alife_perona_malik — 2D `artificial-life` op

• Data kinds: image → image

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

alife_perona_malik: 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.*

Sweeping knob a (0.1 / 0.5 / 0.9, the other knob at its default):

▸ alife_perona_malik: knob a sweep (docs site)

Sweeping knob b (0.1 / 0.5 / 0.9, the other knob at its default):

▸ alife_perona_malik: knob b sweep (docs site)

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

▸ alife_perona_malik: other inputs (docs site)

*The 4th column is a colour (H,W,3) input. This op handles colour without crossing channels (it does not convolve the colour channel as a third spatial axis).*

Usage

Perona-Malik anisotropic (edge-preserving) diffusion.

Explicit 4-neighbour update I <- I + lam * sum_dir g(|grad_dir I|) grad_dir I

with the Perona-Malik conductance g(s) = 1/(1 + (s/kappa)^2): inside a flat

region g -> 1 and the field diffuses like the heat equation, across a strong

edge g -> 0 and the edge is preserved. Unlike a bilateral filter the

conductance is recomputed from the *evolving* field at every iteration, which

is what makes the edges sharpen rather than merely survive. `a` sets the

edge scale kappa = 0.02 + 0.2a, `b` the iteration count 1 + int(15b);

lambda is fixed at 0.2 (<= 0.25, the explicit-scheme stability bound).

Border handling: wrap around to the opposite side (periodic) (measured; tools/impl2/border_probe.py).

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.

alife_perona_malik 0.50 0.50

▸ Load this pipeline · Load & run

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 (`artificial-life`)

alife_gray_scott · alife_turing · alife_life_step · alife_cyclic_ca · alife_curvature_flow · alife_dla · alife_reaction_bz · alife_wolfram1d

*Provenance: ops.py — 2D operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*

alife_perona_malik — 2D artificial-life op