I'm wondering whats the differences between a homography and a transformation matrix?
For me it's kinda look like the same? Or is homography just the more precise word in the area of computer vision and transformation of image plane?
2026-03-26 14:28:05.1774535285
Differences between homography and transformation matrix
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MF.OX's answer still leaves some points of wonder:
Is a homography constrained in some way, or can any matrix ($3\times3$) be a homography matrix in homogeneous 2d space?
I found out that yes, a homography matrix's elements are unconstrained - and it is synonymous to a projectivity. To answer the question of what a homography actually is, it is useful to compare the concept of a homography also to Affinity, Similarity, Euclidean Transforms, etc. Those are all constrained more strongly, so the word homography is useful to explicitly state that the matrix may not adhere to those stronger constraints.
To this purpose, I find this comparison useful:
Source: https://www.cvg.ethz.ch/teaching/3dvision/2020/slides/class02eth20.pdf
So a "transformation matrix" is a general term and a "homography" is technically the same, but I believe it is used mainly to point out that there are no further constraints. That is, I would not say that an Affine Transformation is a Homography when I know that it is always affine. But I would call an Affine Transformation a Transformation - like wikipedia does here, for example.