decomposition op• Data kinds: image → image
• Call: fullseye.apply(img, "dc_rpca_sparse", 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):
▸ dc_rpca_sparse: knob a sweep (docs site)
*Knob b does not change the output (measured: identical at 0.1 / 0.5 / 0.9).*
On other images (synthetic scene / photo / coins. Top row: inputs, bottom row: their outputs. Knobs at default):
▸ dc_rpca_sparse: 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).*
Robust-PCA sparse (defect / anomaly) residual = input - low-rank, at 0.5.
> The detailed description below is the original text — the summary and the headings are translated.
`dc_rpca_lowrank と同じ inexact ALM の PCP 分解 M = L + S` を行い、
スパース項 `S を 0.5 を中心に置いて返す(clip(S + 0.5, 0, 1)`)。背景と
同じ画素は 0.5、背景より明るい孤立点は 0.5 より上、暗い点は下に出る符号つき
残差で、飽和しない範囲で `dc_rpca_lowrank + (この出力 - 0.5) == 入力`。
`a はスパース重み λ = (0.5 + 1.5*a)/sqrt(max(m, n))` で、大きいほど
`S が疎(小さな残差は 0 に丸められ、はっきりした欠陥だけ残る)、a=0`
ではほぼ全画素に残差が出る。`b` は未使用。
長辺 64 超の画像は縮小して `L を解き、S` は元解像度で
`S = soft(M0 - L_up, λ/μ_final) として作り直す(縮小した S` を拡大
すると 1 画素欠陥がにじんで振幅を失うため)。入力は [0,1] の 2 次元に揃え、
返り値は同形 float64、[0,1]。全零画像では `S = 0` で一様 0.5。例外時は
fail-soft で入力のクリップ版が返り、台帳に記録される。
後段では `|出力 - 0.5| が欠陥の強さなので、threshold` 系の op で 0.5 から
離れた画素を拾う(明側・暗側のどちらを拾うかはしきい値の向きで決まる)。周期
背景(織物・格子・ディスプレイ)上の点欠陥・傷の検出向けで、非周期背景では
残差に背景の凹凸がそのまま混ざる。
• gallery2d_texture_freq family guide
• blas_threads_and_memory — 行列分解が遅い理由の知識 — BLAS スレッド・キャッシュ・メモリ配置
• 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.
dc_rpca_sparse 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
decomposition)dc_structure_texture · dc_texture_residual · dc_rpca_lowrank · dc_retinex · dc_local_contrast_norm · dc_homomorphic
*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.