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This study proposes a framework for manifold learning of image patches usingthe 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, butrather the set of their canonical patches obtained by introducing the conceptof equivalence classes and performing manifold learning on their canonicalpatches. Canonical patches represent equivalence classes, and theirauto-encoder constructs a manifold in the quotient space. Based on thisframework, we produce a novel manifold-based image model by introducingrotation-flip-equivalence relations. In addition, we formulate an imagereconstruction problem by fitting the proposed image model to a corruptedobserved image and derive an algorithm to solve it. Our experiments show thatthe proposed image model is effective for various self-supervised imagereconstruction tasks, such as image inpainting, deblurring, super-resolution,and denoising.

Manifold Modeling in Quotient Space: Learning An Invariant Mapping with Decodability of Image Patches