Computer Vision Lecture — Intuitive Understanding of Line & Circle Detection
Hanbyul Joo | Visual Computing Lab, Seoul National University | More Demos ↗
Image Space
Click to add points | Preset mode: drag handles
→
Hough Space (θ–ρ)
Each point → sinusoid | Intersection → line | Hover to preview line
⚙ Line Parameters — drag handles or adjust sliders
Angle θ45°
Offset ρ0 px
# Points5
Noise5 px
💡 Drag yellow handles (●) on the canvas or use sliders | Points auto-regenerate on change
Click on Image Space to add points | or use "Load Preset" to get an adjustable line
💡 How Line Hough Transform Works
Normal form of a line: ρ = x·cos(θ) + y·sin(θ)
Every line through a point (x, y) in image space maps to a sinusoidal curve in Hough space.
Curves from collinear points all intersect at one point in Hough space.
That intersection's (θ, ρ) gives the direction and distance-from-origin of the detected line.
Image Space
Click to add points | Preset mode: drag handles
→
Hough Space (a–b Parameter Space)
Each point → circle of radius r | Intersection → circle center | Hover to preview
90 px
⚙ Circle Parameters — drag handles or adjust sliders
Center X (a)210 px
Center Y (b)210 px
# Points7
Noise5 px
💡 Drag center handle (◆) to move, edge handle (●) to resize | The r slider above also works
Click on Image Space to add points on a circle | or use "Load Preset" for an adjustable circle
💡 How Circle Hough Transform Works
Circle equation: (x−a)² + (y−b)² = r²
With a fixed radius r, each image point (x, y) maps to a
circle of radius r in the (a, b) parameter space.
Circles from points on the same circle all intersect at one point (the center) in parameter space.