A detected voting peak occupies parameter space. The chosen distance and angle discretization is part of that result.
Define the parameter grid
A polar Hough line representation uses normal distance and normal angle. Voting implementations specify their distance and angle resolutions. A peak obtained on that parameter grid should retain those choices, along with the selected input evidence, rather than being reported as an exact line without discretization context. Primary reference: OpenCV Hough line parameter resolution.
For an original geometry sheet, write the normal convention, coordinate origin and parameter-bin spacing. Keep the line hypothesis separate from the input edge samples. An angle label for the normal is not automatically the direction angle of the line itself.
Compare a fictional angular change
Use the teaching expression r = x cos θ + y sin θ. At the point (10,100), θ = 0 degrees gives r = 10. At θ = 1 degree, r is approximately 11.744. A small normal-angle change therefore changes the point's distance parameter by about 1.744 coordinate units here.
This is a constructed projection calculation, not a bound on the error of a Hough detector. Voting grids, finite evidence and peak selection may contribute other effects. The coordinate position and stated angle must remain visible; angle spacing alone does not establish a universal spatial error.
Retain the fitted question
Prepare an original parameter-grid record and overlay the chosen line hypothesis with its contributing edge evidence. If grid spacing changes, retain both results with their respective settings. Do not attribute every changed line report to movement of the actual pack when the parameter definition changed.
This guide recommends no vote threshold and claims no HM line-detection performance. Its decision is whether the result's discretization and normal convention remain available. Any physical geometric inference needs its own image-to-scene basis and relevant evaluation evidence.
Customer Questions
Is the polar angle the line's normal angle here?
Yes, under the stated convention.
What is r at zero degrees in the example?
Ten coordinate units.
Does bin spacing alone prove a spatial error bound?
No. Other geometry and detector effects remain.
Primary References
These references support the technical principles discussed in this guide. The worked examples and review questions are educational.
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