fractal_dimension — 2D `features` op

• Data kinds: image → feature

• Call: fullseye.apply(img, "fractal_dimension", a=0.5, b=0.5) (the 2-D model is one image plus two scalar knobs a,b∈[0,1])

$fractal_dimension: input → output$

*The figure is the actual output on a synthetic 128×128 input. Left: input, right: output. Point clouds are drawn as a top-down scatter (brightness = z), 1-D series as a line plot, volumes as the maximum-intensity projection along z, videos as the middle frame, complex images as magnitude; return values that are not pictures are shown as the values themselves.*

Sweeping knob a (0.1 / 0.5 / 0.9, the other knob at its default):

▸ fractal_dimension: knob a sweep (docs site)

*Knob b does not change the output (measured: identical at 0.1 / 0.5 / 0.9).*

Usage

> This operator's description has not been translated yet. The original text follows as it is.

テクスチャの複雑さを測る Minkowski-Bouligand(ボックスカウント)フラクタル次元。

閾値 `a(既定 0.5)で二値化し、箱サイズ s = 1, 2, 4, …` について「構造を

含む s×s 箱」の数 `N(s) を数え、log N(s) を log(1/s)` に最小二乗回帰した

傾きを返す(Mandelbrot 1982)。直線状の構造は ~1、平面を埋める領域は ~2、自己

相似な縁は中間の非整数(Sierpinski 三角形なら `log 3 / log 2 ≈ 1.585`)。表面

粗さ・組織テクスチャ・地形・破面などの安価な複雑さ特徴に使える。

有限解像度のため塗り潰し領域は 2 をやや下回る(粗いスケールで箱が飽和する既知の

過小評価)。`a が二値化の閾値、b` は未使用。構造が無い/1 スケールしか取れない

ときは 0 を返す。

Detailed usage guide

• gallery2d_features family guide

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.

Try it in Studio

The program below has been verified to run (same input as the figure). In Studio's help this block becomes buttons that load and run it on the spot.

fractal_dimension 0.50 0.50

▸ Load this pipeline · Load & run

Runnable examples (verified samples that actually call this op)

• gallery2d_features — py -3.11 examples/gallery2d_features.py

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

identity · feature_to_img

Same category (`features`)

effective_bit_depth · blob_count · area_frac · count_contours · total_length · vol_count · sk_euler · sk_entropy_feat

*Provenance: ops.py — 2D operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*

fractal_dimension — 2D features op