Semantic scene completion is a combined task of semantic segmentation and shape completion and discovers the hidden information that is present in a 3D scene. For instance, a depth sensor can only capture information from object surfaces that are visible. Most of the geometric and semantic information of the 3D scene is, however, occluded by the objects themselves. As humans, we can estimate the geometry of objects even in the occluded area from experience, providing us instantly an effective model of the 3D scene surrounding us. 3D semantic scene completion tries to achieve the same goal. Given a single depth image, the goal is to predict the entire 3D geometry of all objects in the scene including the occluded areas. The technique has high potential in many areas ranging from domestic robotics and autonomous vehicles to health-care systems. Without the ability to predict full 3D geometry behind the visible surfaces, robots have to exhaustively explore the occluded space, which is not efficient.
3D semantic scene completion has become a popular research problem recently. Some prior works considered completing and labeling 3D scenes as a combined task, but they used separate modules for feature extraction and context modeling[2, 3, 4]. Song et al. 
pioneered in applying deep learning to semantic scene completion. They proposed a 3D convolutional network that leverages dilated convolutions as well as skip connections . Also, this work has been extended by adding a second input stream which contains the 2D semantic labels from RGB images [8, 9]. In , the authors proposed a coarse-to-fine 3D fully convolutional network for processing 3D scenes with arbitrary spatial extents and capturing both local details and the global structure of the scenes.
At the same time, generative adversarial networks have also received a lot of attention. An adversarial approach to learn a deep generative model was first proposed by Goodfellow et al.  and has then been further extended by using conditioning variables in generative adversarial networks . Luc et al.  applied GANs to 2D semantic segmentation by adding an adversarial network after a segmentation network to discriminate segmentation maps coming from either the ground truth or the segmentation network. Some prior works applied GANs to the 3D space, but they focus on either single object reconstruction [14, 15] or dealing with a scene as a composition of objects .
Wang et al. 
recently proposed a first approach to use generative adversarial networks for 3D semantic scene completion. They use two encoder networks producing a compressed latent state vector of the input depth image and the ground truth volume. Moreover, they propose to use multiple discriminator networks attached to both the output of the encoder networks and the output of a subsequent decoder network. The approach, however, has the disadvantage that the encoder of the depth image differs from the encoder for the voxelized ground truth. As a result, the encoders discard too much information to match the different representations yielding a substantial loss in information.
In this paper, we therefore present an approach that can be combined with any 3D convolutional network that does not suffer from the loss of information. In particular, we propose a conditional generative adversarial network (GAN) to predict semantic labels and occupancy in 3D space simultaneously. We thoroughly evaluate the proposed approach and compare it with a standard generative adversarial network as well as in combination with a local adversarial loss. We observe that the conditional generative adversarial network performs best, but also that generative adversarial networks struggle if the ground truth is not well aligned with the depth data as in NYU Kinect.
2 Semantic Scene Completion with GANs
Inspired by the successful application of GANs in other domains, we introduce a novel model to perform semantic scene completion using GANs.
2.1 Network Architecture
Our model takes a 3D Truncated Signed Distance Function (TSDF) extracted from a depth image as input and predicts the fully voxelized 3D scene by a generator network. In this work, we use the network architecture SSCNet classes of size , where , , and are the height, width, and depth of the 3D volume, respectively. The aim of the discriminator network is to distinguish a generated 3D volume from a ground truth volume. To this end, we transform a ground truth sample of the training data to a volume of the same size (
) using one-hot encoding. Although the discriminator network might easily distinguish the ground truth and the generated volume by detecting whether the volume consists of zeros and ones (one-hot encoding) or values between zero and one, Luc et al. have shown that this encoding mechanism does not strongly affect the performance of the discriminator network.
Following the design of Wu et al. 
, the discriminator network consists of several convolutional blocks. Each block comprises a convolution layer with a 3D kernel, a normalization layer, and a leaky ReLU activation layer. The output of the last convolutional layer with the size of
is reshaped to a vector of 1200 dimensions. After that, it is processed by three fully-connected layers with output sizes of 256, 128 and 1, respectively. Hence, the final logit is a binary indicator to determine whether the predicted volumetric data is generated or sampled from the ground truth data. An overview of our proposed architecture is shown in Figure1.
2.2 Loss Function
We propose to use a hybrid loss function that is a weighted sum of two terms. The first term is a multi-class cross-entropy loss that is used for the generator to predict the right class label at each voxel location independently. We useto denote the class probability map over the classes for the volume , which is produced by the generator network.
The second loss term is based on the output of the discriminator network. This loss term is large if the discriminator can differentiate between the predictions of the generator network and the ground truth label maps. We use to represent the probability with which the discriminator network predicts that is the ground truth label map of , as opposed to being a label map produced by the generator network . Given a dataset of training images and a corresponding 3D ground truth volume , we define the loss as:
where and denote the parameters of the generator and discriminator network, respectively. The multi-class cross-entropy loss for prediction is given by:
which equals the negative log-likelihood of the target ground truth volume in a one-hot encoding representation. Similarly, the binary cross-entropy loss is denoted as:
We then minimize the loss according to the parameters of the generator network, while maximizing it with respect to the parameters of the discriminator network.
2.3 Conditional GANs
Conditional GANs have been recently proposed in the literature. Since these works deal with different tasks ( 2D image generation), it is helpful to examine their potential for 3D semantic scene completion.
Using a conditional GAN, the output of the discriminator is conditioned on the input which we denote as . This leads to the following new objective function:
In practice, we achieve the conditioning by concatenating the input depth image with the two kinds of inputs which are fed into the discriminator network respectively.
2.4 Local Adversarial Loss
A key observation for the discriminator network is that it should learn to model the input sample features equally within the whole input space. When we train a single strong discriminator network, the generator network tends to overemphasize certain parts of the features to fool the current discriminator network. In other words, any local cube sampled from the input samples should have similar statistics as a real ground truth cube. Therefore, the idea of a local adversarial loss was proposed to overcome this problem for 2D images . Here, however, we extend this trick to the 3D domain. Rather than defining a global discriminator network, we can define a discriminator network that classifies each voxel separately. This division strategy not only enhances the capacity of the discriminator network, but also provides more samples per input volume for learning.
In practice, we design the discriminator network to be a fully convolutional network that outputs the same dimension as the input. Instead of using fully connected layers to reduce the output into a single probability value, we upsample the output to match the ground truth dimensions. Since the discriminator has shrunk the input volume within the middle three layers by the factor of 12, we again upsample the volume by the factor of 12 using trilinear upsampling. We then calculate the loss term with binary cross-entropy.
We implement our network architecture in PyTorch and use a batch size of 4. For our generator network, we use a SGD optimizer with weight decay of 0.0005 and learning rate of 0.01. For the discriminator network, we use an Adam optimizer with a learning rate of 0.0001. Besides, label smoothing is applied for improving the training process in all the experiments . We perform some experiments to determine the optimal value for the loss weight paramter in (1) and (4). It turns out that performs best.
We separate our evaluation results mainly in two parts: Semantic scene completion (SSC) and scene completion (SC). While scene completion only considers whether a voxel is occupied or empty, semantic scene completion also evaluates whether an occupied voxel is given the correct semantic label. As in 
we measure the precision, recall, and Jaccard index (IoU) for scene completion and the average (avg.) of the IoU across all categories for semantic scene completion.
3.1 Evaluation on NYU Depth v2
We first evaluate our models on the NYU Depth v2 dataset , an indoor scene dataset which contains 1449 depth scenes captured by a Kinect device (795 for training, 654 for testing). The annotations consist of 33 CAD models belonging to 7 different categories which have been fit into the scene by human annotators and finally voxelized. Since the CAD models do not perfectly align with the real objects, we also use depth maps generated from the projections of the 3D annotations for training as described in . For testing, we consider two test sets: NYU Kinect consisting of depth images captured by the Kinect sensor and NYU CAD consisting of rendered depth images generated by projecting the annotated CAD models. Tables 1 and 2 show the results for four different design choices. Firstly, we examine using the standard GANs vs. using conditional GANs which we denote as 'GAN' and 'cGAN'. Secondly, the usage of the global adversarial loss vs. the local adversarial loss is examined, denoted as 'GL' and 'LL', respectively.
Table 1 shows the results on the NYU Kinect test set. In case of the global adversarial loss, the accuracy for semantic scene completion increases from 20.6% to 22.7% when switching from the GAN to the conditional GAN. Applying the local adversarial loss decreases the accuracy by -1.2% for the cGAN and by -0.7% for the GAN. For scene completion, the IoU decreases between -0.4% and -1% if the conditional GAN is used instead of the GAN. Applying the local adversarial loss decreases the performance between -0.1% and -0.7%. Overall our model performs worse than the baseline  for semantic scene completion, which achieves 24.7% on NYU Kinect, whereas our best model only achieves 22.7%. This suggests that our model is less robust to noise in the test data of NYU Kinect than . Due to the inaccurate annotations of the data in NYU Kinect, we conclude that NYU Kinect is not suited to examine the potential of adversarial learning. We therefore focus on the results on the NYU CAD test set.
Table 2 shows the results on the NYU CAD test set. The accuracy for semantic scene completion improves by around +2% (from 39.8% to 42.0%) by the usage of the conditional GAN and further increases slightly to 42.3% by applying the local adversarial loss. The approach outperforms the baseline  not only for semantic scene completion, but also for scene completion. In this case, the best accuracy is also achieved by the conditional GAN with local adversarial loss (74.9%).
In summary, the conditional GAN outperforms the standard GAN setup for both NYU test settings. Local and global adversarial loss, however, perform differently on different test settings. While the local adversarial loss slightly improves the accuracy on NYU CAD, it decreases the accuracy on NYU Kinect. Since the local adversarial loss tends to put more emphasis on the finer local detail of each voxel, it is more sensitive to the inaccurate annotations of NYU Kinect.
We also observe that  achieves a very high recall but a low precision for scene completion. In other words, this method tends to predict more occupied voxels than our approaches, which results in cluttered scene completions. Nevertheless, on NYU CAD, our models outperform the baseline  by a large margin for both scene completion and semantic scene completion. As shown in Table 2, our model SSC-cGAN-LL achieves 42.3% accuracy for semantic scene completion and outperforms the approach  by +4.7%. For scene completion, our model outperforms  by +4.6% IoU.
Apart from the quantitative results, we provide also some qualitative results in Figure 2 to visualize the effect of applying different GAN models. On the one hand, we can observe that the model using the global GAN loss (SSC-cGAN-GL) suffers from partial mode collapse, meaning it constantly generates labeled voxels in parts of the scene, in particular for ceilings and walls. Using a conditional GAN together with the local adversarial loss seems to significantly reduce this problem. On the other hand, the predicted scenes from SSC-cGAN-GL are visually more plausible since they display more fine structure of the objects, tend to contain more empty voxels and therefore look less cluttered. Thus, we propose SSC-cGAN-GL as the most effective model, due to the fact that it performs comparably to the model with the highest accuracy (SSC-cGAN-LL), while being able to generate more realistic results.
Finally, we compare our approach to the state-of-the-art. On NYU Kinect, the proposed approaches perform worse than the baseline  for semantic scene completion, but better for scene completion. The only approach that fairly outperforms the baseline is . All the other approaches use either an additional modality (RGB images) , pretrain on SUNCG , or do both . On NYU CAD, we outperform  even if they pretrain on SUNCG and perform competitively with .
|Zhang et al. ||71.9||71.9||56.2||26.7|
|Garbade et al. ||65.6||87.2||60.0||34.1|
|Liu et al.* ||67.3||85.8||60.6||34.4|
|Garbade et al. ||81.6||92.4||76.1||46.2|
3.2 Evaluation on SUNCG
The SUNCG dataset 
is a synthetic dataset, which provides a large amount of training data with rendered depth images and volumetric ground truth. It contains 45,622 different scenes with realistic room and furniture layouts. However, due to the high computational cost (around 15 days for 10 epochs) of the training procedure, we only run our SSC-cGAN-GL model on SUNCG. The result is shown in Table3. Our model SSC-cGAN-GL outperforms the baseline 
by a large margin of +10% for semantic scene completion. For scene completion the IoU increases from 72.9% to 78.1% with both higher precision and recall. As a result, we conclude that the GAN structure benefits from the large amount of training samples provided by SUNCG.
Compared to other recent approaches, our approach achieves a lower accuracy. However, since our approach is orthogonal to the approaches of [23, 9], we expect that they could be combined and potentially benefit each other.  also used an adversarial learning approach in combination with an encoder-decoder network. However, they do not follow the original evaluation protocol. Instead of reporting numbers on the SUNCG test set, they perform a 10-fold cross validation using random splits. For comparison to the state-of-the-art, we follow the standard evaluation protocol .
|Wang et al.  *||-||-||-||51.4|
|Zhang et al. ||92.6||90.4||84.5||70.5|
|Liu et al. ||80.7||96.5||78.5||64.3|
3.3 Loss Behaviour of the Discriminator
We design an experiment that allows us to assess whether the discriminators show the expected behaviour of producing high losses for unrealistic scene inputs. Therefore, we gradually add noise to the ground truth samples of the NYU CAD test data and feed it as input to the trained discriminator networks. We simulate the noise by randomly changing voxel labels in the occluded space. While increasing the percentage of noise, we calculate the binary cross-entropy loss value using (3). As one can see from Figure 3, the loss curve for SSC-GAN remains stable whereas it increases for SSC-cGAN. This suggests that the conditional GAN model behaves in the expected way while the standard GAN is insensitive to the noise.
We presented a novel GAN architecture to perform 3D semantic scene completion and evaluated two variations, namely conditional GANs and a local adversarial loss. The results show that the conditional GAN improves the network performance on both test sets, while the local adversarial loss only improves the performance on NYU CAD but not on NYU Kinect. In comparison to the baseline , our models yield a significant improvement on NYU CAD. On SUNCG our models outperform the baseline by a large margin. If we compare the results qualitatively, the proposed model SSC-cGAN-GL produces significantly more realistic appearing scenes than the baseline or the local adversarial loss.
-  Massimiliano Scopelliti, Maria Vittoria Giuliani, and Ferdinando Fornara, “Robots in a domestic setting: a psychological approach,” Universal access in the information society, vol. 4, no. 2, pp. 146–155, 2005.
Bo Zheng, Yibiao Zhao, Joey C Yu, Katsushi Ikeuchi, and Song-Chun Zhu,
“Beyond point clouds: Scene understanding by reasoning geometry and physics,”in CVPR, 2013, pp. 3127–3134.
-  Byung-soo Kim, Pushmeet Kohli, and Silvio Savarese, “3D scene understanding by voxel-CRF,” in ICCV, 2013, pp. 1425–1432.
-  Maros Blaha, Christoph Vogel, Audrey Richard, Jan D Wegner, Thomas Pock, and Konrad Schindler, “Large-scale semantic 3d reconstruction: an adaptive multi-resolution model for multi-class volumetric labeling,” in CVPR, 2016, pp. 3176–3184.
-  Shuran Song, Fisher Yu, Andy Zeng, Angel X Chang, Manolis Savva, and Thomas Funkhouser, “Semantic scene completion from a single depth image,” in CVPR, 2017, pp. 190–198.
-  Liang-Chieh Chen, George Papandreou, Iasonas Kokkinos, Kevin Murphy, and Alan L Yuille, “Deeplab: Semantic image segmentation with deep convolutional nets, atrous convolution, and fully connected CRFs,” TPAMI, vol. 40, no. 4, pp. 834–848, 2018.
-  Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun, “Deep residual learning for image recognition,” in CVPR, 2016, pp. 770–778.
-  Martin Garbade, Yueh-Tung Chen, Johann Sawatzky, and Juergen Gall, “Two Stream 3D Semantic Scene Completion,” in CVPR Workshops, 2019.
-  Shice Liu, YU HU, Yiming Zeng, Qiankun Tang, Beibei Jin, Yainhe Han, and Xiaowei Li, “See and Think: Disentangling Semantic Scene Completion,” in NIPS, 2018, pp. 261–272.
-  Angela Dai, Daniel Ritchie, Martin Bokeloh, Scott Reed, Jürgen Sturm, and Matthias Nießner, “ScanComplete: Large-Scale Scene Completion and Semantic Segmentation for 3D Scans,” in CVPR, 2018, pp. 4578–4587.
-  Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio, “Generative adversarial nets,” in NIPS, 2014, pp. 2672–2680.
Alexey Dosovitskiy, Jost Tobias Springenberg, and Thomas Brox,
“Learning to generate chairs with convolutional neural networks,”in CVPR, 2015, pp. 1538–1546.
-  Pauline Luc, Camille Couprie, Soumith Chintala, and Jakob Verbeek, “Semantic segmentation using adversarial networks,” in NIPS Workshops, 2016.
-  Jiajun Wu, Chengkai Zhang, Tianfan Xue, Bill Freeman, and Josh Tenenbaum, “Learning a probabilistic latent space of object shapes via 3d generative-adversarial modeling,” in NIPS, 2016, pp. 82–90.
-  Bo Yang, Stefano Rosa, Andrew Markham, Niki Trigoni, and Hongkai Wen, “Dense 3D object reconstruction from a single depth view,” in TPAMI, 2018.
-  Bo Yang, Zihang Lai, Xiaoxuan Lu, Shuyu Lin, Hongkai Wen, Andrew Markham, and Niki Trigoni, “Learning 3D scene semantics and structure from a single depth image,” in CVPR, 2018, pp. 309–312.
-  Yida Wang, David Joseph Tan, Nassir Navab, and Federico Tombari, “Adversarial semantic scene completion from a single depth image,” in 3DV, 2018, pp. 426–434.
-  Ashish Shrivastava, Tomas Pfister, Oncel Tuzel, Joshua Susskind, Wenda Wang, and Russell Webb, “Learning from simulated and unsupervised images through adversarial training,” in CVPR, 2017, pp. 2242–2251.
-  Adam Paszke, Sam Gross, Soumith Chintala, Gregory Chanan, Edward Yang, Zachary DeVito, Zeming Lin, Alban Desmaison, Luca Antiga, and Adam Lerer, “Automatic differentiation in PyTorch,” in NIPS Workshops, 2017.
-  Tim Salimans, Ian Goodfellow, Wojciech Zaremba, Vicki Cheung, Alec Radford, and Xi Chen, “Improved techniques for training GANs,” in NIPS, 2016, pp. 2234–2242.
-  Nathan Silberman, Derek Hoiem, Pushmeet Kohli, and Rob Fergus, “Indoor segmentation and support inference from RGBD images,” in ECCV, 2012, pp. 746–760.
-  Michael Firman, Oisin Mac Aodha, Simon Julier, and Gabriel J Brostow, “Structured prediction of unobserved voxels from a single depth image,” in CVPR, 2016, pp. 5431–5440.
-  Jiahui Zhang, Hao Zhao, Anbang Yao, Yurong Chen, Li Zhang, and Hongen Liao, “Efficient semantic scene completion network with spatial group convolution,” in ECCV, 2018, pp. 733–749.