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I would like to express image transformation (warping) in a mathematical form. For example, image transformation T may be an affine, homography, and so on.

Relevant codes might be:

# matlab
J = imwarp(I, tform);

# python opencv
J = cv2.warpAffine(I, T, (cols,rows))

Given an image I and a transformation T and its result J, what would be a proper mathematical notation? Is there a stadard for this, or are there references to follow?

I am just thinking:

# latex
$J = W(I, T)$ (in a function form?)
$J = W(I|T)$ (in a function form?)
$J = T * I$ (with a some operator and its definition?)
YW P Kwon
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  • Thanks. Yes, I know that Transformations are matrix multiplications. However, in case of coordinates (eg, `p`), the matrix multiplication makes sense (eg, `T`x`p`). However, if it is an "image", still do you think matrix multiplication notation does work (eg, `T`x`I`)? I am afraid that it can't. – YW P Kwon Oct 18 '17 at 07:57
  • But an image is made of pixels, and each pixel has a unique pair of coordinates.... – r3mainer Oct 18 '17 at 09:12
  • $J = T(I)$ would be somewhat standard. In any event this seems more like a question for [tex.se] or [mathematics.se] rather than Stack Overflow. Mathematical notation is flexible. As long as you are both clear and consistent, a surprisingly large amount is a matter of taste. – John Coleman Oct 18 '17 at 11:21
  • Thanks. I agree and I was just wondering if there is a widely-known standard notation and reference. $J=T(I)$ is a little bit ambiguous to me. In linear transformations such as affine and homography, `T` may be in a form of a matrix. For non-linear cases, `T` may be a set of parameters. So I guessed $J = W(I, T)$. Anyways, I got what you mean. thanks again! – YW P Kwon Oct 18 '17 at 18:44

1 Answers1

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Possibly

J = T(I; P)

Where T denotes a transformation and P the parameters (as is stressed by using a semicolon rather than a comma), which can be a tuple or a matrix.

But, frankly, the exact notation is unimportant provided you define it.