gvf_field — SEGMENTATION `contour` op

• Data kinds: image2d → table

• Call: import fullseye as fs; fs.ledger.gvf_field(image, *, mu: 'float' = 0.2, sigma: 'float' = 1.0, method: 'str' = 'direct', n_iter: 'int' = 2000, dt: 'Optional[float]' = None, edge_map=None) -> 'Dict[str, object]' (to call the implementation directly, import segcontour; segcontour.gvf_field(image, *, mu: 'float' = 0.2, sigma: 'float' = 1.0, method: 'str' = 'direct', n_iter: 'int' = 2000, dt: 'Optional[float]' = None, edge_map=None) -> 'Dict[str, object]'; from the registry, opssegmentation.get("gvf_field"))

Usage

Gradient vector flow (Xu–Prince 1998): the field (u, v) that smoothly diffuses the gradient of the edge map f away from the edges (gvf_field).

> The detailed description below is the original text — the summary and the headings are translated.

E = ∬ μ(u_x² + u_y² + v_x² + v_y²) + |∇f|² |(u, v) − ∇f|² の最小化。Euler 方程式

μ∇²u − (u − f_x)(f_x² + f_y²) = 0、μ∇²v − (v − f_y)(f_x² + f_y²) = 0(線形)。

`method="iterate"` = 論文の時間発展 u ← u + Δt(μ∇²u − b(u − f_x))、b = |∇f|²(陽的、Δt ≤ 1/(4μ + max b))。

`method="direct"` = 同じ離散方程式 (μL − diag b) u = −b f_x を疎行列で直接解く(定常解そのもの)。

辺の地図 f は既定で |∇(G_σ * I)| を最大 1 に正規化したもの(`edge_map` で直接与えてもよい)。境界は Neumann。

u = 列(x)方向、v = 行(y)方向の成分。

返り値: `u / v、edge_map、fx / fy、residual_max(Euler 方程式の残差の最大)、residual_rel`

(残差 / max(b |∇f|))、`n_iter、method、mu`。f が平坦なら場は 0(残差 0)。

Detailed usage guide

• halcon_segmentation family guide

Background guides (the physics and conventions behind this op)

• active_contours_and_level_sets — 変分・動的輪郭とレベルセット — どの輪郭がどこで止まり、何を保証するか

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_active_contours — py -3.11 examples/poc_active_contours.py

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

class_ndim_norm

Same category (`contour`)

snake_evolve · chan_vese_energy · chan_vese_evolve · morph_chan_vese · morph_geodesic_ac · edge_stop_g · level_set_reinit · drle_evolve

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

gvf_field — SEGMENTATION contour op