texture op• Data kinds: image → image
• Call: fullseye.apply(img, "scale_select_std", 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.*
*The output is shown in a viridis-like pseudo-colour (dark purple = low, yellow = high) so that a field of quantities — distance, phase, orientation, depth — can be read.*
Sweeping knob a (0.1 / 0.5 / 0.9, the other knob at its default):
▸ scale_select_std: knob a sweep (docs site)
Sweeping knob b (0.1 / 0.5 / 0.9, the other knob at its default):
▸ scale_select_std: knob b sweep (docs site)
On other images (synthetic scene / photo / coins. Top row: inputs, bottom row: their outputs. Knobs at default):
▸ scale_select_std: other inputs (docs site)
*The 4th column is a colour (H,W,3) input. This op handles colour without crossing channels (it does not convolve the colour channel as a third spatial axis).*
Local standard deviation that chooses the window size per pixel (Lepski / ICI rule).
The wider the window, the more stable the estimate (relative standard error 1/sqrt(2(n-1))), but edges blur and resolution drops — as long as you choose 1 size, this contradiction cannot be resolved. The way out is to "neither in time nor in space but hold a different answer for each location": starting from the smallest window, widen the window only while the confidence intervals of the estimates keep overlapping, and stop at the 1 just before they stop overlapping. In flat places a large window (stable) and near edges a small window (no blur) is chosen automatically.
a is the upper limit of the windows tried (how far along 3,5,7,9,11,13,15), b is the confidence-interval multiplier gamma (1.0-3.0). A larger gamma makes the window extend more easily (leaning towards stability).
Relation to local_std: local_std fixes the window. The trade-off that widening the window to tighten the estimate in flat regions blurs the edges is resolved here per location. Lowering only the error in flat regions while keeping the sharpness of edges is its strength; in exchange the computation grows by the number of windows.
Conditions of use: (1) The "do they overlap" decision depends on the error bounds being correct — with noise that is not white (spatially correlated) the window extends too far. (2) If gamma is too small, the smallest window is always chosen, and the result equals the 3x3 of local_std (this is how to tell it is not working).
• gallery2d_texture_freq 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.
scale_select_std 0.50 0.50
▸ Load this pipeline · Load & run
• gallery2d_texture_freq — py -3.11 examples/gallery2d_texture_freq.py
image as input)identity · gaussian · mean_box · bilateral · unsharp · median · min_filter · max_filter
texture)std_filter · local_bimodality · local_std · bootstrap_std_error · structure_tensor_orientation · structure_tensor_coherence · gabor · sk_frangi
*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.