Randomized algorithms for statistical image analysis and site percolation on square lattices

TL;DR

This paper introduces a probabilistic algorithm leveraging percolation and random graph theories for real-time detection of objects in noisy images, demonstrating high accuracy and efficiency.

Contribution

It presents a novel, linear-complexity algorithm for detecting unknown-shaped objects in noisy images using percolation theory, with proven consistency and efficiency.

Findings

Algorithm achieves exponential accuracy in object detection.

Method operates in linear time suitable for real-time applications.

Proven theoretical guarantees on consistency and complexity.

Abstract

We propose a novel probabilistic method for detection of objects in noisy images. The method uses results from percolation and random graph theories. We present an algorithm that allows to detect objects of unknown shapes in the presence of random noise. The algorithm has linear complexity and exponential accuracy and is appropriate for real-time systems. We prove results on consistency and algorithmic complexity of our procedure.