ph_mean_curvature_motion — 2D physics op

• Data kinds: image → image

• 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])

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.

Runnable examples (verified samples that actually call this op)

• gallery2d_physics_alife_3d — py -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.