3DV 2025

RISE-SDF

a Relightable Information-Shared Signed Distance Field for Glossy Object Inverse Rendering面向高光物体逆渲染的可重打光、信息共享符号距离场(a Relightable Information-Shared Signed Distance Field)

Deheng Zhang1,2*, Jingyu Wang1*, Shaofei Wang1, Marko Mihajlovic1, Sergey Prokudin1, Hendrik P.A. Lensch2, Siyu Tang1

1ETH Zürich   2University of Tübingen  ·  *equal contribution*共同一作

Chrome镜面金属m = 1 · ρ = 0.05Brushed gold磨砂金m = 1 · ρ = 0.35Red plastic红色塑料m = 0 · ρ = 0.3

Split-sum shading (the appearance model RISE-SDF uses), rendered live in your browser under a rotating environment map.用 split-sum 着色(RISE-SDF 使用的外观模型)在浏览器里实时渲染,环境光在缓慢旋转。

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Inverse rendering: from photos to a relightable asset逆渲染:从照片到可重打光的资产

Given multi-view images and camera poses of an object, recover what produced them, so the object can be rendered again under any new light.给定一个物体的多视角图像和相机位姿,恢复生成这些图像的因素,从而在任意新光照下重新渲染它。

Geometry几何

signed distance field \(s(\mathbf x)\); surface \(s=0\), normal \(\mathbf n\)符号距离场 \(s(\mathbf x)\);表面 \(s=0\),法线 \(\mathbf n\)

Material材质

albedo \(\mathbf a\), metallic \(m\), roughness \(\rho\) of a simplified Disney BRDF简化 Disney BRDF 的反照率 \(\mathbf a\)、金属度 \(m\)、粗糙度 \(\rho\)

Lighting光照

a distant environment map \(L\)远处的环境贴图 \(L\)

Glossy objects are the hard case: a mirror-like surface shows its surroundings, not itself, so reflections are easily baked into the texture or the shape.高光物体是难点:镜面一样的表面映出的是周围环境而不是自己,反射很容易被错当成纹理或几何。

What prior methods miss现有方法缺什么

Inverse-rendering methods for glossy objects, as compared in the paper. Click a row to see its relighting of the toaster.论文对比的高光物体逆渲染方法。点击一行,查看它对烤面包机的重打光结果。

Method方法Representation表示PBE2ERTrain训练Relighting failure (paper)重打光的问题(论文所述)

PB: physically based BRDF. E2ER: end-to-end relightable; NeRO and ENVIDR need extra steps per new light (a Blender export, or training an MLP to hold the environment map). Training times from the paper's Table 1.PB:基于物理的 BRDF。E2ER:端到端可重打光;NeRO 和 ENVIDR 每换一种光照都要额外步骤(导出到 Blender,或训练一个 MLP 来存环境贴图)。训练时间来自论文表 1。

Ground-truth relighting of the toaster
GT
NeRO

And no glossy dataset had ground-truth material and relighting, so material quality could not be measured.此外,没有任何高光数据集提供材质和重打光的真值,材质好坏无法定量评测。

RISE-SDF at a glanceRISE-SDF 概览

RISE-SDF pipeline: a progressive hash grid and geometry MLP give the SDF and a feature; separate MLPs give albedo, metallic, roughness, diffuse and specular colour and indirect colour; values are volume rendered, then a secondary ray gives the occlusion probability that blends direct and indirect light
1

Stage 1: geometry first阶段一:先学几何

A neural SDF (NeuS on a progressive hash grid) with a reflection-aware radiance field: diffuse, specular and blend MLPs.神经 SDF(渐进式哈希网格上的 NeuS),配一个感知反射的辐射场:漫反射、高光和混合三个 MLP。

2

Stage 2: information sharing阶段二:信息共享

The same MLP heads also predict albedo and metallic; split-sum PBR with a cube-mipmap environment; trained jointly with the radiance field.同一组 MLP 头同时预测反照率和金属度;用 split-sum PBR 和立方体 mipmap 环境光,与辐射场联合训练。

3

Indirect light间接光

Training: an MLP predicts the indirect specular light. Relighting: a second split-sum traces one bounce.训练时:一个 MLP 预测高光的间接光。重打光时:用第二次 split-sum 追踪一次反弹。

4

A dataset to measure it一个能评测它的数据集

Five glossy scenes with ground-truth albedo, roughness and relighting under nine environment maps.五个高光场景,提供反照率、粗糙度的真值,以及九张环境贴图下的重打光真值。

Geometry: volume rendering a signed distance field几何:对符号距离场做体渲染

NeuS turns the SDF along a camera ray into opacities, so a surface can be learned from images alone. Sharpen the density and the weights collapse onto the first surface.NeuS 把相机光线上的 SDF 转成不透明度,于是只用图像就能学出表面。把密度调尖,权重会集中到第一个表面上。

first surface第一个表面 t = 0.400expected depth期望深度 \(\sum w_i\) weight on 2nd object第二个物体的权重
volume rendering体渲染
\[\mathbf C=\sum_{i=1}^{N} w_i\,\mathbf c_i,\qquad w_i=\alpha_i\prod_{j<i}(1-\alpha_j)\]
NeuS opacity from the SDF由 SDF 得到 NeuS 不透明度
\[\alpha_i=\max\!\Big(\frac{\Phi_\sigma(s(\mathbf x_i))-\Phi_\sigma(s(\mathbf x_{i+1}))}{\Phi_\sigma(s(\mathbf x_i))},\,0\Big)\]
surface and normal表面与法线
\[\mathcal S=\{\mathbf x\mid s(\mathbf x)=0\},\qquad \mathbf n=\frac{\nabla s}{\lVert\nabla s\rVert}\]

\(1/\sigma\) is learned and shrinks during training. RISE-SDF predicts \(s\) and a feature \(\boldsymbol\beta\) from a progressive hash grid, with Eikonal and curvature losses.\(1/\sigma\) 是可学习的,训练中会变小。RISE-SDF 用渐进式哈希网格预测 \(s\) 和特征 \(\boldsymbol\beta\),并加 Eikonal 和曲率损失。

Appearance: Monte Carlo is noisy, split-sum is not外观:Monte Carlo 有噪声,split-sum 没有

Shading needs an integral over the hemisphere. Split-sum replaces it with two lookups. Drag the sphere to turn the light.着色需要在半球上积分。split-sum 把它换成两次查表。拖动小球可以旋转光照。

rendering equation, simplified Disney BRDF渲染方程,简化 Disney BRDF
\[\mathbf c=\int_{H^2} f_r\,L(\boldsymbol\omega)\,(\mathbf n\cdot\boldsymbol\omega)\,d\boldsymbol\omega,\quad f_r=(1-m)\frac{\mathbf a}{\pi}+\frac{D(\rho)\,F(m,\mathbf a)\,G}{4\,|\mathbf d\cdot\mathbf n|\,|\boldsymbol\omega\cdot\mathbf n|}\]
split-sum
\[\mathbf c\approx\underbrace{\int f_r\,(\mathbf n\cdot\boldsymbol\omega)\,d\boldsymbol\omega}_{\text{BRDF integral: 2D LUT}}\cdot\underbrace{\int L(\boldsymbol\omega)\,p(\boldsymbol\omega;\hat{\mathbf d},\rho)\,d\boldsymbol\omega}_{\text{light integral: mipmap}(\hat{\mathbf d},\rho)}\]
\[\mathbf c_s=(F_0F_1+F_2)\,\mathbf l^s(\hat{\mathbf d},\rho),\quad \mathbf c_d=(1-m)\,\mathbf a\,\mathbf l^d(\mathbf n),\quad F_0=0.04(1-m)+m\,\mathbf a\]

Demo: GGX lobes; the 2D LUT is replaced by Lazarov's analytic fit. Not the paper's code.演示:GGX 波瓣;二维查找表用 Lazarov 的解析拟合代替。并非论文代码。

Two stages, shared heads两个阶段,共享的网络头

Radiance field · stage 1辐射场 · 阶段一
MLP headsMLP 头
Physically based · stage 2基于物理 · 阶段二
\(\mathbf c_d\)diffuse colour漫反射颜色
\(f_{\text{diff}}(e(\mathbf x),\boldsymbol\beta)\)
\(\mathbf a\)albedo反照率
\(b\)blend weight混合权重
\(f_{\text{blend}}(e(\mathbf x),\boldsymbol\beta)\)
\(m\)metallic金属度
\(\mathbf c_s\)specular colour高光颜色
\(f_{\text{spec}}(e(\hat{\mathbf d}))\)
from BRDF × light由 BRDF × 光照得到
–
\(f_{\text{rough}}(e(\mathbf x),\boldsymbol\beta)\)
\(\rho\)roughness粗糙度
–
cube mipmap, 6×512²立方体 mipmap,6×512²
\(\mathbf l^d,\mathbf l^s\)light integrals光照积分
\[\mathbf C=\sum_i w_i\big[(1-\class{eq-b}{b_i})\,\class{eq-cd}{\mathbf c_{d,i}}+\class{eq-b}{b_i}\,\mathbf c_{s,i}\big]\]
\[\mathbf C^{pbr}=\sum_i w_i\big[(1-\class{eq-b}{m_i})\,\class{eq-cd}{\mathbf a_i}\,\mathbf l^d_i+(F_0F_1+F_2)\,\mathbf l^s_i\big]\]
b ↔ m

Both mix diffuse and specular. One MLP outputs the blend weight and the metallic value.两者都在混合漫反射和高光。同一个 MLP 同时输出混合权重和金属度。

cd ↔ a

Both are view-independent and low-entropy. One MLP outputs the diffuse colour and the albedo.两者都与视角无关、信息量低。同一个 MLP 同时输出漫反射颜色和反照率。

\(\mathcal L_{\text{stage 2}}\)
\[\lambda_c\mathcal L_c+\lambda_c\mathcal L_{pbr}+\lambda_{eik}\mathcal L_{eik}+\lambda_{curv}\mathcal L_{curv}\]

Geometry keeps training. The radiance-field loss stays on in stage 2, unlike NeRO, InvRender and NRTF, which freeze geometry before material estimation.几何继续训练。阶段二仍保留辐射场损失;NeRO、InvRender、NRTF 则在估计材质前就冻结了几何。

Sharing gives better material and geometry共享让材质和几何都更好

Toaster, with and without information sharing. Without it, the model is shown at 5k iterations (the full model's material-optimization time) and at 15k (its geometry time).烤面包机,有无信息共享的对比。无共享的模型分别在 5k 次迭代(完整模型优化材质的时长)和 15k 次迭代(完整模型优化几何的时长)时展示。

GTOurs, 15k完整模型,15kno sharing, 5k无共享,5kno sharing, 15k无共享,15k albedo反照率
GT albedo
Our albedo
Albedo without sharing, 5k iterations
Albedo without sharing, 15k iterations
roughness粗糙度
GT roughness
Our roughness
Roughness without sharing, 5k
Roughness without sharing, 15k
normal法线
GT normal
Our normal
Normal without sharing, 5k
Normal without sharing, 15k

Average over the five synthetic scenes (paper Table 1): without sharing → full model.五个合成场景的平均(论文表 1):无共享 → 完整模型。

Training time: 2 h without sharing, 2.5 h for the full model.训练时间:无共享 2 小时,完整模型 2.5 小时。

Indirect light: an MLP to train, a second split-sum to relight间接光:训练用 MLP,重打光用第二次 split-sum

A glossy surface also reflects the object itself. Drag the hit point along the floor.高光表面还会映出物体自身。沿地面拖动交点。

occlusion遮挡概率 \(O\)0.00
\(\mathbb 1[\rho\le\rho_t]\)1

Cheap: the secondary ray queries only the geometry MLP, plus one indirect-colour query at \(\hat{\mathbf x}\): \(M+1\) queries, against \(2N\) for NeRO and \(4M\) for TensoIR/ENVIDR-style marching (with one density and three colour MLPs).开销小:次级光线只查询几何 MLP,再在 \(\hat{\mathbf x}\) 处查询一次间接颜色:共 \(M+1\) 次;NeRO 要 \(2N\) 次,TensoIR/ENVIDR 式的二次行进要 \(4M\) 次(一个密度 MLP 加三个颜色 MLP 时)。

Both indirect terms matter when relighting重打光时两个间接光项都不可少

Toaster relit with the fireplace environment map. Bottom row: the boxed region, enlarged.用壁炉环境贴图重打光的烤面包机。下排是框中区域的放大。

GTOurs完整模型no indirect MLP无间接光 MLPno 2nd split-sum无第二次 split-sum
GT relighting
Our relighting
Relighting without the indirect MLP
Relighting without the second split-sum
GT, enlarged
Ours, enlarged
Without indirect MLP, enlarged
Without second split-sum, enlarged

relighting PSNR of the full model, averaged over the five scenes.完整模型的重打光 PSNR,五个场景平均。

No indirect MLP: reflections of the object on itself look less realistic.去掉间接光 MLP:物体映在自身上的反射不够真实。

No second split-sum: the indirect MLP, trained under the training light, gives unnatural contrast under a new one.去掉第二次 split-sum:间接光 MLP 是在训练光照下学的,换了光照就出现不自然的对比。

A glossy dataset with material ground truth一个带材质真值的高光数据集

Five Shiny Blender objects (teapot, coffee, muscle car, toaster, helmet), re-shaded so that data and model use the same BRDF.取 Shiny Blender 的五个物体(茶壶、咖啡、肌肉车、烤面包机、头盔),重新设置着色器,使数据与模型使用同一种 BRDF。

Dataset数据集Material材质Relighting重打光# env maps环境贴图数Shiny高光
NeRF Synthetic✗✗0✗
Shiny Blender✗✗0✓
NeRO Synthetic✗✓3✓
NeRFactor Synthetic✓✓8✗
TensoIR Synthetic✓✓8✗
Ours本文✓✓9✓
  • Aligned BRDF: every shader becomes a Principled BRDF, default except base colour, metallic and roughness.BRDF 对齐:所有着色器都换成 Principled BRDF,除基础色、金属度和粗糙度外都用默认值。
  • Ten lights: one for training, nine for relighting.十种光照:一种用于训练,九种用于重打光。
  • Exact material maps: re-rendered with a Diffuse BSDF that carries the albedo or roughness value.精确的材质图:用携带反照率或粗糙度数值的 Diffuse BSDF 重新渲染得到。
toaster烤面包机helmet头盔muscle car肌肉车
Toaster, relit ground truth
Helmet, relit ground truth
Muscle car, relit ground truth
Toaster ground-truth albedo and roughness
Helmet ground-truth albedo and roughness
Muscle car ground-truth albedo and roughness

Top: a relighting ground truth. Bottom: ground-truth albedo (left half) and roughness (right half).上:重打光真值。下:反照率真值(左半)和粗糙度真值(右半)。

Results on the shiny dataset高光数据集上的结果

Side by side并排对比

GT
RISE-SDF

In motion动态效果

Ablations: every part pays off消融:每个部分都有用

Averages over the five synthetic scenes (paper Table 1). The second split-sum only acts at relighting, so that variant has relighting numbers only.五个合成场景的平均(论文表 1)。第二次 split-sum 只在重打光时起作用,所以该变体只有重打光的数字。

Monte Carlo instead of split-sum用 Monte Carlo 代替 split-sum

Real captures: NeRO's Glossy-Real set真实拍摄:NeRO 的 Glossy-Real 数据集

novel view新视角
extracted mesh提取的网格

Trained 4 h with ground-truth object masks; meshes from marching cubes at 512³.训练 4 小时,使用物体真值掩码;网格由 512³ 的 marching cubes 提取。

Geometry: second best. Chamfer distance averages 0.0032 against NeRO's 0.0019; NDR, NDRMC and ours use ground-truth masks.几何:第二好。平均 Chamfer 距离 0.0032,NeRO 为 0.0019;NDR、NDRMC 和本文用了真值掩码。

Material falls short here: the distant-light assumption breaks. The masked-out plate causes near-field indirect light, and the photographer's reflection is not modelled.材质在这里不够好:远处光源的假设不成立。被掩掉的底盘带来近场间接光,拍摄者自己的反射也没有建模。

Limitations局限

01

Isotropic BRDF各向同性 BRDF

No transparent or anisotropic materials.处理不了透明或各向异性的材质。

02

No shadows on diffuse surfaces漫反射表面没有阴影

Weaker under point lights, and shadows can be mistaken for geometry (right). A shadow cache after stage 1, as in GS-IR, is a possible fix.点光源下效果较差,阴影还可能被误当成几何(右图)。可行的改进是像 GS-IR 那样在阶段一之后缓存阴影。

03

Ambiguity remains歧义仍然存在

Light, material and geometry trade off; the material can still be far off in some cases.光照、材质和几何之间可以互相抵消;某些情况下材质仍会偏离很多。

04

Not interactive还不能实时

05

Diffuse scenes: comparable, not best漫反射场景:相当,但不是最好

TensoIR synthetic set (lego, hotdog, armadillo, ficus), averages from the paper's supplementary.TensoIR 合成数据集(lego、hotdog、armadillo、ficus),数字为论文补充材料中的平均值。

Failure case: a shadow is explained as geometry, giving artifacts in normal, albedo, roughness and relighting

Paper's failure example: the shadow is explained by geometry, which leaves artifacts.论文中的失败例子:阴影被解释成几何,留下伪影。

Take-away要点

RISE-SDF reconstructs glossy objects into geometry, material and lighting that can be relit end to end, with no Blender export and no per-light training.RISE-SDF 把高光物体重建成可端到端重打光的几何、材质和光照,不需要导出到 Blender,也不需要为每种光照单独训练。

1

Share what the two branches have in common. Blend weight ↔ metallic and diffuse colour ↔ albedo come from the same MLPs, which stabilizes material and geometry.让两个分支共享共同的东西。混合权重 ↔ 金属度、漫反射颜色 ↔ 反照率由同一组 MLP 输出,材质和几何都因此更稳定。

2

Split-sum everywhere, including one secondary bounce for relighting: noise-free and faster than Monte Carlo.处处用 split-sum,重打光时的一次二次反弹也是:没有噪声,比 Monte Carlo 更快。

3

Measure material, not just pictures. A glossy dataset with ground-truth albedo, roughness and relighting.评测材质,而不只是评测图像。一个带反照率、粗糙度和重打光真值的高光数据集。

Open problems named in the paper论文中提到的开放问题

  • Shadows on diffuse surfaces (a shadow cache after stage 1)漫反射表面的阴影(在阶段一之后缓存阴影)
  • Near-field light from the surroundings of real captures真实拍摄中周围环境带来的近场光照
  • The photographer's reflection on the object拍摄者自己在物体上的反射
  • Anisotropic and transparent materials各向异性和透明材质

Contact联系方式

Deheng Zhang

Thanks!谢谢!

deheng.zhang@insait.ai

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