The Hough Transform
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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.
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