typed op• 資料種類:points → feature
• 呼叫:fullseye.apply(img, "tb_dynsys_correlation_dimension", a=0.5, b=0.5)(2-D 的模型是一張圖 + 兩個純量旋鈕 a,b∈[0,1])
*圖為在 128×128 合成輸入上實際執行的輸出。左為輸入，右為輸出。點雲以俯視散點顯示(亮度 = z)，一維序列為折線，體資料為沿 z 的最大值投影，影片為中間影格，複數影像為振幅；無法成像的回傳值直接顯示數值。*
掃描旋鈕 a(0.1 / 0.5 / 0.9，另一旋鈕取預設):
▸ tb_dynsys_correlation_dimension: 旋鈕 a 掃描 (文件網站)
*旋鈕 b 不改變輸出(實測: 0.1 / 0.5 / 0.9 相同)。*
階段(前置運算子 → 本運算子，由左至右):
▸ tb_dynsys_correlation_dimension: 處理階段 (文件網站)
Grassberger–Procaccia 關聯維數 —— log C(r) 的斜率。
> 以下的詳細說明為原文 —— 摘要與標題已翻譯。
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.
• 範例資料目錄(下載 URL / 授權) —— 2-D 用 skimage.data(BSD/公有領域)加合成圖,3-D 給出真實資料源(Stanford/PDS 等)的下載 URL。
• 運算子來歷與參考文獻 —— 該運算子族所依據的研究/方法出處。
下面的程式已確認可以執行(與圖相同的輸入)。在 Studio 說明中，此區塊會變成按鈕，可當場載入並執行。
img_to_points 0.50 0.50 tb_dynsys_correlation_dimension 0.50 0.50
下面的範例呼叫的是底層帳本運算子 dynsys_correlation_dimension。此橋接運算子只是把同一實作適配為 fn(v, a, b) 慣例，行為完全相同(只是呼叫形式不同)。
• poc_what_a_picture_cannot_check — py -3.11 examples/poc_what_a_picture_cannot_check.py
feature 作為輸入)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 運算子登記表。本條目由 tools/opdocs.py md 自動產生(請勿手動編輯)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.