hx_polar_trans_inv — 2D `halcon_ext` op

• Data kinds: contour → contour

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

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

hx_polar_trans_inv: 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_polar_trans_inv: stages (docs site)

On other images (synthetic scene / photo / coins. Top row: inputs, bottom row: their outputs. Knobs at default):

▸ hx_polar_trans_inv: other inputs (docs site)

Usage

Take the contour points as (radius, angle) and transform them back to Cartesian coordinates (the inverse of polar_trans).

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

各 contour の点を `(row, col) = (半径 rad, 角度) とみなし、ang = col / W * 2*pi` として

`(cy + rad*sin(ang), cx + rad*cos(ang))(cy, cx = H/2, W/2`)の直交座標に戻した contour を返す。

• `a, b` は未使用。

• 半径は行の値をそのまま画素距離として使い、角度は列を画像幅で 0〜2π に写す。

注意: 順変換 `polar_trans_contour_xld は行を r / max(H, W) * H、列を (θ + π) / 2π * W` として

出力するため、この op はその厳密な逆にはなっていない。角度に π のずれ(点が中心対称の位置に写る)、非正方画像では

半径に `max(H, W)/H` 倍のずれが出る(往復で半径の 2 倍の誤差が出る実測)。順変換との往復を期待するときは

この差を織り込むか、この op を「列=角度・行=半径の一般的な極座標表現から直交へ」の変換として単独で使う。

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_polar_trans_inv 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 `contour` as input)

identity · select_contours · smooth_contours · fit_line_contours · contours_to_region · count_contours · total_length · select_contours_xld

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_polar_trans_inv — 2D halcon_ext op