Add `Projective` transformation about imagetransformations.jl HOT 2 OPEN

This issue can be seperated into two parts:

1. we want an invertible projective transformation so that warp's default inds = autorange(img, inv(tform)) is happy with it.
2. we might want a high-level API in ImageTransformations so that normal users don't need to talk to warp directly. We currently only have imrotate and imresize.

we want an invertible projective transformation

The Projective version you propose definitely works, but maybe the following is a better patch (since it doesn't introduce new concepts to the codebase):

function Base.inv(tform::CoordinateTransformations.ComposedTransformation{PerspectiveMap})
    PerspectiveMap() ∘ inv(tform.t2)
end

julia> tform = PerspectiveMap() ∘ inv(AffineMap(RotX(0.3), SVector((0, 0, 0))));

julia> inv(tform)
(PerspectiveMap() ∘ AffineMap([1.0 0.0 0.0; 0.0 0.955336489125606 -0.29552020666133955; 0.0 0.29552020666133955 0.955336489125606], [-0.0, 0.0, -0.0]))

I didn't yet check whether this is equivalent to the Projective homography, though...

we might want a high-level API in ImageTransformations

This is highly application-oriented so I don't know what your target usage is. Perhaps one just need to properly document it with some small examples #141.

FYI, I'm reaching @c42f for the privilege to CoordinateTransformations

from imagetransformations.jl.

Agreed!

I didn't yet check whether this is equivalent to the Projective homography, though...

Hmm, the tform seems ℝ³→ℝ², so the following error occours:

julia> warp(img, tform)
ERROR: "Dimension mismatch: cannot rotate a vector of length 2"
...

I don't know what your target usage is

I mainly use homography for image registration.
(Sorry for Japanese, but this might be a good exaple: https://zenn.dev/hyrodium/articles/5dc951f378b46bedb211)

we might want a high-level API in ImageTransformations so that normal users don't need to talk to warp directly.

I think we can create impinch method:

• impinch(img, a1=>b1), this cause parallel translation.
• impinch(img, a1=>b1, a2=>b2), this cause similarity transformation.
• impinch(img, a1=>b1, a2=>b2, a3=>b3), this cause affine transformation.
• impinch(img, a1=>b1, a2=>b2, a3=>b3, a4=>b4), this cause projective transformation.

(I'm not sure "pinch" is an appropriate name for it.)

from imagetransformations.jl.