hx_estimate_tilt_zc — 2D `halcon_ext` op

• Data kinds: image → feature

• Call: fullseye.apply(img, "hx_estimate_tilt_zc", a=0.5, b=0.5) (the 2-D model is one image plus two scalar knobs a,b∈[0,1])

• HALCON equivalent: estimate_tilt_zc (the HALCON reference is a useful guide to its meaning and parameters)

hx_estimate_tilt_zc: 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).*

Usage

Zheng-Chellappa: estimate the tilt from the mean direction of the normalised gradient (independent of local contrast).

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

Sobel 勾配 `(Ex, Ey) を各画素で振幅 hypot(Ex, Ey) + 1e-9` で割った単位ベクトルにしてから平均し、

`tilt = arctan2(<Ey/|E|>, <Ex/|E|>) を (tilt / 2π) mod 1 で [0,1) に写した np.float64` を返す

(Zheng-Chellappa の tilt 推定)。

• `a, b` は未使用。

• 角度の規約は `hx_estimate_tilt_lr` と同じ(0 が +列方向、0.25 が +行方向)。

各画素の寄与が方向だけになるため、強いエッジや明るい部分に引きずられにくい。反面、勾配がほぼ 0 の平坦部でも

(`1e-9` で割った)雑音の方向が等しく 1 票を持つので、平坦な背景が広い画像では推定がぼやける。前段で

`gauss_filter` を掛けて雑音の勾配を減らすと安定する。

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.

hx_estimate_tilt_zc 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_estimate_tilt_zc — 2D halcon_ext op