I know that a projective transformation, also known as homography, projects a plane in one camera view into another camera view. This transformation preserves collinearity but not parallelism.
However, I'm not sure if perspective projection (i.e., the transformation that happens when taking a picture with a camera) is included under the umbrella of "projective transformations." In perspective projection parallelism is not preserved but collinearity is still maintained too.
So my question is: Is a perspective projection considered to be a type of projective transformation? If not, why not?
It may be a matter of context and definitions but in my experience a projective transformation is defined to be reversible. A projection, on the other hand, reduces the dimension and as such can't be reversible. Thus a perspective projection would not be considered a projective transformation.