PATHFINDER (PAckage for Tracking by Hough trafo FINDing including a chisquare fittER) is a software package which provides a track finding algorithm for TPC prototypes using the Hough Transformation. PATHFINDER is a standalone package which can be used in frameworks such as MarlinTPC.
How does Hough Transformation work?
The Hough Transformation is one possibility to do pattern recognition. It is a global method which means that all hits (points in 3D space) enter into the algorithm at the same time and in the same way. The aim is to find hits which are on one track (curves which can be parametrized by one set of parameters such as straight lines or helices). In the following the algorithm for straight lines in a 2D plane is described.
To describe a straight line in a 2D plane two parameters are needed. Let these two parameters be (see Figure 1)
- the closest distance of the track to the origin of the coordinate system.
- the angle between the x-axis and the direction of the closest distance.
The equation describing this straight line is shown in Figure 2. This equation is then transformed into a function shown in Figure 3
As a next step the positions of the hits are inserted into the function. Each hit then gives one function. If the hits are all on one straight line all functions intersect in one point in Hough Space. The point of intersection gives the parameters describing the straight line the hits are on (see Figure 4).
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