physarum_transport_image — GRAPH `flow` op

• Data kinds: image2d × image2d → table

• Call: import fullseye as fs; fs.ledger.physarum_transport_image(a, b, connectivity=4, normalize=True, dt=0.1, max_iters=5000, tol=1e-06, gap_tol=1e-06, snapshots=0) (to call the implementation directly, import physarum_search; physarum_search.physarum_transport_image(a, b, connectivity=4, normalize=True, dt=0.1, max_iters=5000, tol=1e-06, gap_tol=1e-06, snapshots=0); from the registry, opsgraph.get("physarum_transport_image"))

Usage

Earth mover's distance between two mass images by the slime mould's tube dynamics.

Every pixel is a node; neighbouring pixels (`connectivity` 4 or 8) are joined by a tube of

length 1 (`sqrt(2)` on diagonals), so the ground metric is the grid path length (Manhattan

for 4, octile for 8). Mass `a enters and mass b leaves: the supply is a - b` after

both are scaled to unit mass (`normalize=True; with False` they must already carry the

same mass). Dynamics, convergence and the two-sided bound as in

:func:graph_physarum_transport; larger images run on the sparse Laplacian with conjugate

gradients.

Returns `cost` (the 1-Wasserstein distance estimate in pixel units, an upper bound),

`dual_bound (Kantorovich–Rubinstein lower bound), gap, conductance` (an image: each

pixel's thickest incident tube), `flow_field ((H, W, 2)`: the mean of the flow vectors

of the tubes at each pixel, in `(row, col)` units of mass per unit length, for drawing

arrows), `potential ((H, W) pressures), iters, converged, gap_converged`,

`history, cost_history, dual_history, and with snapshots = m > 0 also snapshots (m`

conductance images at evenly spaced iterations, the last one final), `snapshot_iters` and

`snapshot_cost (sum_e L_e |Q_e|` at those iterations) for watching the tubes form.

Raises `ValueError`: images not 2-D, finite, non-negative, of the same shape with at

least 2 rows and columns, or without mass; unequal masses when `normalize=False`;

`connectivity not 4 or 8; snapshots < 0; and as :func:graph_physarum_transport`.

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)

• poc_physarum_transport — py -3.11 examples/poc_physarum_transport.py

Ops the type connects to (they accept `table` as input)

graph_edge_consensus · graph_core_persistence · tree_morphometry · tree_sholl · tree_run_length

Same category (`flow`)

graph_physarum_path · physarum_route · graph_physarum_transport

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

physarum_transport_image — GRAPH flow op