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I am reading the book Multiple View Geometry in Computer Vision(Second Edition) and encounter some questions.

On Page 7, it says

In applying projective geometry to the imaging process, it is customary to model the world as a 3D projective space, equal to $\mathbb{R}^3$ along with points iat infinity. Similarly the model for the image is the 2D projective plane $\mathbb{P}^2$. Central projection is simply a map from $\mathbb{P}^3$ to $\mathbb{P}^2$.

Does it mean that central projection is a projective transformation? If not, what is the reason? From other pages, it seems that projective transformation can only be the map between two spaces of the same dimension. Any help are appreciated.

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Central projection from 3D space to 2D space is not a projective transformation, as you have correctly concluded.

Central projection from 2D space to 2D space is a projective transformation as the text concludes in the last line of the same section you have highlighted. You can also see an example of the latter case on Page 34, Fig. 2.3.

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