Discrete tomography reconstructions with small boundary

TL;DR

This paper addresses reconstructing binary images from monotone projections with minimal boundary length, providing methods to achieve small boundaries and examples showing optimality limits.

Contribution

It introduces a construction method for binary images with minimal boundary length given monotone projections and demonstrates cases where smaller boundaries are impossible.

Findings

Constructed images with minimal boundary length under monotone projections

Proved the optimality of boundary size in certain cases

Provided examples where no smaller boundary can be achieved

Abstract

We consider the problem of reconstructing binary images from their horizontal and vertical projections. For any reconstruction we define the length of the boundary of the image. In this paper we assume that the projections are monotone, and we construct an image satisfying these projections that has a relatively small boundary. We also give families of examples for which we show that no smaller boundary is possible.