halcon_ext op• Data kinds: contour → feature
• Call: fullseye.apply(img, "hx_fit_circle_contour", a=0.5, b=0.5) (the 2-D model is one image plus two scalar knobs a,b∈[0,1])
• HALCON equivalent: fit_circle_contour_xld (the HALCON reference is a useful guide to its meaning and parameters)
*The figure is the actual output on a synthetic 128×128 input. Left: input, right: output. Point clouds are drawn as a top-down scatter (brightness = z), 1-D series as a line plot, volumes as the maximum-intensity projection along z, videos as the middle frame, complex images as magnitude; return values that are not pictures are shown as the values themselves.*
*Knob a does not change the output (measured: identical at 0.1 / 0.5 / 0.9).*
*Knob b does not change the output (measured: identical at 0.1 / 0.5 / 0.9).*
Stages (the ops that come before → this op, left to right):
▸ hx_fit_circle_contour: stages (docs site)
Fit a circle to the contour points by the algebraic (Kåsa) method and return the fit residual (RMS) — small = close to a circle.
Pools the points of all contours, fits a circle with Kåsa's algebraic method (solve [x, y, 1]·sol = x^2 + y^2 by least squares; centre (sol0/2, sol1/2), radius sqrt(sol2 + cx^2 + cy^2)), and returns the RMS of the difference between each point's distance from the centre and the radius, divided by max(H, W) and capped at 1, as np.float64. The circle parameters themselves are not returned.
• a, b are unused.
• 0.0 if there are fewer than 3 points (indistinguishable from a perfect circle). If the value under the radius square root is negative, the radius is treated as 0.
The algebraic method does not minimise geometric distance, so the radius is biased for short arcs (narrow angular range) and for outliers. For nearly collinear points the minimum-norm solution gives a very large radius and a small residual (a line looks like "a large circle"). To judge circularity, combine with hx_regress_contours to exclude lines. The radius of the enclosing circle is hx_smallest_circle_xld.
• gallery2d_halcon_ext family guide
• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).
• Operator provenance and references — the sources of the research/methods this op family came from.
• The canonical algorithm (author, year) and its uses are named in the family usage guide above.
The program below has been verified to run (same input as the figure). In Studio's help this block becomes buttons that load and run it on the spot.
threshold 0.50 0.50 sk_find_contours 0.50 0.50 hx_fit_circle_contour 0.50 0.50
▸ Load this pipeline · Load & run
• gallery2d_halcon_ext — py -3.11 examples/gallery2d_halcon_ext.py
feature as input)halcon_ext)hx_gen_circle · hx_gen_ellipse · hx_gen_rectangle2 · hx_gen_checker_region · hx_gen_grid_region · hx_gabor · hx_fit_surface1 · hx_fit_surface2
*Provenance: ops.py — 2D operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.