Recurrent Neural Network for (Un-)supervised Learning of Monocular Video Visual Odometry and Depth
Deep learning-based, single-view depth estimation methods have recently shown highly promising results. However, such methods ignore one of the most important features for determining depth in the human vision system, which is motion. We propose a learning-based, multi-view dense depth map and odometry estimation method that uses Recurrent Neural Networks (RNN) and trains utilizing multi-view image reprojection and forward-backward flow-consistency losses. Our model can be trained in a supervised or even unsupervised mode. It is designed for depth and visual odometry estimation from video where the input frames are temporally correlated. However, it also generalizes to single-view depth estimation. Our method produces superior results to the state-of-the-art approaches for single-view and multi-view learning-based depth estimation on the KITTI driving dataset.
The tasks of depth and odometry (also called ego-motion) estimation are longstanding tasks in computer vision providing valuable information for a wide variety of tasks, e.g. autonomous driving, AR/VR applications, and virtual tourism.
Recently, convolutional neural networks (CNN) [20, 4, 8, 42, 32] have begun to produce results of comparable quality to traditional geometric computer vision methods for depth estimation in measurable areas and achieve significantly more complete results for ambiguous areas through the learned priors. However, in contrast to traditional methods, most CNN methods treat depth estimation as a single view task and thus ignore the important temporal information in monocular or stereo videos. The underlying rationale of these single view depth estimation methods is the possibility of human depth perception from a single image. However, they neglect the fact that motion is actually more important for the human to infer distance . We are constantly exposed to moving scenes, and the speed of things moving in the image is related to the combination of their relative speed and effect inversely proportional to their depth.
In this work, we propose a framework that simultaneously estimates the visual odometry and depth maps from a video sequence taken by a monocular camera. To be more specific, we use convolutional Long Short-Term Memory (ConvLSTM)  units to carry temporal information from previous views into the current frame’s depth and visual odometry estimation. We have improved upon existing deep single- and two-view stereo depth estimation methods by interleaving ConvLSTM units with the convolutional layers to effectively utilize multiple previous frames in each estimated depth maps. Since we utilize multiple views, the image reprojection constraint between multiple views can be incorporated into the loss, which shows significant improvements for both supervised and unsupervised depth and camera pose estimation.
In addition to the image reprojection constraint, we further utilize a forward-backward flow-consistency constraint . Such a constraint provides additional supervision to image areas where the image reprojection is ambiguous. Moreover, it improves the robustness and generalizability of the model. Together these two constraints can even allow satisfactory models to be produced when groundtruth is unavailable at training time. Figure 1 shows an example of forward-backward image reprojection and optical flow as well as the resulting predicted depth maps.
We summarize our innovations as follows: 1) An RNN architecture for monocular depth and odometry estimation that uses multiple consecutive views. It does so by incorporating LSTM units, as used in natural language processing, into depth and visual odometry estimation networks. 2) These LSTM units importantly allow the innovation of using depth and camera motion estimation to benefit from the richer constraints of a multi-view process. In particular, they use multi-view image reprojection and forward-backward flow-consistency constraints to produce a more accurate and consistent model. 3) This design allows two novel capabilities: a) it can be trained in both supervised and unsupervised fashion; b) it can continuously run on arbitrary length sequences delivering a consistent scene scale.
We demonstrate on the KITTI  benchmark dataset that our method can produce superior results over the state-of-the-art for both supervised and unsupervised training. We will release source code upon acceptance.
2 Related work
Traditionally, the 3D reconstruction and localization are mostly solved by pure geometric reasoning. SfM and SLAM are the two most prevalent frameworks for sparse 3D reconstruction of rigid geometry from images. SfM is typically used for offline 3D reconstruction from unordered image collections, while visual SLAM aims for a real-time solution using a single camera [3, 26]. More recent works on SLAM systems include ORB-SLAM  and DSO . Schönberger and Frahm  review the state-of-the-art in SfM and propose an improved incremental SfM method.
Recently, CNNs are increasingly applied to 3D reconstruction, in particular, to the problem of 3D reconstruction of dense monocular depth, which is similar to the segmentation problem and thus the structure of the CNNs can be easily adapted to the task of depth estimation .
Supervised methods. Eigen et al.  and Liu et al.  proposed end-to-end networks for single-view depth estimation, which opened the gate for deep learning-based supervised single-view depth estimation. Following their work, Laina et al.  proposed a deeper residual network for the same task. Qi et al.  jointly predicted depth and surface normal maps from a single image. Fu et al.  further improved the network accuracy and convergence rate by learning it as an ordinal regression problem. Li et al.  used modern structure-from-motion and multi-view stereo (MVS) methods together with multi-view Internet photo collections to create the large-scale MegaDepth dataset providing improved depth estimation accuracy via bigger training dataset size. We improve upon these single-view methods by utilizing multiple views through an RNN architecture to generate more accurate depth and pose.
Two-view or multi-view stereo methods have traditionally been the most common techniques for dense depth estimation. For the interested reader, Scharstein and Szeliski  give a comprehensive review on two-view stereo methods. Recently, Ummenhofer et al.  formulated two-view stereo as a learning problem. They showed that by explicitly incorporating dense correspondences estimated from optical flow into the two-view depth estimation, they can force the network to utilize stereo information on top of the single view priors. There is currently a very limited body of CNN-based multi-view reconstruction methods. Choy et al.  use an RNN to reconstruct the object in the form of a 3D occupancy grid from multiple viewpoints. Yao et al.  proposed an end-to-end deep learning framework for depth estimation from multiple views. They use differentiable homography warping to build a 3D cost volume from one reference image and several source images. Kumar et al.  proposed an RNN architecture that can learn depth prediction from monocular videos. However, their simple training pipeline, e.g., no explicit temporal constraints, failed to explore the full capability of the network. Our method is trained with more sophisticated multi-view reprojection losses and can perform both single-view and multi-view depth estimation.
Unsupervised methods. Recently, by incorporating elements of view synthesis  and Spatial Transformer Networks , monocular depth estimation has been trained in an unsupervised fashion. This was done by transforming the depth estimation problem into an image reconstruction problem where the depth is the intermediate product that integrates into the image reconstruction loss. Godard et al., and Garg et al. use stereo pairs to train CNNs to estimate disparity maps from single views. Luo et al.  leverage both stereo and temporal constraints to generate improved depth at known scale. Zhou et al.  further relax the needs of stereo images to monocular video by combining a single view depth estimation network with a multi-view odometry estimation network. Following Zhou et al. ’s work, Mahjourian et al.  further enforced consistency of the estimated 3D point clouds and ego-motion across consecutive frames. In addition to depth and ego-motion, Yin et al.  also jointly learn optical flow in an end-to-end manner which imposed additional geometric constraints. However, due to scale ambiguity and the lack of temporal constraints, these methods cannot be directly applied for full trajectory estimation on monocular videos. By leveraging recurrent units, our method can run on arbitrary length sequences delivering a consistent scene scale.
In this section we introduce our method for multi-view depth and visual odometry estimation. We first describe our recurrent neural network architecture and then the multi-view reprojection and forward-backward flow-consistency constraints for the network training.
3.1 Network Architecture
Our architecture, shown in Figure 3, is made up of two networks, one for depth and one for visual odometry.
Our depth estimation network uses a U-shaped network architecture similar to DispNet . Our main innovation is to interleave recurrent units into the encoder which allows the network to leverage not only spatial but also temporal information in the depth estimation. The spatial-temporal features computed by the encoder are then fed into the decoder for accurate depth map reconstruction. The ablation study in Secion 4.5 confirms our choice for the placements of the ConvLSTM  units. Table 1 shows the detailed network architecture. The input to the depth estimation network is a single RGB frame and the hidden states from the previous time-step ( are initialized to be all zero for the first time-step). The hidden states are transmitted internally through the ConvLSTM units. The output of our depth estimation network are the depth map and the hidden states for the current time-step .
Our visual odometry network uses a VGG16  architecture with recurrent units interleaved. Table 2 shows the detailed network architecture. The input to our visual odometry network is the concatenation of and together with the hidden states from the previous time-step. The output is the relative 6DoF camera pose between the current view and the immediately preceeding view. The main differences between our visual odometry network and most current deep learning-based visual odometry methods are 1) At each time-step, instead of a stack of frames, our visual odometry network only takes the current image as input; the knowledge about previous frames is in the hidden layers. 2) Our visual odometry network also takes the current depth estimation as input, which ensures a consistent scene scale between depth and camera pose (important for unsupervised depth estimation, where the scale is ambiguous). 3) Our visual odometry network can run on a full video sequence while maintaining a single scene scale.
|Conv (output)||6@11 512||1 16|
3.2 Loss Functions
3.2.1 Multi-view Reprojection Loss
Zhou et al.  showed that the learning of depth and visual odometry estimation can be formulated as an image reconstruction problem using a differentiable geometric module (DGM). Thus we can use the DGM to formulate an image reconstruction constraint between and using the estimated depth and camera pose as introduced in the previous subsection. However, such a pairwise photometric consistency constraint is very noisy due to illumination variation, low texture, occlusion, etc. Recently, Iyer et al.  proposed a composite transformation constraint for self-supervised visual odometry learning. By combining the pairwise image reconstruction constraint with the composite transformation constraint, we propose a multi-view image reprojection constraint that is robust to noise and provides strong self-supervision for our multi-view depth and visual odometry learning. As shown in Figure 2(c), the output depth maps and relative camera poses together with the input sequence are fed into a differentiable geometric module (DGM) that performs differentiable image warping of every previous view of the sub-sequence into the current view. Denote the input image sequence (shown in Figure 2(a)) as , the estimated depth maps as , and the camera poses as the transformation matrices from frame to : }. The multi-view reprojection loss is
where is the view warped into view, is the image domain, is a binary mask indicating whether a pixel of has a counterpart in , and is a weighting term that decays exponentially based on . Image pairs that are far away naturally suffer from larger reprojection error due to interpolation and moving foreground so we use to reduce the effect of such artifacts. and are obtained as
where is a dense flow field for 2D pixels from view to view , which is used to compute flow consistency. is the camera intrinsic matrix. The pose change from view to , can be obtained by a composite transformation as
The function in Equation 2 warps image into using and . The function is a DGM , which performs a series of differentiable 2D-to-3D, 3D-to-2D projections, and bi-linear interpolation operations .
In the same way, we reverse the input image sequence and perform another pass of depth and camera pose estimation, obtaining the backward multi-view reprojection loss . This multi-view reprojection loss can fully exploit the temporal information in our ConvLSTM units from multiple previous views by explicitly putting constraints between the current view and every previous view.
A trivial solution to Equation 1 is to be all zeros. To prevent the network from converging to the trivial solution, we add a regularization loss to , which gives a constant penalty to locations where is zero.
3.2.2 Forward-backward Flow Consistency Loss
A forward-backward consistency check has become a popular strategy in many learning-based tasks, such as optical flow, registration , and depth estimation [38, 11, 33], which provides additional self-supervision and regularization. Similar to [38, 33] we use the dense flow field as a hybrid forward-backward consistency constraint for both the estimated depth and pose. We first introduce a forward-backward consistency constraint on a single pair of frames and then generalize to a sequence. Let us denote a pair of consecutive frames as and , and their estimated depth maps and relative poses as , , , and . We can obtain a dense flow field from frame to using Equation 2. Similarly we can obtain using , . Using we can compute a pseudo-inverse flow (due to occlusion and interpolation) as
This is similar to Equation 2 except that we are interpolating from instead of from . Therefore, we can formulate the flow consistency loss as
This is performed for every consecutive pair of frames in the input sequence. Unlike the multi-view reprojection loss we only compute flow-consistency on pairs of consecutive frames given the fact that the magnitude of the flow increases, for frame pairs that are far apart, leading to inaccurate pseudo-inverses due to interpolation.
3.2.3 Smoothness Loss
Local smoothness is a common assumption for depth estimation. Following Zhan et al. , we use an edge-aware smoothness constraint which is defined as
where is the inverse depth.
3.2.4 Absolute depth loss
The combination of multi-view reprojection loss , defined in Equation 1, forward-backward flow-consistency loss defined in Equation 5, and smoothness loss defined in Equation 6 can form an unsupervised training strategy for the network. This manner of training is suitable for cases where there is no groundtruth depth available, which is true for the majority of real world scenarios. However, the network trained in this way only produces depth at a relative scale. So optionally, if there is groundtruth depth available, even sparsely, we can train a network to estimate depth at absolute scale by adding the absolute depth loss defined as
In addition, we can replace the local smoothness loss in Equation 6 by a gradient similarity to the groundtruth depth, which can be defined as
3.3 Training Pipeline
The full training pipeline of our method is shown in Figure 2. Every consecutive key frames (we use in all our experiments) are grouped together as an input sequence . The frames are grouped in a sliding window fashion such that more training data can be generated. Here the key frame selection is based on the motion between successive frames. Because the image reprojection constraints are ambiguous for very small baselines, we discard frames with baseline motion smaller than . Before passing the sequence to the network for training, we also reverse the sequence to create a backward sequence , which not only serves as a data augmentation but also is used to enforce the forward-backward constraints. The input sequence is generated offline during the data preparation stage while the backward sequence is generated online during the data preprocessing stage. and are fed into two networks with shared weights; each generates a sequence of depth maps and camera poses as shown in Figure 2. The estimated depth maps and camera poses are then utilized to generate dense flows to warp previous views to the current view through a differentiable geometric module (DGM) [43, 38]. Furthermore, we utilize DGMs to generate the pseudo-inverse flows for both the forward and backward flows. By combining image warping loss, flow-consistency loss, and optionally absolute depth loss, we form the full training pipeline for our proposed framework.
Once trained, our framework can run on arbitrary length sequences without grouping frames into fixed length sub-sequences. To bootstrap the depth and pose estimation, the hidden states for the ConvLSTM units are initialized by zero for the first frame. All following estimations will then depend on the hidden states from the previous time-step.
|Methods||Dataset||Supervised||Error metric||Accuracy metric|
|depth||pose||RMSE||RMSE log||Abs Rel||Sq Rel|
|Zhou et al. ||CS+K||6.709||0.270||0.183||1.595||0.734||0.902||0.959|
|Liu et al. ||K||✓||6.523||0.275||0.202||1.614||0.678||0.895||0.965|
|Eigen et al. ||K||✓||6.307||0.282||0.203||1.548||0.702||0.890||0.958|
|Yin et al.||K||5.857||0.233||0.155||1.296||0.806||0.931||0.931|
|Zhan et al. ||K||✓||5.585||0.229||0.135||1.132||0.820||0.933||0.971|
|Zou et al. ||K||5.507||0.223||0.150||1.124||0.793||0.933||0.973|
|Godard et al. ||CS+K||✓||5.311||0.219||0.124||1.076||0.847||0.942||0.973|
|Atapour et al. ||K+S*||✓||4.726||0.194||0.110||0.929||0.923||0.967||0.984|
|Kuznietsov et al. ||K||✓||✓||4.621||0.189||0.113||0.741||0.875||0.964||0.988|
|Yang et al. ||K||✓||4.442||0.187||0.097||0.734||0.888||0.958||0.980|
|Fu et al. (ResNet) ||K||✓||2.727||0.120||0.072||0.307||0.932||0.984||0.994|
In this section we show a series of experiments using the KITTI driving dataset [9, 10] to evaluate the performance of our RNN-based depth and visual odometry estimation method. As mentioned in Section 1, our architecture can be trained in a supervised or unsupervised mode. Therefore, we evaluated both supervised and unsupervised versions of our framework. In the following experiments we named the supervised version as ours-sup and the unsupervised version as ours-unsup. We also performed detailed ablation studies to show the impact of the different constraints, architecture choices, and estimations at different time-steps.
4.1 Implementation Details
We set the weights for depth loss, smoothness loss, forward-backward consistency loss, and mask regularization to 1.0, 1.0, 0.05, and 0.05, respectively. The weight for the image reprojection loss is , where is the number of frame intervals between source and target frame. We use the Adam  optimizer with , . The initial learning rate is 0.0002. The training process is very time-consuming for our multi-view depth and odometry estimation network. One strategy we use to speed up our training process, without losing accuracy, is first to pretrain the network with the consecutive view reprojection loss for 20 epochs. Then we fine-tune the network with the multi-view reprojection loss for another 10 epochs.
4.2 Training datasets
We used the KITTI driving dataset  to evaluate our proposed framework. To perform a consistent comparison with existing methods, we used the Eigen Split approach  to train and evaluate our depth estimation network. From the 33 training scenes, we generated 45200 10-frame sequences. Here we used the stereo camera as two monocular cameras. A sequence of 10 frames contains either 10 left-camera or 10 right-camera frames. We resized the images from 375 1242 to 128416 for computational efficiency and to be comparable with existing methods. The image reprojection loss is driven by motion parallax, so we discarded all static frames with baseline motion less than meters during data preparation. 697 frames from the 28 test scenes were used for quantitative evaluation. For odometry evaluation we used the KITTI Odometry Split , which contains 11 sequences with ground truth camera poses. We follow [42, 39], which use sequences 00-08 for training and 09-10 as evaluation.
4.3 Depth Estimation
To evaluate the depth estimation component of our multi-view depth and odometry network, we compare to the state-of-the-art CNN-based depth estimation methods. Our network takes advantage of previous images and depths through recurrent units and thus achieves best performance when running on a continuous video sequence. However, it would be unfair to compare against single view methods when our method uses multiple views. On the other hand, if we also use only a single view for our method, then we fail to reveal the full capacity of our framework. Therefore, in order to present a more comprehensive depth evaluation, we report both our depth estimation results with and without previous views’ assistance. Ours-sup (single-view) is the single view (or first view) depth estimation result of our framework, which also shows the bootstrapping performance of our approach. Ours-sup (multi-view) is the tenth view depth estimation result from our network. As shown in Table 3, ours-sup (multi-view) performs significantly better than all of the other supervised [20, 4, 1, 36, 7, 17] and unsupervised [42, 38, 44, 39, 11] methods. The unsupervised version of our network outperforms the state-of-the-art unsupervised methods as well as several supervised methods. Both the supervised and unsupervised version of our network outperform the respective state-of-the-art by a large margin. Figure 4 shows a visual comparison of our method with other methods. Our method consistently captures more detailed structures, e.g., the motorcycle and columns in the lower right corner of the figures in rows 2 and 3.
4.4 Pose Estimation
We used the KITTI Odometry Split to evaluate our visual odometry network. For pose estimation we directly ran our method through the whole sequence instead of dividing into 10-frame sub-sequences. We compared to the state-of-the-art learning-based visual odometry methods [39, 42, 38] as well as a popular monocular SLAM method: ORB-SLAM . We used the KITTI Odometry evaluation criterion , which computes the average translation and rotation errors over sub-sequences of length (100m, 200m, … , 800m).
|Methods||Seq 09||Seq 10|
|Zhou et al. ||17.84||0.068||37.91||0.178|
|Zhan et al. ||11.92||0.036||12.62||0.034|
|DeepVO et al. ||-||-||8.11||0.088|
Both the monocular ORB-SLAM and the unsupervised learning-based visual odometry methods are suffering from scale ambiguity, so we aligned their trajectories with groundtruth prior to evaluation using evo111github.com/MichaelGrupp/evo. The supervised version of our method (absolute depth supervision) and the stereo supervised method  are able to estimate camera translations at absolute scale, so there is no post-processing for these two methods.
Table 4 shows quantitative comparison results based on the KITTI Visual Odometry criterion. Figure 5 shows a visual comparison of the full trajectories for all the methods. Including our method, all the full trajectories of learning-based visual odometry methods are produced by integrating frame-to-frame relative camera poses over the whole sequence without any drift correction.
The methods [42, 38] take a small sub-sequence (5 frames) as input and estimate relative poses between frames within the sub-squence. There is no temporal correlation between different sub-sequences and thus the scales are different between those sub-sequences. However, our method can perform continuous camera pose estimation within a whole video sequence for arbitrary length. The temporal information is transmitted through recurrent units for arbitrary length and thus maintains a consistent scale within each full sequence.
4.5 Ablation study
In this section we investigate the important components: placements of the recurrent units, multi-view reprojection and forward-backward consistency constraints in the proposed depth and visual odometry estimation network.
Placements of recurrent units. Convolutional LSTM units are essential components for our framework to leverage temporal information in depth and visual odometry estimation. Thus we performed a series of experiments to demonstrate the influence of these recurrent units as well as the choice for the placements of recurrent units in the network architecture. We tested three different architecture choices which are shown in Figure 6. The first one is interleaving LSTM units across the whole network (full LSTM). The second one is interleaving LSTM units across the encoder (encoder LSTM). The third one is interleaving LSTM units across the decoder (decoder LSTM). Table 5 shows the quantitative comparison results. It can be seen that the encoder LSTM performs significantly better than the full LSTM and the decoder LSTM. Therefore, we chose the encoder LSTM as our depth estimation network architecture.
|Method||RMSE||RMSE log||Abs Rel||Sq Rel|
Multi-view reprojection and forward-backward consistency constraints. To investigate the performance gain from the multi-view reprojection and forward-backward consistency constraints, we conducted another group of experiments. Table 6 shows the quantitative evaluation results. We compared among three methods: with only the consecutive image reprojection constraint (Ours-d), with the consecutive image reprojection constraint and the forward-backward consistency constraint (Ours-dc), and with the multi-view reprojection constraint and the forward-backward consistency constraint (Ours-mc). The multi-view reprojection loss is more important in the unsupervised training, which is shown by the results of the last two rows in Table 6. Figure 7 shows a qualitative comparison between networks trained using consecutive image reprojection loss and those using multi-view reprojection loss. It can be seen that multi-view reprojection loss provides better supervision to areas that lack groundtruth depth.
|Method||RMSE||RMSE log||Abs Rel||Sq Rel|
|Window size||RMSE||RMSE log||Abs Rel||Sq Rel|
Estimation with different temporal-window sizes. Table 7 shows a comparison between depth estimation with different temporal-window sizes, i.e., the number of frames forming the temporal summary. Here we use the Eigen Split 697 testing frames for these sliding-window-based evaluations. In addition, we also ran through each whole testing sequence and again performed evaluation on those 697 testing frames. The result demonstrates that 1) the performance of the depth estimation is increasing with the number of depth estimations performed before the current estimation; 2) the performance of the depth estimation is not increasing after 10 frames; 3) even though our network is trained on 10-frame based sub-sequences, it can succeed on an arbitrary length sequences.
In this paper we presented an RNN-based, multi-view method for depth and camera pose estimation from monocular video sequences. We demonstrated that our method can be trained either supervised or unsupervised and that both produce superior results compared to the state-of-the-art in learning-based depth and visual odometry estimation methods. Our novel network architecture and the novel multi-vew reprojection and forward-backward consistency constraints let our system effectively utilize the temporal information from previous frames for current frame depth and camera pose estimation. In addition, we have shown that our method can run on an arbitrary length video sequences while producing temporally coherent results.
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