Curved Track Segment Finding Using Tiny Triplet Finder (TTF)

We describe the applications of a track segment recognition scheme called the Tiny Triplet Finder (TTF) that involves the grouping of three hits satisfying a constraint forming of a track segment. The TTF was originally developed solving straight track segment finding problem, however, it is also suitable in many curved track segment finding problems. The examples discussed in this document are among popular detector layouts in high-energy/nuclear physics experiments. Although it is not practical to find a universal recipe for arbitrary detector layouts, the method of the TTF application is illustrated via the discussion of the examples. Generally speaking, whenever the data item to be found in a pattern recognition problem contains two free parameters, and if the constraint connecting the measurements and the two free parameters has an approximate shift invariant property, the tiny triplet finder can be used.