Neural Inverse Rendering of an Indoor Scene From a Single Image

Soumyadip Sengupta1,2,3,†, Jinwei Gu1,4,†, Kihwan Kim1, Guilin Liu1, David W. Jacobs2, and Jan Kautz1

1NVIDIA, 2University of Maryland, College Park, 3University of Washington, 4SenseTime

1. OverviewIn this supplementary material, we provide more details

of our network architecture and the loss functions alongwith additional qualitative evaluations. Specifically, in Sec-tion 2 we discuss the details of the IRN and RAR networkarchitectures for reproducibility. Details of our training lossfunctions on real data are provided in Section 3. In Sec-tion 5 we present additional qualitative evaluations.

2. Network ArchitecturesOur proposed Inverse Rendering Network (IRN), shown

again in Figure 1 for reference, is trained on real datausing the Residual Appearance Renderer (RAR), whichlearns to capture the complex appearance effects (e.g. inter-reflection, cast shadows, near-field illumination, and realis-tic shading). In the following, we describe the implementa-tion details of IRN and RAR.

2.1. IRN

In Figure 2 we present the network architecture of IRN.The input to IRN is an image of spatial resolution 240×320,and the output is an albedo and normal map of same spatialresolution along with a 18×36 resolution environment map.Here we provide the details of the each block in IRN.‘Enc’: C64(k7) - C*128(k3) - C*256(k3)‘CN(kS)’ denotes convolution layers with N S × S filterswith stride 1, followed by Batch Normalization and ReLU.‘C*N(kS)’ denotes convolution layers with N S × Sfilters with stride 2, followed by Batch Normalization andReLU. The output of ‘Enc’ layer produces a blob of spatialresolution 256 × 60 × 80.

‘Normal ResBLKs’: 9 ResBLKThis consists of 9 Residual Blocks, ‘ResBLK’s, which op-erate at a spatial resolution of 256 × 60 × 80. Each ‘Res-BLK’ consists of Conv256(k3) - BN -ReLU - Conv256(k3)- BN, where ‘ConvN(kS)’ and ‘BN’ denote convolution lay-ers with N S×S filters of stride 1 and Batch Normalization.‘Albedo ResBLKs’: Same as ‘Normal Residual Blocks’

(weights are not shared).

‘Dec.’: CD*128(k3)-CD*64(k3)-Co3(k7)‘CD*N(kS)’ denotes Transposed Convolution layers withN S × S filters with stride 2, followed by Batch Normal-ization and ReLU. ‘CN(kS)’ denotes convolution layerswith N S × S filters with stride 1, followed by BatchNormalization and ReLU. The last layer Co3k(7) consistsof only convolution layers of 3 7 × 7 filters, followed byTanh layer.

‘Light Est.’: It first concatenates the responses of ‘Enc’,‘Normal ResBLKs’ and ‘Albedo ResBLKs’ to produce ablob of spatial resolution 768 × 60 × 80. It is further pro-cessed by the following module:C256(k1) - C*256(k3) - C*128(k3) - C*3(k3) - BU(18,36)‘CN(kS)’ denotes convolution layers with N S × S filterswith stride 1, followed by Batch Normalization and ReLU.‘C*N(kS)’ denotes convolution layers with N S × S filterswith stride 2, followed by Batch Normalization and ReLU.BU(18,36) upsamples the response to produce 18 × 36 × 3resolution environment map.

2.2. RAR

As shown in Figure 1, Residual Appearance Renderer(RAR) consists of a U-Net architecture and a convolutionencoder. The U-Net consists of the following architecture,with normals and albedo as its input:‘Encoder’: C64(k3) - C*64(k3) - C*128(k3) - C*256(k3) -C*512(k3)‘Decoder’: CU512(k3) - CU256(k3) - CU128(k3) -CU64(k3) - Co3(k1)‘CN(kS)’ denotes convolution layers with N S × S filterswith stride 1, followed by Batch Normalization and ReLU.‘C*N(kS)’ denotes convolution layers with N S × S filterswith stride 2, followed by Batch Normalization and ReLU.‘CUN(kS)’ represents a bilinear up-sampling layer , fol-lowed by convolution layers with N S×S filters with stride1, followed by Batch Normalization and ReLU. ‘Co3(k1)’consists of 3 1× 1 convolution filters to produce Normal or

IRN

Direct Renderer

Inverse Rendering Network (IRN)

Self-Supervised LearningWeak Supervision

EncEnc

Dec

Residual Appearance Renderer (RAR)

RAR

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Figure 1: Our Proposed Architecture.

Dec

.

Enc.

Normal ResBLKs (9)

Albedo ResBLKs (9) Dec

.

Light est.

Figure 2: IRN.

Albedo. Skip-connections exists between ‘C*N(k3)’ lay-ers of encoder and ‘CUN(k3)’ layers of decoder. The en-coder ‘Enc’ that encodes image features to a latent D =300 dimensional subspace is given by: ‘Enc’: C64(k7) -C*128(k3) - C*256(k3) - C128(k1) - C64(k3) - C*32(k3) -C*16(k3) - MLP(300)‘CN(kS)’ denotes convolution layers with N S × S filterswith stride 1, followed by Batch Normalization and ReLU.‘C*N(kS)’ denotes convolution layers with N S × S filterswith stride 2, followed by Batch Normalization and ReLU.MLP(300) takes the response of the previous layer and out-puts a 300 dimensional feature, which is concatenated withthe last layer of the U-Net ‘Encoder’.

2.3. Environment Map Estimator

As discussed in Section 3.1 of the main paper, theground-truth environment map is estimated from the im-age, ground-truth albedo and normal using a deep networkhe(·,Θe). The detailed architecture of this network is pre-sented below:C64(k7) - C*128(k3) - C*256(k3) - 4 ResBLKS - C256(k1)- C*256(k3) - C*128(k3) - C*3(k3) - BU(18,36),where, ‘CN(kS)’ denotes convolution layers with N S × S

filters with stride 1, followed by Batch Normalization andReLU. ‘C*N(kS)’ denotes convolution layers with N S×Sfilters with stride 2, followed by Batch Normalization andReLU. BU(18,36) upsamples the response to produce 18 ×36 × 3 resolution environment map. Each ‘ResBLK’ con-tains Conv256(k3) - BN -ReLU - Conv256(k3) - BN, where‘ConvN(kS)’ denotes convolution layers with N S×S filtersof stride 1, ‘BN’ denoted Batch Normalization.

3. Training Details3.1. Training with weak supervision over albedo

IIW dataset presents relative reflectance judgments fromhumans. For any two points R1 and R2 on an image, aweighted confidence score classifiesR1 to be same, brighteror darker than R2. We use these labels to construct ahinge loss for sparse supervision based on WHRD met-ric presented in [2]. Specifically, if users predict R1 tobe darker than R2 with confidence wt, we use a losswt max(1 + δ − R2/R1, 0). If R1 and R2 are predictedto have similar reflectance, we use wt[max(R1/R2 − 1 −δ, 0) + max(R2/R1 − 1 − δ, 0)]. We observed empiricallythat this loss function performs better than WHRD metric,which is an L0 version of our loss. We train on real datawith the following losses: (i) Psuedo-supervision loss overalbedo (La), normal (Ln) and lighting (Le) based on [6], (ii)Photometric Reconstruction loss with RAR (Lu) (iii) Pair-wise weak supervision (Lw). Thus the net loss function isdefined as:

L = 0.5 ∗ La + 0.5 ∗ Ln + 0.1 ∗ Le + Lu + 30 ∗ Lw. (1)

3.2. Training with weak supervision over normals

We also train on NYUv2 dataset with weak supervisionover normals, obtained from Kinect depth data of the scene.We train with the following losses: (i) Psuedo-supervision

loss over albedo (La) and lighting (Le) based on [6], (ii)Photometric Reconstruction loss with RAR (Lu) (iii) Super-vision (Lw) over kinect normals. Thus the net loss functionis defined as:

L = 0.2 ∗ La + 0.05 ∗ Le + Lu + 20 ∗ Lw. (2)

4. Our CG-PBR DatasetWe present more example images of our CG-PBRS

dataset in Figure 3. We also compare the renderings of ourCG-PBR Dataset with that of PBRS [7], under the same il-lumination condition in Figure 4 and 5. CG-PBR providesmore photo-realistic and less noisy images with specularhighlights. Both CG-PBR and PBRS are rendered with Mit-suba [4].

5. More Experimental ResultsComparison with SIRFS. We present more detailedqualitative evaluations in this supplementary material. InFigure 6 we compare the results of our algorithm with thatof SIRFS [1]. SIRFS is an optimization-based method forinverse rendering, which estimates surface normals, albedoand spherical harmonics lighting from a single image. Com-pared to SIRFS we obtain more accurate normals and betterdisambiguation of reflectance from shading.

Comparison with Li et al. [5]. In Figure 7 and 8 we com-pare the albedo predicted by our method with that of Li etal. [5], which performs intrinsic image decomposition of animage, on the real IIW and the synthetic CG-PBR datasetrespectively. Intrinsic image decomposition methods do notexplicitly recover geometry, illumination or glossiness ofthe material, but rather combine them together as shading.In contrast, our goal is to perform a complete inverse ren-dering which has a wider range of applications in AR/VR.

Evaluation of lighting estimation. In Figure 9 wepresent a qualitative evaluation of lighting estimation byinserting a diffuse hemisphere into the scene and render-ing it with the inferred light from the image. We com-pare this with the method proposed by Gardner et al. [3],which also estimates an environment map from a single in-door image. he(·,Θe) is a deep network that predicts theenvironment map given the image, normals, and albedo.‘GT+he(·)’ estimates the environment map given the im-age, ground-truth normals and albedo, and thus serves asan achievable upper-bound in the quality of the estimatedlighting. ‘Ours’ estimates environment map from an imagewith IRN. ‘Ours+he(·)’ predicts environment map by com-bining the inferred albedo and normals from IRN to predictlighting with he(·). Both ‘Ours’ and ‘Ours+he(·)’ outper-form Gardner et al. [3] as they seem to produce more re-alistic environment maps. ‘Ours+he(·)’ improves lighting

estimation over ‘Ours’ by utilizing the predicted albedo andnormals to a greater degree.

Our Results and Ablation study. Figure 10 shows ex-amples of our results, with the albedo, normal and light-ing predicted by the network, as well as the reconstructedimage with the direct renderer and the proposed ResidualAppearance Renderer (RAR). In Figure 11 and 12, we per-form a detailed ablation study of different components ofour method. We show that it is important to train on realdata, as networks trained on synthetic data fail to generalizewell on real data. We also show that training our methodwithout RAR (‘w/o RAR’) produces piece-wise smooth,low contrast albedo due to over-reliance on the weak super-vision of pair-wise relative reflectance judgments. Trainingour network with only RAR, without any weak supervision(‘w/o weak’), often fails to produce consistent albedo acrosslarge objects like walls, floor, ceilings etc. Finally, trainingwithout RAR and weak supervision (‘w/o weak + RAR’)produces albedo which contains the complex appearanceeffects like cast shadows, inter-reflections, highlights etc.,as the reconstruction loss with direct renderer alone cannotmodel these effects.

References[1] Jonathan T Barron and Jitendra Malik. Shape, illumination,

and reflectance from shading. IEEE Transactions on PatternAnalysis and Machine Intelligence (TPAMI), 2015. 3, 6

[2] Sean Bell, Kavita Bala, and Noah Snavely. Intrinsic images inthe wild. ACM Transactions on Graphics (TOG), 33(4):159,2014. 2

[3] Marc-Andre Gardner, Kalyan Sunkavalli, Ersin Yumer, Xiao-hui Shen, Emiliano Gambaretto, Christian Gagne, and Jean-Francois Lalonde. Learning to predict indoor illuminationfrom a single image. ACM Transactions on Graphics (TOG),36(6):176, 2017. 3, 8

[4] Wenzel Jakob. Mitsuba renderer, 2010. http://www.mitsuba-renderer.org. 3

[5] Zhengqi Li and Noah Snavely. CGIntrinsics: Better intrin-sic image decomposition through physically-based rendering.European Conference on Computer Vision (ECCV), 2018. 3,7

[6] Soumyadip Sengupta, Angjoo Kanazawa, Carlos D. Castillo,and David W. Jacobs. Sfsnet: Learning shape, refectance andilluminance of faces in the wild. In IEEE Conference on Com-puter Vision and Pattern Recognition (CVPR), 2018. 2, 3

[7] Yinda Zhang, Shuran Song, Ersin Yumer, Manolis Savva,Joon-Young Lee, Hailin Jin, and Thomas Funkhouser.Physically-based rendering for indoor scene understandingusing convolutional neural networks. IEEE Conference onComputer Vision and Pattern Recognition (CVPR), 2017. 3, 5

Image (specular) Image (diffuse) Depth Surface Normal Albedo Phong Model Semantic Segmentation Glossiness Segmentation

Figure 3: Our CG-PBR Dataset concists of 235,893 images of a scene assuming specular and diffuse reflectance along with ground truthdepth, surface normals, albedo, Phong model parameters, semantic segmentation and glossiness segmentation.

PBRS

Ours

Figure 4: Comparison with PBRS [7]. Our dataset provides more photo-realistic and less noisy images with specular highlights undermultiple lighting conditions.

PBRS

Ours

Figure 5: Comparison with PBRS [7]. Our dataset provides more photo-realistic and less noisy images with specular highlights undermultiple lighting conditions.

Normal Albedo Shading

Our

sSI

RFS

Input Image

Input Image

Our

sSI

RFS

SIRF

S

Input Image

Our

sSI

RFS

Input Image

Our

sSI

RFS

Input Image

Our

s

Figure 6: Comparison with SIRFS [1]. Using deep CNNs our method performs better disambiguation of reflectance from shading andpredicts better surface normals.

Ours

Li[5]

Image

Figure 7: Comparison with CGI (Li et. al. [5]) on IIW dataset. In comparison with Li et al. [5], our method performs betterdisambiguation of reflectance from shading and preserves the texture in the albedo.

Ours

Li[5]

Image

GT

Figure 8: Comparison with CGI (Li et. al. [5]) on CG-PBR (synthetic) dataset. In comparison with Li et al. [5], our method performsbetter disambiguation of reflectance from shading and preserves the texture in the albedo.

Image GT+he Gardner [3] Ours+heOurs

Figure 9: Evaluation of lighting estimation. We compare with Gardner et al. [3]. ‘GT+he(·)’ predicts lighting conditioned on theground-truth normals and albedo. ‘Ours+he(·)’ predicts the environment map by conditioning it on the albedo and normals inferred byIRN.

Image Normal Albedo Recon. with RARLighting

Figure 10: Our Result. We show the estimated intrinsic components; normals, albedo, and lighting predicted by the network, along withthe reconstructed image with our direct renderer and the RAR.

Image Synthetic w/o weak + RAR w/o weak Oursw/o RAR

Figure 11: Ablation Study. We present the predicted albedo for each input image (in column 1) in column 2-6. We show the albedopredicted by IRN trained on our CG-PBR only in column 2. In column 6 (‘Ours’) we show the albedo predicted by IRN finetuned on realdata with RAR and weak supervision over albedo. In column 4 and 5 we show the albedo predicted by IRN finetuned on real data withoutweak supervision (‘w/o weak’) and RAR (‘w/o RAR’) respectively. We present the albedo predicted by IRN finetuned without RAR andweak supervision on real data in column 3 (‘w/o weak + RAR’). More images in Figure 12.

Image Synthetic w/o RAR + weak w/o weak Oursw/o RAR

Figure 12: Ablation Study. We present the predicted albedo for each input image (in column 1) in column 2-6. We show the albedopredicted by IRN trained on our CG-PBR only in column 2. In column 6 (‘Ours’) we show the albedo predicted by IRN finetuned on realdata with RAR and weak supervision over albedo. In column 4 and 5 we show the albedo predicted by IRN finetuned on real data withoutweak supervision (‘w/o weak’) and RAR (‘w/o RAR’) respectively. We present the albedo predicted by IRN finetuned without RAR andweak supervision on real data in column 3 (‘w/o weak + RAR’).