hx_fit_circle_contour — 2D `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)

hx_fit_circle_contour: input → output

*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)

Usage

Fit a circle to the contour points by the algebraic (Kåsa) method and return the fit residual (RMS) — small = close to a circle.

> The detailed description below is the original text — the summary and the headings are translated.

全 contour の点をまとめ、Kåsa の代数法(`[x, y, 1]·sol = x^2 + y^2` を最小二乗で解き、中心

`(sol0/2, sol1/2)、半径 sqrt(sol2 + cx^2 + cy^2)`)で円を当て、各点の中心からの距離と半径の差の RMS を

`max(H, W) で割って 1 で頭打ちした np.float64` で返す。円のパラメータ自体は返さない。

• `a, b` は未使用。

• 点が 3 個未満なら 0.0(完全な円と区別できない)。半径の根号の中が負になれば半径 0 として扱う。

代数法は幾何学的な距離の最小化ではないので、円弧が短い(角度範囲が狭い)点群や外れ値では半径が偏る。

ほぼ直線上の点群では最小ノルム解の半径が非常に大きくなり、残差は小さく出る(直線が「大きな円」に見える)。

円らしさの判定には `hx_regress_contours と併用して直線を除く。包含円の半径は hx_smallest_circle_xld`。

Detailed usage guide

• gallery2d_halcon_ext family guide

References (sample data, literature)

• 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.

Try it in Studio

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

Runnable examples (verified samples that actually call this op)

• gallery2d_halcon_ext — py -3.11 examples/gallery2d_halcon_ext.py

Ops the type connects to (they accept `feature` as input)

identity · feature_to_img

Same category (`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).*

hx_fit_circle_contour — 2D halcon_ext op