Bivariate normal distribution for finding inliers in Hough space for a Time Projection Chamber

Abstract

A Time Projection Chamber (TPC) is foreseen as the main tracking detector for the International Large Detector (ILD), one of the two detectors for the next candidate collider named International Linear Collider (ILC) [1]. GridPix, a combination of a micropattern gaseous detector with a pixelized readout, is one of the candidate readout systems for the TPC [2] [3]. One of the challenges in the track reconstruction is the large number of individual hits along a track (around 100 per cm). Due to the small pixel size of 55 x 55 μm2, the distance between the individual ionization processes in the gas is larger than the size of the pixels. Consequently, the hits in the GridPix are not contiguous. This leads to the challenge of assigning the individual hits to the correct track. Hits within a given distance from a reconstructed track are called inliers. Consequently, finding inliers within the large number of hits and in the presence of noise is difficult for pattern recognition. This difficulty is increased by diffusion effects in the TPC. One of the current algorithms which are utilized for track finding is the Hough transform. Using a bivariate normal distribution based on the covariance matrix calculated from the diffusion effect improves collecting inliers in the Hough space directly [5].