A Continuous Max-Flow Approach to Cyclic Field Reconstruction

TL;DR

This paper introduces a cyclic continuous max-flow model for image reconstruction that explicitly accounts for the cyclic topology of certain intensities like hue or phase, improving upon existing models.

Contribution

It presents a novel cyclic continuous max-flow framework that models cyclic intensity topologies, extending the Ishikawa model for better image reconstruction.

Findings

Models cyclic intensity topology effectively.

Compatible with arbitrary intensity resolution.

Enhances image reconstruction quality.

Abstract

Reconstruction of an image from noisy data using Markov Random Field theory has been explored by both the graph-cuts and continuous max-flow community in the form of the Potts and Ishikawa models. However, neither model takes into account the particular cyclic topology of specific intensity types such as the hue in natural colour images, or the phase in complex valued MRI. This paper presents \textit{cyclic continuous max-flow} image reconstruction which models the intensity being reconstructed as having a fundamentally cyclic topology. This model complements the Ishikawa model in that it is designed with image reconstruction in mind, having the topology of the intensity space inherent in the model while being readily extendable to an arbitrary intensity resolution.