snake_evolve — SEGMENTATION `contour` op

• Data kinds: image2d × pairs → table

• Call: import fullseye as fs; fs.ledger.snake_evolve(image, init_points, *, alpha: 'float' = 0.1, beta: 'float' = 0.1, gamma: 'float' = 1.0, external: 'str' = 'edge', w_line: 'float' = 0.0, w_edge: 'float' = 1.0, sigma: 'float' = 1.0, kappa: 'float' = 1.0, gvf=None, gvf_mu: 'float' = 0.2, max_px_move: 'Optional[float]' = None, n_iter: 'int' = 300, spline_order: 'int' = 3, tol: 'float' = 0.0, resample_every: 'int' = 0, record_every: 'int' = 0) -> 'Dict[str, object]' (to call the implementation directly, import segcontour; segcontour.snake_evolve(image, init_points, *, alpha: 'float' = 0.1, beta: 'float' = 0.1, gamma: 'float' = 1.0, external: 'str' = 'edge', w_line: 'float' = 0.0, w_edge: 'float' = 1.0, sigma: 'float' = 1.0, kappa: 'float' = 1.0, gvf=None, gvf_mu: 'float' = 0.2, max_px_move: 'Optional[float]' = None, n_iter: 'int' = 300, spline_order: 'int' = 3, tol: 'float' = 0.0, resample_every: 'int' = 0, record_every: 'int' = 0) -> 'Dict[str, object]'; from the registry, opssegmentation.get("snake_evolve"))

Usage

Semi-implicit update of the discrete snake (Kass–Witkin–Terzopoulos 1988): x_t = (A + γI)^(-1)(γ x_(t-1) − f_x) (eqs. (19)(20)) (snake_evolve).

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

閉じた snake(周期境界)の点 `init_points`(N, 2)= [row, col]、N ≥ 5。内部エネルギー

E_int = ½ Σ (α |v_(i+1) − v_i|² + β |v_(i+1) − 2v_i + v_(i−1)|²) = ½ xᵀ A x(陰的)。外力(陽的)は `external` で選ぶ:

`"edge"` = ポテンシャル P = w_line · G_σ*I + w_edge · |∇(G_σ*I)|²、E_ext = −κ Σ P(v_i)(Kass の E_line と E_edge)、

`"potential" = image` をそのまま P として使う(第 2 実装と同じ P を渡すため)、

`"gvf" = 力そのものが −κ (v, u)(GVF、gvf に gvf_field の返りを渡すか、gvf_mu` で内部で作る)、

`"none" = 外力 0。P は spline_order` 次の補間スプライン(値と微分が整合)で点の位置へ。

`max_px_move` を与えると 1 反復の移動を max_px_move · tanh(Δ) に制限(skimage と同じ。近接勾配の性質は失う)。

`resample_every` > 0 なら k 反復ごとに弧長で等間隔に打ち直す(凹部へ入るとき点が疎になるのを防ぐ。エネルギーの

単調性はその時点で途切れる)。点は画像の範囲 [0, H−1] × [0, W−1] に切り詰める。

返り値: `points(N, 2)、mask(折れ線の内側)、energy / energy_internal / energy_external`(反復ごと、

先頭 = 初期。GVF では外力のエネルギーが定義されないので total と external は NaN)、`n_increase`(エネルギーが

増えた反復の数、GVF なら None)、`max_increase、lipschitz`(κP のヘッセ行列のスペクトルノルムの格子上の最大 =

外力の勾配の Lipschitz 定数の見積り)、`gamma_ge_lipschitz`(γ ≥ L なら降下補題で単調非増加が保証される)、

`radius_factor(外力 0 の円の 1 反復の縮み γ/(γ + λ_1) の閉形式)、history`(record_every ごとの点)、

`n_iter、converged`。

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`)

gvf_field · 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).*

snake_evolve — SEGMENTATION contour op