alpha_tree — SEGMENTATION `graph` op

• Data kinds: image2d → table

• Call: import fullseye as fs; fs.ledger.alpha_tree(image, alphas: 'Sequence[float]' = (0.0,), *, connectivity: 'int' = 4) -> 'Dict[str, object]' (to call the implementation directly, import seggraph; seggraph.alpha_tree(image, alphas: 'Sequence[float]' = (0.0,), *, connectivity: 'int' = 4) -> 'Dict[str, object]'; from the registry, opssegmentation.get("alpha_tree"))

Usage

α-tree: builds the minimum spanning tree of the grid weighted by neighbour differences (Kruskal in scipy) and returns the partition for each α using only the tree edges of weight ≤ α (alpha_tree).

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

scipy は重み 0 の辺を「辺が無い」と読むので、重み 0 の辺だけを「正の重みの最小の半分」に置き換えてから木を作る

(辺の順序は変わらない = 最小全域木は同じ)。全辺に 1 を足す手は使わない: 0.3 の差が浮動小数で 0.29999999999999993 と

0.30000000000000004 に割れている時、+1 の丸めで 2 つが同点になり、木が重い方を選んで α = 0.3 の切断がずれた(実測、

テスト test_quasi_flat_zones_equal_mst_cut)。木の辺の重みは添字から |f_p − f_q| を計算し直す。

返す: `labels(α ごとの (H, W) を積んだ (A, H, W))、n_zones、mst_i / mst_j / mst_w、merge_levels`

(木の辺の重みの昇順 = 併合の高さ)、`nested`(α の昇順で入れ子か)。

Detailed usage guide

• halcon_segmentation family guide

Background guides (the physics and conventions behind this op)

• graph_hierarchy_and_thresholds — グラフ・階層・閾値の定理でつくる分割 — 何が厳密で、どこで割れ方が倒れるか

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_graph_hierarchy_segmentation — py -3.11 examples/poc_graph_hierarchy_segmentation.py

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

class_ndim_norm

Same category (`graph`)

graph_cut_binary · alpha_expansion · statistical_region_merging · max_tree · area_opening_attr · quasi_flat_zones · hierarchical_watershed · ultrametric_contour_map

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

alpha_tree — SEGMENTATION graph op