The
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...

[lagru]

It seems that D (as in "length D") is used to mean n, i.e., the image's number of dimensions. We write "an nD image" so n takes values 2, 3, ... (not D).

I don't mind updating this to "n" or "N". Though I do notice that translation is only supported for 2D and 3D. So the ... should be removed as specifying more than xyz wouldn't work?

params : (dim+1, dim+1) (below) should also be updated according to whatever we agree on here.

[mkcor]

Oh, thanks @lagru.

We can't use N because this already denotes something else (number of points):

scikit-image/skimage/transform/_geometric.py

Line 42 in d6ba6db

points : (N, D) array

[scott-vsi]

I find D (Dimensionality) to be much clearer than n, particularly when next to N (Number of points)

[mkcor]

@scott-vsi I hear you. Have you scanned the other modules to see which usage would currently dominate? Should we update "nD image" everywhere with "D-dim image?" In a sentence, "nD image" seems much more natural though...

[scott-vsi]

I agree, nD reads better, although it looks like n-D and N-D are also used pretty commonly (there are actually not that many uses of nD. I could see changing those to n-D or N-D).

skimage is a large package, so I doubt you could ever get complete consensus, but it looks like D dominates for the dimensionality of the image. It is used in skimage._shared.utils.check_nD, skimage.measure._moments.moments_coords, skimage.measure._regionprops_utils.euler_number, and skimage.feature.template.match_template. And that is just from a quick spot check.

[mkcor]

Thanks for looking into this, @scott-vsi! I'll mark this PR as draft, because I realize some discussion is needed before we can move forward.

I could see changing those to n-D or N-D

I would avoid uppercase N because, in addition to number of points #7194 (comment), this notation is also used for number of columns, e.g.:

scikit-image/skimage/transform/_geometric.py

Line 98 in d6ba6db

src : (M, N) array_like

[mkcor]

Uh oh, this is getting more involved than I originally thought... e0baa7b