Peeling Digital Potatoes
Lo\"ic Crombez, Guilherme D. da Fonseca, Yan G\'erard

TL;DR
This paper introduces polynomial-time algorithms for finding the largest digital convex subsets within a set of lattice points, addressing a digital version of the classical potato-peeling problem with practical approximation guarantees.
Contribution
It presents the first polynomial-time algorithms for the digital potato-peeling problem and its union variant, with complexity bounds of roughly O(n^3) and O(n^9).
Findings
Algorithms effectively find largest digital convex subsets.
The algorithms approximate continuous convex peeling.
New complexity bounds for digital convex subset problems.
Abstract
The potato-peeling problem (also known as convex skull) is a fundamental computational geometry problem and the fastest algorithm to date runs in time for a polygon with vertices that may have holes. In this paper, we consider a digital version of the problem. A set is digital convex if , where denotes the convex hull of . Given a set of lattice points, we present polynomial time algorithms to the problems of finding the largest digital convex subset of (digital potato-peeling problem) and the largest union of two digital convex subsets of . The two algorithms take roughly and time, respectively. We also show that those algorithms provide an approximation to the continuous versions.
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Taxonomy
TopicsDigital Image Processing Techniques · Computational Geometry and Mesh Generation · Optimization and Packing Problems
