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])
*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).*
Minkowski–Bouligand (box-counting) fractal dimension, which measures the complexity of a texture.
Binarises with the threshold a (default 0.5), counts for box sizes s = 1, 2, 4, … the number N(s) of "s×s boxes containing structure", and returns the slope of the least-squares regression of log N(s) on log(1/s) (Mandelbrot 1982). Line-like structures give ~1, plane-filling regions ~2, and self- similar borders an intermediate non-integer (log 3 / log 2 ≈ 1.585 for the Sierpinski triangle). Usable as a cheap complexity feature for surface roughness, tissue texture, terrain, fracture surfaces and the like.
Because of finite resolution, filled regions come out slightly below 2 (a known underestimate caused by boxes saturating at coarse scales). a is the binarisation threshold, b is unused. If there is no structure or only 1 scale can be taken, it returns 0.
• gallery2d_features family guide
• 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.
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
• gallery2d_features — py -3.11 examples/gallery2d_features.py
• poc_endless_zoom_and_turning_solids — py -3.11 examples/poc_endless_zoom_and_turning_solids.py
• poc_theorems_as_pictures — py -3.11 examples/poc_theorems_as_pictures.py
feature as input)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).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.