Which image transformations are considered continuous transformations? In the article J. Matas, O. Chum, M. Urban, T. Pajdla: Robust Wide Baseline Stereo from Maximally Stable Extremal Regions it is stated that:


  The set (of extremal regions) is closed under continuous (and thus perspective) transformation of image coordinates, ...


I know what perspective transformations (and consequently, affine transformations) are, but could anyone give examples of other transformations that fall under the category of continuous transformations of image coordinates? How would such transformations be characterized?
I think "continuous" is meant in the strict mathematical sense here, i.e. no abrupt changes in the coordinate mapping.

Most non-rigid image alignment algorithms (try to) produce continuous mappings. Distortion filters in popular photo-editing applications (like Photoshop's Warp effect) are usually continuous mappings, too.

ADD: Here are two examples of transformations that are continuous but not affine or perspective:

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