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).

Interprets each contour point as (row, col) = (radius rad, angle), sets ang = col / W * 2*pi, and returns the contour converted back to the Cartesian coordinates (cy + rad*sin(ang), cx + rad*cos(ang)) (cy, cx = H/2, W/2).

• a, b are unused.

• The radius uses the row value directly as a pixel distance; the angle maps the column to 0 to 2π over the image width.

Note: the forward transform polar_trans_contour_xld outputs the row as r / max(H, W) * H and the column as (θ + π) / 2π * W, so this op is not its exact inverse. The angle is off by π (points land at the point-symmetric position), and on non-square images the radius is off by a factor of max(H, W)/H (a round trip measured an error of 2 times the radius). If you expect a round trip with the forward transform, account for this difference, or use this op on its own as a conversion "from a generic polar representation with column = angle and row = radius to Cartesian".

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