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

TL;DR

This paper introduces a manifold learning framework in quotient space for image patches, enabling invariant image reconstruction and demonstrating effectiveness in tasks like inpainting, deblurring, super-resolution, and denoising.

Contribution

It proposes a novel manifold modeling approach using quotient space and equivalence classes, incorporating rotation-flip invariance for improved image reconstruction.

Findings

Effective in various self-supervised image reconstruction tasks

Demonstrates invariance to rotations and flips in image patches

Provides a new framework for invariant manifold learning in images

Abstract

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.