The Hough Transform

  • Thomas Owen JamesEmail author
Part of the Springer Theses book series (Springer Theses)


The Hough Transform is widely used to detect parametrically described curves in an image that can contain noise or partial occlusion. It is shown how a two dimensional linear Hough Transform can be used to identify track candidates within the CMS tracker. Three implementations of this algorithm in FPGA firmware are presented: a systolic array, a pipelined array, and an optimised pipelined solution called the daisy-chained array. For each, the performance in terms of track finding efficiency and fake rate is presented, alongside the corresponding FPGA resource utilisation and latency. The method used to pre-process and distribute the tracker hits is also described. Potential algorithmic and technical improvements are discussed, in addition to the scaling of the implementation to a variety of FPGA devices.


  1. 1.
    Hough PVC (1962) Method and means for recognizing complex patterns, US Patent 3,069,654, Dec 1962.
  2. 2.
    Duda RO (1972) Use of the Hough transformation to detect lines and curves in pictures. Commun Assoc Comput Mach 15(1):11–15.
  3. 3.
    Xilinx Inc (2017) 7 series FPGAs data sheet: overview, product specification, DS180 (v2.5).
  4. 4.
    Schuh T (2017) Entwicklung des CMS-spurtriggers für den Hochluminositätsbetrieb des Large Hadron Colliders. Karlsruher Institut für Technologie Ph.D. thesis,
  5. 5.
    Aggleton R et al (2017) An FPGA based track finder for the L1 trigger of the CMS experiment at the High Luminosity LHC. JINST 12:P12019.

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of PhysicsImperial College LondonLondonUK

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