physics op• 資料種類:image → image
• 呼叫:fullseye.apply(img, "ph_total_variation_flow", a=0.5, b=0.5)(2-D 的模型是一張圖 + 兩個純量旋鈕 a,b∈[0,1])
• GPU:有(許可清單中的機械式 GPU 路徑,CuPy)。device="auto" 在實測尺寸(4,194,304 像素)以上選擇 GPU
*圖為在 128×128 合成輸入上實際執行的輸出。左為輸入，右為輸出。點雲以俯視散點顯示(亮度 = z)，一維序列為折線，體資料為沿 z 的最大值投影，影片為中間影格，複數影像為振幅；無法成像的回傳值直接顯示數值。*
*輸出以類 viridis 偽彩色顯示(深紫 = 小，黃 = 大)，便於讀取距離、相位、方向、深度這類「量的場」。*
掃描旋鈕 a(0.1 / 0.5 / 0.9，另一旋鈕取預設):
▸ ph_total_variation_flow: 旋鈕 a 掃描 (文件網站)
掃描旋鈕 b(0.1 / 0.5 / 0.9，另一旋鈕取預設):
▸ ph_total_variation_flow: 旋鈕 b 掃描 (文件網站)
換別的影像(合成場景 / 照片 / 硬幣。上排為輸入，下排為對應輸出。旋鈕取預設):
▸ ph_total_variation_flow: 其他輸入影像 (文件網站)
*第 4 欄是彩色 (H,W,3) 輸入。此運算子能正確處理顏色而不跨通道(不把顏色通道當作第三個空間軸摺積)。*
全變分（Rudin-Osher-Fatemi）去雜訊流（HALCON 無對應運算子，""）。
> 以下的詳細說明為原文 —— 摘要與標題已翻譯。
Gradient descent of the ROF energy TV(I) + (lam/2)||I - I0||^2:
I_t = div(grad I / |grad I|) - lam (I - I0).
The TV term (curvature of the level sets) flattens noise while preserving sharp edges; the fidelity term keeps the result anchored to the noisy input I0 so it denoises rather than collapsing to a constant. a sets the step count (1..80 explicit steps of dt=0.008), b the fidelity weight lam in [10, 30] (b=0 smooths most, b=1 stays closest to the input).
The steps march towards the ROF minimiser, a fixed point: once the fidelity has had time to act (lam * steps * dt of a few units, reached by a ~ 0.5 at b=0) more steps no longer change the answer, so raising a never turns a denoiser into a blur. A flat region of perimeter P and area A loses about (P/A)/lam of its contrast at the fixed point, so small features fade more than large ones (the usual ROF bias); raise b for light noise.
Until 2026-11-05 lam was 0.02..0.22: its time constant 1/lam (4.5..50) was far longer than the whole run (80 * 0.008 = 0.64), so the fidelity did nothing, the op was a pure TV flow drifting to a constant, and the error against the clean image grew with a (noisy square, sigma 0.05: 0.019 at a=0.1, 0.067 at a=1, worse than the noisy input's 0.050; even a clean input lost 0.067).
The curvature term is the mean of the four forward/backward staggerings (forward gradient + backward divergence and its mirror, per axis), so the flow commutes with flipping the image. Until 2026-11-05 (adversarial review round 2) only the forward-gradient / backward-divergence pair was used, and flipping the input changed the result by up to 0.15.
• gallery2d_physics_alife_3d 族使用指南
• 範例資料目錄(下載 URL / 授權) —— 2-D 用 skimage.data(BSD/公有領域)加合成圖,3-D 給出真實資料源(Stanford/PDS 等)的下載 URL。
• 運算子來歷與參考文獻 —— 該運算子族所依據的研究/方法出處。
• 演算法的正典(作者、年份)與用途見上面的族使用指南。
下面的程式已確認可以執行(與圖相同的輸入)。在 Studio 說明中，此區塊會變成按鈕，可當場載入並執行。
ph_total_variation_flow 0.50 0.50
• find_ops_by_meaning — py -3.11 examples/find_ops_by_meaning.py
• gallery2d_physics_alife_3d — py -3.11 examples/gallery2d_physics_alife_3d.py
image 作為輸入)identity · gaussian · mean_box · mean_box_wh · bilateral · kuwahara · unsharp · median
physics)ph_perona_malik · ph_coherence_enhancing_diffusion · ph_reaction_diffusion · ph_heat_flow · ph_mean_curvature_motion
*Provenance: ops.py — 2D 運算子登記表。本條目由 tools/opdocs.py md 自動產生(請勿手動編輯)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.