What does "pre-image" mean in this context?
I am comparing the performance of feature detection algorithms like Harris, ORB, MSER (OpenCV Python). I have two images of the same object taken from different viewpoints. Since I am just a beginner to this area, I am having trouble understanding what "pre-image" means in this context. How do I get the "pre-image"?
Detecting regions covariant with a class of transformations has now reached some maturity in the computer vision literature. The requirement for these regions is that they should correspond to the same pre-image for different viewpoints, i.e., their shape is not fixed but automatically adapts, based on the underlying image intensities, so that they are the projection of the same 3D surface patch.
This seems to be a quote from "A comparison of affine region detectors" paper.
You can interpret the term "pre-image" to mean the "3D surface patch" (that corresponds to a region in 2D). In other words, it’s a part of the "scene"/"3D environment" that’s being photographed.
The confusion arises because authors are using the term to refer to the mathematical object, rather than anything to do with photographs/images.
To elaborate more — consider the process of taking a photograph of a 3D scene as a mathematical function. This function has several inputs: the 3D scene itself, the viewpoint, illumination, and so on. The output is a 2D array of pixel intensities. Given a 2D array of pixel intensities, and focusing on a particular 2D region, the corresponding 3D surface patch forms the "pre-image" of the function.
