flow op• データ種: image2d × image2d → table
• 呼び出し: 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) (実装を直接呼ぶなら 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)、台帳から引くなら opsgraph.get("physarum_transport_image"))
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`.
• サンプルデータ カタログ(DL URL / ライセンス) — 2-D は skimage.data(BSD/public)+ 合成、3-D は実データ源(Stanford/PDS 等)の DL URL。
• 演算子の来歴・参考文献 — この op 族の元になった研究/手法の出典。
• アルゴリズムの正典(著者・年)と用途は上記ファミリ使い方ガイドに記載。
• poc_physarum_transport — py -3.11 examples/poc_physarum_transport.py
table を入力に取れる)graph_edge_consensus · graph_core_persistence · tree_morphometry · tree_sholl · tree_run_length
flow)graph_physarum_path · physarum_route · graph_physarum_transport
*Provenance: physarum_search.py — GRAPH operator registry. この per-op ノートは tools/opdocs.py md が自動生成(手編集しない)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.