Manifold Modeling in Quotient Space: Learning An Invariant Mapping with Decodability of Image Patches
This work addresses the challenge of invariant feature learning for image processing, offering a novel framework that could benefit computer vision applications, but it appears incremental as it builds on existing manifold learning concepts.
The paper tackles the problem of learning invariant representations for image patches by proposing a manifold modeling framework in quotient space (MMQS), which uses equivalence classes to handle transformations like rotation and flipping. The method shows effectiveness in self-supervised image reconstruction tasks such as inpainting, deblurring, super-resolution, and denoising, though no concrete numerical results are provided in the 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.