typed op• データ種: points → feature
• 呼び出し: fullseye.apply(img, "tb_dynsys_correlation_dimension", a=0.5, b=0.5) (2-D は 1 画像 + 2 スカラつまみ a,b∈[0,1] のモデル)
*図は合成の入力 128×128 で実際に走らせた出力。左が入力、右が出力。点群は上から見た散布(明るさ = z)、1-D 列は折れ線、体積は z 方向の最大値投影、動画は中央フレーム、複素画像は振幅、絵にならない返り値は値そのもの。*
つまみ a を振る(0.1 / 0.5 / 0.9、もう一方は既定):
▸ tb_dynsys_correlation_dimension: つまみ a を振った図 (docs サイト)
*つまみ b は出力を変えない(実測: 0.1 / 0.5 / 0.9 で同一)。*
段階(前置きの op → この op。左から順):
▸ tb_dynsys_correlation_dimension: 段階の図 (docs サイト)
Grassberger-Procaccia correlation dimension — the slope of log C(r).
C(r) is the fraction of point pairs closer than r; for a self-similar set it grows like r**D, and *D* is read off the straight part of the log-log plot (fitted on the middle 60 % of the radii, where the curve is free of the small-r noise floor and the large-r saturation).
★Why this earns its place: unlike box counting it needs no grid, and its answers are known for simple sets — a circle gives 1, a filled square 2, a Cantor set log2/log3 = 0.6309. It measures a different quantity from the existing fractal_dimension (box counting), so the two are an independent pair rather than two names for one number.
Returns a measurement: the fitted dimension.
Raises ValueError: fewer than 32 points; not a 2-D array; non-finite input; a degenerate cloud (every point identical); a radius range that leaves no pairs.
Limits: sub-sampled to *max_points* (pairs grow quadratically). ★The dominant error is not the sub-sampling but the radius window: the default range is the 1st-25th percentile of pair distances, and on a *bounded* set its upper end runs into the boundary, where C(r) saturates and flattens the slope. Measured on a unit square (true D = 2): 1.879 with the default window and 1.873 / 1.879 / 1.871 at 400 / 1,500 / 3,000 points —— more points do not help; narrowing the window to r_lo=0.01, r_hi=0.1 gives 1.947 and 0.002 / 0.05 gives 2.050. Pass *r_lo* / *r_hi* explicitly when the answer matters, and report the window with the number.
Typed bridge of the math op dynsys_correlation_dimension into the 2-D evolution registry: the same implementation, called under the op(v, a, b) convention. a drives n_radii (default 24); b is unused.
• 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。
下のプログラムは実際に走ることを確かめてある(図と同じ入力)。Studio のヘルプではこのブロックがボタンになり、その場で読み込んで実行できる。
img_to_points 0.50 0.50 tb_dynsys_correlation_dimension 0.50 0.50
次の例は元の台帳 op dynsys_correlation_dimension を呼ぶもの。この橋渡し op は同じ実装を fn(v, a, b) 規約に合わせただけなので、挙動はそのまま当てはまる(呼び出し形だけ違う)。
• poc_what_a_picture_cannot_check — py -3.11 examples/poc_what_a_picture_cannot_check.py
feature を入力に取れる)typed)tb_points_to_voxel · tb_estimate_point_normals · tb_iss_keypoints · tb_project_points · tb_render_point_depth · tb_statistical_outlier_removal · tb_radius_outlier_removal · tb_voxel_grid_downsample
*Provenance: ops.py — 2D 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.