What are affine covariant regions I am trying to understand this seminal paper. I read this post on what affine transformations and my understanding is that affine transformations are transformations that preserve parallelism of lines such as rotation, translation, etc, but NOT distortions of partials of the image, and other related transformations that cause previously parallel lines to no longer be parallel. 

I also understand that covariant regions are the same region being detected from two different view points. 

However, in the paper, they use the term "affine covariant regions" and state that they can be "exploited to cope with geometric and photometric deformations" (5th paragraph if introduction). This sentence throws off my understanding because I don't quite understand what it means when both terms are combined (affine - covariant). It's probably a subtle difference. Can someone please clarify?
Actually what it meant by Affine Covariant regions is that covariant regions in two images which are related by some affine transformation. So the regions found in one image and those are exactly same regions in other image which have been transformed through affine transformation.