Is there any approach to computer vision that doesn't make use of geometry? I've long been interested in applying my background in functional analysis (especially wavelets) and other related areas to actually create something with "real world" value (not that I don't enjoy math for it's own sake) and I thought that computer vision would be a natural place to start until I discovered that many of the books I found were littered with geometry. Not that there is anything wrong with geometry, I just find that it isn't my cup of tea. Thus, I am curious as to whether there any serious approaches to computer vision that do not make use of geometry (projective or otherwise)? Just to keep this from getting closed, please don't turn this into a debate on whose approach is better etc.
 A: It depends on what exactly you want to achieve. The reason most of the programs contain a lot of geometry is that they try to process images from a 3D point of view, and the reality of 3D arrangement and motion of objects is best described in a geometric way. However, there might be problems where there is no need to use geometry. One example that comes to mind is optical character recognition.
A: I'd say that classical computer vision is indeed dominated by differential geometry and projective geometry. As the other answerer says, such works are coming from a 3D model of the world, and how it could have generated the image.
However, lately, I think the dominant force in computer vision is machine learning, particularly deep learning (just peruse the latest vision conference proceedings!). Here, they are starting from a 2D pixel world and trying to obtain information about the 3D world putatively captured.
Here I think functional analysis can play a larger role, in feature extraction from images (including wavelet methods) as well as in machine learning itself, of course. 
