typed op• 数据种类:points → feature
• 调用:fullseye.apply(img, "tb_dynsys_correlation_dimension", a=0.5, b=0.5)(2-D 的模型是一张图 + 两个标量旋钮 a,b∈[0,1])
*图为在 128×128 合成输入上实际运行的输出。左为输入，右为输出。点云以俯视散点显示(亮度 = z)，一维序列为折线，体数据为沿 z 的最大值投影，视频为中间帧，复数图像为幅值；无法成像的返回值直接显示数值。*
扫描旋钮 a(0.1 / 0.5 / 0.9，另一旋钮取默认):
▸ tb_dynsys_correlation_dimension: knob a sweep (docs site)
*旋钮 b 不改变输出(实测: 0.1 / 0.5 / 0.9 相同)。*
阶段(前置算子 → 本算子，从左到右):
▸ tb_dynsys_correlation_dimension: stages (docs site)
Grassberger–Procaccia 关联维数 —— `log C(r)` 的斜率。
> 以下的详细说明为原文 —— 摘要与标题已翻译。
`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.
• 示例数据目录(下载 URL / 许可证) —— 2-D 用 skimage.data(BSD/公有领域)加合成图,3-D 给出真实数据源(Stanford/PDS 等)的下载 URL。
• 算子来历与参考文献 —— 该算子族所依据的研究/方法出处。
下面的程序已确认可以运行(与图相同的输入)。在 Studio 帮助中，此块会变成按钮，可当场加载并运行。
img_to_points 0.50 0.50 tb_dynsys_correlation_dimension 0.50 0.50
▸ Load this pipeline · Load & run
下面的示例调用的是底层账本算子 dynsys_correlation_dimension。此桥接算子只是把同一实现适配为 fn(v, a, b) 约定，行为完全相同(只是调用形式不同)。
• poc_what_a_picture_cannot_check — py -3.11 examples/poc_what_a_picture_cannot_check.py
feature 作为输入)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 算子登记表。本条目由 tools/opdocs.py md 自动生成(请勿手工编辑)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.