### Track reconstruction through the application of the Legendre Transform on ellipses *[Cross-Listing]*

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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.