Tolerant Testers of Image Properties
Piotr Berman, Meiram Murzabulatov, Sofya Raskhodnikova

TL;DR
This paper develops efficient tolerant property testing algorithms for images, approximating how much pixels must change for images to satisfy properties like being a half-plane, convex, or connected, with query complexity independent of image size.
Contribution
It introduces the first tolerant testing algorithms for three fundamental image properties with query complexity independent of image size.
Findings
Algorithms approximate distance within small additive error.
Query complexity is polynomial in 1/ε and independent of image size.
Tolerant testers for convexity and connectedness are newly established.
Abstract
We initiate a systematic study of tolerant testers of image properties or, equivalently, algorithms that approximate the distance from a given image to the desired property (that is, the smallest fraction of pixels that need to change in the image to ensure that the image satisfies the desired property). Image processing is a particularly compelling area of applications for sublinear-time algorithms and, specifically, property testing. However, for testing algorithms to reach their full potential in image processing, they have to be tolerant, which allows them to be resilient to noise. Prior to this work, only one tolerant testing algorithm for an image property (image partitioning) has been published. We design efficient approximation algorithms for the following fundamental questions: What fraction of pixels have to be changed in an image so that it becomes a half-plane? a…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMachine Learning and Algorithms · Computability, Logic, AI Algorithms · Complexity and Algorithms in Graphs
