  This study proposes a framework for manifold learning of image patches using
the concept of equivalence classes: manifold modeling in quotient space (MMQS).
In MMQS, we do not consider a set of local patches of the image as it is, but
rather the set of their canonical patches obtained by introducing the concept
of equivalence classes and performing manifold learning on their canonical
patches. Canonical patches represent equivalence classes, and their
auto-encoder constructs a manifold in the quotient space. Based on this
framework, we produce a novel manifold-based image model by introducing
rotation-flip-equivalence relations. In addition, we formulate an image
reconstruction problem by fitting the proposed image model to a corrupted
observed image and derive an algorithm to solve it. Our experiments show that
the proposed image model is effective for various self-supervised image
reconstruction tasks, such as image inpainting, deblurring, super-resolution,
and denoising.
