typed op• 数据种类:rgbimage → rgbimage
• 调用:fullseye.apply(img, "tb_specular_diffuse_split", a=0.5, b=0.5)(2-D 的模型是一张图 + 两个标量旋钮 a,b∈[0,1])
*图为在 128×128 合成输入上实际运行的输出。左为输入，右为输出。点云以俯视散点显示(亮度 = z)，一维序列为折线，体数据为沿 z 的最大值投影，视频为中间帧，复数图像为幅值；无法成像的返回值直接显示数值。*
*旋钮 a 不改变输出(实测: 0.1 / 0.5 / 0.9 相同)。*
*旋钮 b 不改变输出(实测: 0.1 / 0.5 / 0.9 相同)。*
阶段(前置算子 → 本算子，从左到右):
▸ tb_specular_diffuse_split: stages (docs site)
换别的图像(合成场景 / 照片 / 硬币。上排为输入，下排为对应输出。旋钮取默认):
▸ tb_specular_diffuse_split: other inputs (docs site)
将线性 RGB 图像分离为漫反射（体色）和镜面反射（界面）两部分。→ (diffuse, specular)，均为 (H, W, 3)。
> 以下的详细说明为原文 —— 摘要与标题已翻译。
Shafer's dichromatic reflection model writes the radiance of a dielectric as
`I(x) = m_d(x) * L(x) + m_s(x) * G`: a body term carrying the surface
colour `L and an interface term carrying the **illuminant** colour G`.
The specular part therefore occupies a single direction in RGB, and
separating it is a projection with a closed form — no iteration, no
optimisation, no learned prior.
Two regimes, chosen by *body_rgb*:
• **`body_rgb given** — a (3,) colour or an (H, W, 3)` map. Each
pixel solves the 3-equation, 2-unknown least-squares system exactly. This
is the textured-surface path: on a synthetic image built from a known
`(m_d, m_s)` it returns them with a maximum absolute error of 4.0e-15
for a uniform body colour and 2.9e-15 for a per-pixel colour map
(measured in `tests/test_specularity.py`).
• **`body_rgb` omitted** — one material is assumed. The
illuminant-orthogonal part of the image is then exactly rank one, so the
body direction is its leading singular vector; the unobservable component
of `L along G is fixed by requiring m_s >= 0` with the minimum
over the image equal to zero. Maximum absolute error 5.0e-16 on the same
synthetic image. At least one lit pixel must be specular-free — see
below, this is the assumption that actually bites.
*illuminant_rgb* is a direction; only its orientation matters and it is
unit-normalised internally. `(1, 1, 1)` is the white-balanced case. Get it
from :func:illuminant_from_dichromatic_planes when you have two or more
materials in frame.
Two guards protect the uniform-body path, and both are needed — the
adversarial pass found the first one alone lets a two-material image
through:
• *max_rank_ratio* — the second singular value of the illuminant-orthogonal
part over the first. Measured on the synthetic bump: 4.6e-16 noiseless,
0.0175 at 0.5% Gaussian noise, 0.0348 at 1%, 0.0694 at 2%, 0.173 at 5%;
a two-material image with cyclically permuted albedos gives 0.574. The
default 0.1 sits between the 2% and 5% noise measurements. `None`
disables it.
• *max_negative_frac* — the fraction of pixels whose fitted body
coefficient comes out negative, which cannot happen for one material.
This is what catches the case the rank test misses: two albedos whose
illuminant-orthogonal chromaticities are nearly anti-parallel still span
one line, and that image measured 0.0815 on the rank test — under the
default threshold, i.e. accepted — while 50% of its pixels fit a negative
body coefficient. With both guards disabled that image returns a diffuse
map wrong by 1.03 in absolute radiance on an image whose maximum is 0.99,
with no exception and no NaN. `None` disables it.
**Both guards bound gross violations only, and that is not fixable by a
better threshold.** A texture whose chromaticity drifts *along* the body
direction rather than away from it measured a rank ratio of 0.0641 — under
the default — with every body coefficient positive, so neither guard fires,
and the returned diffuse map was wrong by 0.198. It cannot be separated from
noise by any threshold, because it is the same measurement: 1% Gaussian
noise on that scene gives 0.0348 and 2% gives 0.0694, and the texture sits
between them. The answer for a surface that might be textured is
`body_rgb`, not a cleverer number here.
Honest limits. (1) *Without `body_rgb`, one lit pixel must be
specular-free.* The rendered-lobe measurement shows exactly what it costs
when none is: for a Blinn-Phong highlight on a Gaussian bump the maximum
diffuse error is 6.5e-11 at shininess 200 (where the lobe tail underflows to
9.1e-11), 0.0019 at shininess 48 (tail 0.0026) and 0.175 at shininess 8
(tail 0.243) — the error *is* the darkest highlight in the frame, because
that is the constant the constraint cannot see. (2) *The known-body path is
conditioned by `1/(1 - b^2) where b` is the cosine between the body
and illuminant colours.* A texture reaching `|b| = 0.99999` (an almost
neutral grey under a white lamp, amplification 6.4e+04) measured 5.9e-12
against 2.9e-15 for the same texture kept at `|b| <= 0.965`. Near-grey
surfaces are where colour-based separation is weakest, and no amount of
arithmetic care changes that.
Raises `ValueError: *image_rgb* is not (H, W, 3)`, is complex /
masked / non-finite / string-typed, or exceeds :data:MAX_PIXELS;
*illuminant_rgb* is not a non-zero 3-vector; the image is identically zero;
the image has no component orthogonal to the illuminant (body colour
parallel to it, so no split exists); either guard above fires; *body_rgb*
has the wrong shape, a zero-length colour, or is parallel to the
illuminant.
Returns `(diffuse, specular) with diffuse + specular == image_rgb` to
machine precision in both regimes: measured 1.1e-16 on the uniform-body
route, which forms the diffuse as `image - specular`, and 2.1e-15 on the
known-body route, which forms both parts from the solved coefficients and
so accumulates a little more.
Typed bridge of the specular op `specular_diffuse_split into the 2-D evolution registry: the same implementation, called under the op(v, a, b) convention. a drives max_rank_ratio (default 0.1) and b drives max_negative_frac` (default 0.02).
• 示例数据目录(下载 URL / 许可证) —— 2-D 用 skimage.data(BSD/公有领域)加合成图,3-D 给出真实数据源(Stanford/PDS 等)的下载 URL。
• 算子来历与参考文献 —— 该算子族所依据的研究/方法出处。
下面的程序已确认可以运行(与图相同的输入)。在 Studio 帮助中，此块会变成按钮，可当场加载并运行。
img_to_rgb 0.50 0.50 tb_specular_diffuse_split 0.50 0.50
▸ Load this pipeline · Load & run
下面的示例调用的是底层账本算子 specular_diffuse_split。此桥接算子只是把同一实现适配为 fn(v, a, b) 约定，行为完全相同(只是调用形式不同)。
• specular_photometric — py -3.11 examples/specular_photometric.py
rgbimage 作为输入)identity · tb_wetness · tb_sensor_capture · tb_specular_coefficient_map · tb_specular_free_transform · tb_rgb_to_quaternion
typed)tb_points_to_voxel · tb_estimate_point_normals · tb_iss_keypoints · tb_project_points · tb_render_point_depth · tb_statistical_outlier_removal · tb_radius_outlier_removal · tb_voxel_grid_downsample
*Provenance: ops.py — 2D 算子登记表。本条目由 tools/opdocs.py md 自动生成(请勿手工编辑)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.