Restriction and interpolation operators for digital images and their boundaries

TL;DR

This paper introduces a framework for transforming boundary pairs of digital images across resolutions, enabling multiresolution processing and boundary reduction without full image data, aiding computational dynamics and control algorithms.

Contribution

It presents a novel approach for boundary transformation that supports multiresolution processing without requiring complete image information.

Findings

Framework effectively transforms boundary pairs across resolutions.

Supports multiresolution processing and boundary reduction.

Applicable to computational dynamics and control algorithms.

Abstract

The aim of this paper is to provide a coherent framework for transforming boundary pairs of digital images from one resolution to another without knowledge of the full images. It is intended to facilitate the simultaneous usage of multiresolution processing and boundary reduction, primarily for algorithms in computational dynamics and computational control theory.