ph_mean_curvature_motion — 2D physics op

Data kinds: imageimage

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

ph_mean_curvature_motion: 入力 → 出力

*The figure is the real output on a synthetic 128×128 input. Left: input, right: output (a non-image return value is shown as the value itself).*

Usage

Mean-curvature motion / curve-shortening flow (HALCON `mean_curvature_flow`).

Level-set curvature flow I_t = |grad I| * div(grad I / |grad I|), discretised

in the numerically stable form

I_t = (I_xx I_y^2 - 2 I_x I_y I_xy + I_yy I_x^2) / (I_x^2 + I_y^2 + eps).

Each level curve moves inward proportionally to its curvature, so a bright disk

shrinks and its boundary shortens (denoising / small-structure removal).

`a sets the step count; b` is unused.

Detailed usage guide

gallery2d_physics_alife_3d 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.

ph_mean_curvature_motion 0.50 0.50

▸ Load this pipeline  ·  Load & run

Runnable examples (verified samples that actually call this op)

gallery2d_physics_alife_3dpy -3.11 examples/gallery2d_physics_alife_3d.py

Ops the type connects to (they accept image as input)

identity · gaussian · mean_box · bilateral · unsharp · median · min_filter · max_filter

Same category (physics)

ph_perona_malik · ph_coherence_enhancing_diffusion · ph_reaction_diffusion · ph_heat_flow · ph_total_variation_flow


*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.