Hough Circle Detection

Extend the vote from lines to rings: every edge pixel nominates candidate centers along its gradient, and the busiest candidates win their radii too.

A radius 21 ring casts about 132 votes, so param2 near 60 accepts half visible rings while param2 near 120 demands the impossible full ring

Why Does This Exist?

Coins, cells, irises, and traffic signs are circles, but the line machinery from Hough lines cannot describe them: a circle needs a center plus a radius, three numbers instead of two. The parent Hough transform voting idea extends directly, except the accumulator gains a dimension and naive voting gets a hundred times hungrier. This page covers the gradient shortcut that makes circles practical and the five parameters that control it.

Broken or partial rings that voting cannot close may trace better as contours instead.

Think of It Like This

Triangulating a bell by ear

Three listeners hear a bell from different spots and each points along the direction the sound came from. Their pointing lines cross at the bell, and the loudness hints at the distance. Gradient direction is the pointing finger, vote count is the loudness, and the crossing is the center no single listener could locate alone.

It stops holding in an echo chamber. Reflections point everywhere at once, the same way textured interiors spray gradient votes across the accumulator until the true crossing drowns. Clean ring edges in, true centers out; clutter in, fog out.

How It Actually Works

One dimension more, one hundred times hungrier

A circle $(x - a)^2 + (y - b)^2 = r^2$ needs center $(a, b)$ plus radius $r$ , a 3D accumulator. If every edge pixel voted for every plausible center and radius, a $500 \times 500$ image with $50$ radii would cast over a billion votes. The gradient method (Yuen and co.) cuts this down: each edge pixel votes only along its gradient direction, since the center must lie perpendicular to the edge, collapsing most of the search before radius voting begins.

The five parameters that matter

dp downsamples the accumulator (1 keeps full resolution, 2 halves it). minDist separates centers so one coin yields one detection instead of five. param1 is the upper Canny threshold guarding edge quality. param2 is the accumulator threshold: votes needed to declare a circle. minRadius and maxRadius bound the search and are the cheapest speedup available.

Work the coin numbers: radius $21$ pixels gives circumference $2\pi \times 21 \approx 132$ edge pixels. Setting param2 near $60$ demands under half the ring visible, which survives overlap and shadow; setting it near $120$ demands the near-impossible full ring and misses occluded coins entirely.

Code

The canonical coin-counting call shape:

1import cv22
3blurred = cv2.medianBlur(gray, 5)4circles = cv2.HoughCircles(5    blurred, cv2.HOUGH_GRADIENT, 1, 40,6    param1=100, param2=60, minRadius=15, maxRadius=30,7)8# circles holds (x, y, r) rows; None means nothing cleared 60 votes

Blur first to calm texture, centers at least $40$ pixels apart, radii confined to $15$ - $30$ where the coins actually live.

Watch Out For

Five detections per coin from minDist neglect

Symptom: every coin reports a cluster of overlapping circles with slightly different centers and radii. Each strong ring feeds several neighbouring accumulator cells past threshold. Set minDist near the smallest expected center separation (about one diameter for packed coins) so only the strongest candidate per neighbourhood survives.

Phantom circles from a low param2

Symptom: background texture returns dozens of confident-looking circles that vanish when the threshold rises slightly. Random texture crossings routinely collect modest votes. Raise param2 until phantoms die, then recover missed true circles by tightening the radius range and improving edges, never by lowering the threshold back down.

The Quick Version

Circles need a 3D center-plus-radius vote, so gradient direction prunes the search to stay affordable.
minRadius and maxRadius are the cheapest speedup: bound them to the objects you actually expect.
param2 sets the votes a circle needs; under half the circumference survives occlusion.
minDist near one diameter stops one coin reporting as five overlapping circles.
Texture-heavy interiors spray false votes, so blur and edge quality decide success before parameters do.