Track reconstruction through the application of the Legendre Transform on ellipses

TL;DR

This paper introduces a novel pattern recognition technique that uses the Legendre transform to identify common tangent lines of ellipses, aiding in particle track reconstruction in detector simulations.

Contribution

It presents a new method applying the Legendre transform to ellipses for detecting common tangents, improving particle trajectory identification in layered detectors.

Findings

Effective in identifying tangent lines in simulated detector data

Applicable to pattern recognition in particle physics detectors

Demonstrates potential for real-time track reconstruction

Abstract

We propose a pattern recognition method that identifies the common tangent lines of a set of ellipses. The detection of the tangent lines is attained by applying the Legendre transform on a given set of ellipses. As context, we consider a hypothetical detector made out of layers of chambers, each of which returns an ellipse as an output signal. The common tangent of these ellipses represents the trajectory of a charged particle crossing the detector. The proposed method is evaluated using ellipses constructed from Monte Carlo generated tracks.