Hough Transform Filter

1. Hough Transform Filter D. A. Petyt July 1st 2004 • What? • A fast and simple algorithm to find linear features (i.e. tracks) in event images • Used previously to find narrow em showers in NOnA events and pion tracks in Soudan 2 events • Currently runs off SR ntuple strip information and provides a list of filtered digits in UZ and VZ views • Could/should be extended to use CandDigits • Why? • Use it to find short tracks in CC events that may be missed by SR tracker (either v. short qel or high y events with low momentum muon track) • Could also be useful for nmne

2. The Hough Transform • Transform points in x,y space into trajectories in Hough space. The axes of the Hough space are the parameters of the feature you wish to identify • For a straight line: • If hits lie on a straight line, the trajectories in Hough space will cross at a single point • Since m for vertical tracks, the following form is often used: d r

3. The filter • Transform hits in x,y space into trajectories in Hough space (a 2D histogram) • Find peak in Hough space • Only accept hits whose trajectories in Hough space pass within a minimum distance of this peak

4. Previous application #1: nmne in NOnA

5. Filter Previous application #2: tp in Soudan 2

6. Example of HT filtering in MINOS Filtered event: 80x80 hough space r=1 bin Filtered event: 40x40 hough space r=1 bin Filtered event: 160x160 hough space r=1 bin Original event This bin width works best for short tracks Upper plots – U-Z projection, Lower plots – V-Z projection

7. Hough space – top: raw, bottom: filtered

8. Curved tracks Filtered event: 80x80 hough space r=1 bin Filtered event: 40x40 hough space r=1 bin Filtered event: 160x160 hough space r=1 bin Original event HT algorithm loses hits off the end of curved tracks. Not a big problem as principal application of HT is for short (<50 plane) tracks

9. HT algorithm example #1 – “easy” event HT hits are shown by black dots

10. HT algorithm example #2 – short track

11. HT algorithm example #3 – short track

12. HT algorithm example #4 – shower

13. HT algorithm example #5 – failure Weighting hits by z position may eliminate these errors

14. Iterating filter to find secondary tracks Unfiltered Filtered

15. Hough space of previous event Secondary peak Secondary peak

16. Apply filter to hits rejected in 1st pass Rejected hits After HT filter

17. nmne • HT filter was used in NOnA to isolate e.m. showers • These are narrow and dense showers which are often spatially separated from the rest of the event • In MINOS, e.m. showers will have fewer hits, and will generally overlap with the hadronic component of the event. The standard HT filter will probably not be very efficient at isolating these showers. • A simple modification to the HT algorithm is to weight the hits by their pulse height. This should enable the filter to pick out the core of e.m. showers, even if they are buried in the middle of a larger event • Can then attempt to use NOnA-like estimators in MINOS ne ID studies (fraction of ph contained in HT filtered hits etc.)

18. ne event – standard HT filter Pink hits are high pulse height Arrow denotes electron direction

19. ne event – ph weighted HT filter HT hits more closely follow electron direction

20. What next? • Integrate code into CC analysis framework? • Convert to offline framework for more general use • Apply to physics analyses…