typed op• 資料種類:lightfield → image
• 呼叫:fullseye.apply(img, "tb_lf_epi_slope", 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(589,824 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。*
*旋鈕 a 不改變輸出(實測: 0.1 / 0.5 / 0.9 相同)。*
*旋鈕 b 不改變輸出(實測: 0.1 / 0.5 / 0.9 相同)。*
階段(前置運算子 → 本運算子，由左至右):
▸ tb_lf_epi_slope: 處理階段 (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):
▸ tb_lf_epi_slope: 其他輸入影像 (文件網站)
由 EPI 線的方向得到逐像素斜率(結構張量,再以剪切細化)。
> 以下的詳細說明為原文 —— 摘要與標題已翻譯。
A scene point traces a straight line in the epipolar-plane image (lf_epi), so along that line the intensity is constant:
E_u + s * E_x = 0. Accumulating that constraint over the whole angular grid and a window x window spatial neighbourhood gives the closed-form least-squares slope s = -(J_ux + J_vy) / (J_xx + J_yy) with J_ab = sum(E_a * E_b) — both the horizontal and vertical EPI directions pooled.
Why it is iterated (fixed 2026-11-03). A finite difference across views measures a displacement of s px per view, while a finite difference across pixels measures one of 1 px; for a texture component of angular frequency w the ratio is sin(w s) / sin(w) (the pre-fix central differences), equal to s only at |s| in {0, 1}. That is the classic statement that the structure tensor is accurate only for disparities in a small range around zero (Wanner & Goldluecke, CVPR 2012 and TPAMI 36(3) 2014, who handle larger ranges by shearing the light field). So the estimator shears the field by an integer slope k (integer shifts: no resampling blur), measures the residual r = s - k, sets k <- round(k + r) per pixel and repeats until no pixel changes (at most EPI_MAX_ROUNDS rounds, at most EPI_MAX_SHEARS distinct shears). The residual is measured with a matched discretisation (adjacent-view difference against the mean of the two views' Gaussian derivatives, inner scale EPI_INNER_SIGMA), whose error is O(r^3 w^2) with |r| <= 1/2.
Measured 2026-11-03, median over the interior of single-layer lf_synthesize fields (64x64, edge="wrap"), s in [-3, 3] in steps of 0.25: error <= 0.006 px for 5x5 and 9x9 views, <= 0.007 px for 4x4 (even count) and <= 0.012 px for 3x3 and for a single row of 6 views, at texture sigma 1.0 / 1.5 / 2.0 / 5.0 px, for windows 5 / 9 / 15 (the pre-fix estimator read -1.388 for -1.5 at sigma 2 and 1.46 for 2.0 at sigma 1.5). Integer slopes are exact to 1e-9 on a wrapped field. Valid range: the shear ladder starts at k = 0, so the first pass must see the right sign and a non-vanishing magnitude: that holds for |s| <= 3 at any texture correlation length >= 1 px, and (measured) up to |s| = 8 at sigma >= 2; at sigma 1 it fails beyond |s| = 5 (s = 6 read as 0.25 — the texture is aliased: it moves more than its correlation length several times per view). Near an occlusion boundary the window mixes two slopes (no estimator of a single orientation per window can avoid that). With edge="nearest" input the outer |k|*(N-1)/2 px of the frame see clamped border pixels.
Returns (slope_map, energy): the (H, W) slope map (centre-view coordinates) and the (H, W) gradient energy J_xx + J_yy of the unsheared field (the first pass's denominator). Pixels whose energy is below *min_energy* have no measurable parallax (a flat patch of sky); their slope is set to 0 and their energy reported as-is, so you threshold on energy instead of being handed a plausible-looking number divided by ~0.
Raises ValueError: *lf* not a valid light field, an angular/spatial shape where *neither* EPI direction carries information (the horizontal EPI needs U >= 2 and W >= 2, the vertical needs V >= 2 and H >= 2), an even or non-positive *window*, a non-positive *min_energy*.
Typed bridge of the lightfield op lf_epi_slope into the 2-D evolution registry: the same implementation, called under the op(v, a, b) convention. This op has no tunable parameter; a and b are unused.
• 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。
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。
img_to_lightfield 0.50 0.50 tb_lf_epi_slope 0.50 0.50
下面的範例呼叫的是底層帳本運算子 lf_epi_slope。此橋接運算子只是把同一實作適配為 fn(v, a, b) 慣例，行為完全相同(只是呼叫形式不同)。
• lightfield_depth — py -3.11 examples/lightfield_depth.py
• poc_lightfield_depth — py -3.11 examples/poc_lightfield_depth.py
image 作為輸入)identity · gaussian · mean_box · mean_box_wh · bilateral · kuwahara · unsharp · median
typed)tb_points_to_voxel · tb_estimate_point_normals · tb_iss_keypoints · tb_project_points · tb_render_point_depth · tb_points_render · tb_statistical_outlier_removal · tb_radius_outlier_removal
*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.