flow op• Data kinds: voxel × voxel → flow_dense
• Call: import fullseye as fs; fs.ledger.vol_flow_3d(vol_a, vol_b, win: 'int' = 3, pyr_levels: 'int' = 3, iters: 'int' = 5, reg: 'float' = 0.001) -> 'np.ndarray' (to call the implementation directly, import live4d; live4d.vol_flow_3d(vol_a, vol_b, win: 'int' = 3, pyr_levels: 'int' = 3, iters: 'int' = 5, reg: 'float' = 0.001) -> 'np.ndarray'; from the registry, opslive4d.get("vol_flow_3d"))
Dense displacement field (3, Z, Y, X) between two volumes (flow_dense, components dz, dy, dx [voxel]).
vol_b(x) ≈ vol_a(x − d), i.e. the structure of vol_a moves by +d to become vol_b (the same convention as the torch version scene_flow_lk). A 3-D version of Lucas–Kanade with numpy + scipy only: win is the half-width of the window (side length of the window 2·win + 1), pyr_levels is the number of pyramid levels (increase for large displacements; each level 1/2), iters is the warp iterations per level, reg is the regularisation of the structure tensor diagonal (avoids division by 0 in flat regions; the larger, the more the flow in flat regions tends to 0). In flat regions without texture the flow is undetermined (aperture problem) -- trust it only where there is a gradient.
>>> a = volseq_synth_dividing((16, 24, 24), n_frames=4, split_frame=0, speed=1.0)
>>> d = vol_flow_3d(a[1], a[2]); d.shape
(3, 16, 24, 24)
• 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.
• poc_live4d — py -3.11 examples/poc_live4d.py
flow_dense as input)—
flow)volseq_speed · volseq_pathline_render · volseq_pathline_orbit
*Provenance: live4d.py — LIVE4D 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.