Accurately perceiving surrounding 3D information from passive and active sensors is crucial for numerous applications such as localization and mapping , autonomous driving , obstacle detection and avoidance , and 3D reconstruction [10, 33]. However, each kind of sensors alone suffers from its inherent drawbacks. Stereo cameras are well-known for suffering from computational complexities and their incompetence in dealing with textureless/repetitive areas and occlusion regions , while Lidar sensors often provide accurate but relatively sparse depth measurements .
Therefore, it is highly desired to fuse measurements from Lidar and stereo cameras to achieve high-precision depth perception by exploiting their complementary properties. However, it is a non-trivial task as accurate Stereo-Lidar fusion requires a proper registration between Lidar and stereo images and noise-free Lidar points. Existing methods are not satisfactory due to the following drawbacks:
Due to rolling-shutter effects of Lidar and other calibration imperfections, a direct registration will introduce significant alignment errors between Lidar and stereo depth. Furthermore, existing methods tend to assume the Lidar measurements are noise-free [19, 30]. However, as illustrated in Fig. 1, the misalignment and noisy Lidar measurements cause significant defects in Stereo-Lidar fusion.
In this paper, we tackle the above challenges and propose a novel framework “LidarStereoNet” for accurate Stereo-Lidar fusion, which can be trained in an end-to-end unsupervised learning manner. Our framework is noise-aware in the sense that it explicitly handles misalignment and noise in Lidar measurements.
Firstly, we propose to exploit photometric consistency between stereo images, and depth consistency between stereo cameras and Lidar to build an unsupervised training loss, thus removing the need of ground truth depth/disparity maps. It enables a strong generalization ability of our framework to various real-world applications.
Secondly, to alleviate noisy Lidar measurements and slight misalignment between stereo cameras and Lidar, we present a novel training strategy that gradually removes these noisy points during the training process automatically. Furthermore, we have also presented a novel structural loss (named plane fitting loss) to handle the inaccurate Lidar measurements and stereo matching.
Under our problem setting, we make no assumption on the inputs such as the pattern/number of Lidar measurements, the probability distribution of Lidar points or stereo disparities. Our network allows the sparsity of input Lidar points to be varied, and can even handle an extreme case when the Lidar sensor is completely unavailable.
Experimental results on different datasets demonstrate that our method is able to recover highly accurate depth maps through Lidar-Stereo fusion. It outperforms existing stereo matching methods, depth completion methods and Lidar-Stereo fusion methods with a large margin (at least twice better than previous ones). To the best of our knowledge, there is no deep learning based method available that can achieve this goal under our problem setting.
2 Related Work
Deep convolutional neural networks (CNNs) based stereo matching methods have recently achieved great success. Existing supervised deep methods either formulate the task as depth regression or multi-label class classifications . Recently, unsupervised deep stereo matching methods have also been introduced to relief from a large amount of labeled training data. Godard et al.  proposed to exploit the photometric consistency loss between left images and the warped version of right images, thus forming an unsupervised stereo matching framework. Zhong et al. 
presented a stereo matching network for estimating depths from continuous video input. Very recently, Zhanget al.  extended the self-supervised stereo network  from passive stereo cameras to active stereo scenarios. Even though stereo matching has been greatly advanced, it still suffers from challenging scenarios such as texture-less and low-lighting conditions.
Lidar scanners can provide accurate but sparse and incomplete 3D measurements. Therefore, there is a highly desired requirement in increasing the density of Lidar scans, which is crucial for applications such as self-driving cars. Uhrig et al.  proposed a masked sparse convolution layer to handle sparse and irregular Lidar inputs. Chodosh et al.  utilized compressed sensing to approach the sparsity problem for scene depth completion. With the guidance of corresponding color images, Ma et al.  extended the up-projection blocks proposed by  as decoding layers to achieve full depth reconstruction. Jaritz et al.  handled sparse inputs of various densities without any additional mask input.
Existing studies mainly focus on fusing stereo and time-of-flight (ToF) cameras for indoor scenarios [7, 23, 24, 12, 8], while Lidar-Stereo fusion for outdoor scenes has been seldom approached in the literature. Badino et al.  used Lidar measurements to reduce the searching space for stereo matching and provided predefined paths for dynamic programming. Later on, Maddern et al.  proposed a probabilistic model to fuse Lidar and disparities by combining prior from each sensor. However, their performance degrades significantly when the Lidar information is missing. To tackle this issue, instead of using a manually selected probabilistic model, Park et al. 
utilized CNNs to learn such a model, which takes two disparities as input: one from the interpolated Lidar and the other from semi-global matching. Compared with those supervised approaches, our unsupervised method can be end-to-end trained using stereo pairs and sparse Lidar points without using external stereo matching algorithms.
3 Lidar-Stereo Fusion
In this section, we formulate Lidar-Stereo fusion as an unsupervised learning problem and present our main ideas in dealing with the inherent challenges encountered by existing methods, i.e., noise in Lidar measurements.
3.1 Problem Statement
Lidar-Stereo fusion aims at recovering a dense and accurate depth/disparity map from sparse Lidar measurements and a pair of stereo images , . We assume the Lidar and stereo camera have been calibrated with extrinsic matrix and the stereo camera itself is calibrated with intrinsic matrices , and projection matrices , . We can then project sparse Lidar points onto the image plane of by . Since disparity is used in the stereo matching task, we convert the projected depth to disparity using , where is the baseline between the stereo camera pair and is the focal length. The same process is applied to the right image as well. Mathematically this problem can be defined as:
where is the learned Lidar-Stereo fusion model (a deep network in our paper) parameterized by , are the fusion outputs defined on the left and right coordinates.
Under our problem setting, we do not make any assumption on the Lidar points’ configuration (e.g., the number or the pattern) or error distribution of Lidar points and stereo disparities. Removing all these restrictions makes our method more generic and wider applicability.
3.2 Dealing with Noise
In Lidar-Stereo fusion, existing methods usually assume the Lidar points are noise free and the alignment between Lidar and stereo images is perfect. We argue that even for dedicated systems such as the KITTI dataset, the Lidar points are never perfect and the alignment cannot be consistently accurate, c.f. Fig. 1. The errors in Lidar scanning are inevitable for two reasons: (1) Even for well calibrated Lidar-stereo systems, e.g., KITTI, and after eliminating the rolling shutter effect in Lidar scans by compensating the ego-motion, Lidar errors still persist even for stationary scenes, as shown in Fig. 2. According to the readme file in the KITTI VO dataset, the rolling shutter effect has already been removed in Lidar scans. However, we still find Lidar errors on transparent (white box) and reflective (red box) surfaces. Also, due to the displacement between Lidar and cameras, the Lidar can see through tiny objects as shown in the yellow box. (2) It is hard to perform motion-compensation on dynamic scenes, thus the rolling shutter effect will persist for moving objects.
It is possible to eliminate these errors by manually inserting 3D models and other post-processing steps . However, lots of human efforts will be involved. Our method can automatically deal with these Lidar errors without the need of human power. Hence the problem we are tackling (“Noise-Aware Lidar-Stereo Fusion”) is not a simple “system-level” problem that can be solved through “engineering registration”.
It is known that the ability of deep CNNs to overfit or memorize the corrupted labels can lead to poor generalization performance. Therefore, we aim to deal with the noise in Lidar measurements properly to train deep CNNs.
Robust functions such the norm, Huber function or the truncated norm are natural choices in dealing with noisy measurements. However, these functions will not eliminate the effects caused by noises but only suppress them. Further, these errors also exist in the input. Automatically correct/ignore these erroneous points creates an extra difficulty for the network. To this end, we introduce a feedback loop in our network to allow the input also to depend on the output of the network. In this way, the input Lidar points can be cleaned before being fed into the network.
The Feedback Loop
We propose a novel framework to progressively detect and remove erroneous Lidar points during the training process and generate a highly accurate Lidar-Stereo fusion. Fig. 3 illustrates an unfolded structure of our network design, namely the feedback loop. It consists of two phases: “Verify” phase and “Update” phase. Each phase shares the same network structure of Core Architecture, and the details will be illustrated in Section 4.1.
In the Verify phase, the network takes stereo image pairs (,) and noisy Lidar disparities (, ) as input, and generates two disparity maps (,). No back-propagation takes place in this phase. We then compare (,) and (,) and retain the sparse Lidar points (,) that are consistent in both stereo matching and Lidar measurements. In the Update phase, the network takes both stereo pairs (,) and cleaned sparse Lidar points (,) as the inputs to recover dense disparity maps (,
). All loss functions are evaluated on the final disparity outputs (,) only. Once the network is trained, we empirically find that there is no performance drop if we directly feed the Core Architecture with noisy Lidar points. Therefore, we remove the feedback loop module and only use the Core Architecture in testing.
Our feedback loop detects erroneous Lidar points by measuring the consistency between Lidar points and stereo matching. Lidar and stereo matching are active and passive depth acquisition techniques. Hence, it is less likely that they would make the same errors. It may also filter out some correct Lidar points at the first place but we have image warping loss and other regularization losses to keep the network training on the right track.
4 Our Network Design
In this section, we present our “LidarStereoNet” for Lidar-Stereo fusion, which can be learned in an unsupervised end-to-end manner. To remove the need of large-scale training data with ground truth, we propose to exploit the photometric consistency between stereo images, and the depth consistency between stereo cameras and Lidar. This novel network design enables the following benefits: 1) A wide generalization ability of our framework in various real-world scenarios; 2) Our network design allows the sparsity of input Lidar points to be varied, and can even handle the extreme case when the Lidar sensor is completely unavailable. Furthermore, to alleviate noisy Lidar measurements and the misalignment between Lidar and stereo cameras, we incorporate the “Feedback Loop” into the network design to connect the output with the input, which enables the Lidar points to be cleaned before fed into the network.
4.1 Core Architecture
We illustrate the detailed structure of the Core architecture of our LidarStereoNet in Fig. 4. LidarStereoNet consists of the following blocks: 1) Feature extraction and fusion; 2) Feature matching and 3) Disparity computing. The general information flow of our network is similar to  but has some crucial modifications in the feature extraction and fusion block. In view of different characteristics between dense colour images and sparse disparity maps, we leverage different convolution layers to extract features from each of them. For colour images, we use the same feature extraction block from  while for sparse Lidar inputs, the sparse invariant convolution layer  is used. The final feature maps are produced by concatenating stereo image features and Lidar features. Feature maps from left and right branches are concatenated to form a 4D feature volume with a maximum disparity range of 192. Then feature matching is processed through an hourglass structure of 3D convolutions to compute matching cost at each disparity level. Similar to , we use the soft-argmin operation to produce a 2D disparity map from the cost volume.
Dealing with dense and sparse inputs
To extract features from sparse Lidar points, Uhrig et al.  proposed a sparsity invariant CNN after observing the failure of conventional convolutions. However, Ma et al.  and Jaritz et al.  argued that using a standard CNN with special training strategies can achieve better performance and also handle varying input densities. We compared both approaches and realized that standard CNNs can handle sparse inputs and even get better performance but they request much deeper network (ResNet38 encoded VS 5 Convolutional layers) with 500 times more trainable parameters ( VS ). Using such a “deep” network as a feature extractor will make our network not feasible for end-to-end training and hard to converge.
In our network, we choose sparsity invariant convolutional layers 
to assemble our Lidar feature extractor which can handle varying Lidar points distribution elegantly. It consists of 5 sparse convolutional layers with a stride of 1. Each convolution has an output channel of 16 and is followed by a ReLU activation function. We attached a plain convolution with a stride of 4 to generate the final 16 channels Lidar features in order to make sure the Lidar features compatible with the image features.
4.2 Loss Function
Our loss function consists of two data terms and two regularization terms. For data terms, we directly choose the image warping error as a dense supervision for every pixel and discrepancy on filtered sparse Lidar points . For regularization terms, we use colour weighted smoothness term and our novel slanted plane fitting loss . Our overall loss function is a weighted sum of the above loss terms:
we empirically set .
4.2.1 Image Warping Loss
We assume photometric consistency between stereo pairs such that corresponding points between each pair should have similar appearance. However, in some cases, this assumption does not hold. Hence, we also compare the difference between small patches’ Census transform as it is robust for photometric changes. Our image warping loss is defined as follow:
where stands for photometric loss, represents Census loss and is the image gradient loss. We set to balance different terms.
The photometric loss is defined as the difference between the observed left (right) image and the warped left (right) image, where we have weighted each term with the observed pixels to account for the occlusion:
where and the occlusion mask is computed through left-right consistency check.
To further improve the robustness in evaluating the image warping error, we used the Census transformation to measure the difference:
Lastly, we have also used the difference between image gradients as an error metric:
4.2.2 Lidar Loss
The cleaned sparse Lidar points after our feedback verification can also be used as a sparse supervision for generating disparities. We leverage the truncated function to handle noises and errors in these sparse Lidar measurements,
where is the mask computed in the Verify phase. The truncated fuction is defined as:
4.2.3 Smoothness Loss
4.2.4 Plane Fitting Loss
We also introduce a slanted plane model into deep learning frameworks to enforce structural constraint. This model has been commonly used in conventional Conditional Random Field (CRF) based stereo matching/optical flow algorithms. It assumes that all pixels within a superpixel lie on a 3D plane. By leveraging this piecewise plane fitting loss, we could enforce strong regularization on 3D structure. Although our slanted plane model is defined on disparity space, it has been proved that a plane in disparity space is still a plane in 3D space . Mathematically, the disparity of each pixel is parameterized by a local plane,
where is the image coordinate, the triplet denotes the parameters of a local disparity plane.
Define as the matrix representation of pixel’s homogeneous coordinates within a SLIC superpixel  with a dimension of where is number of pixels within a segment, and denote as the planar parameters. Given the current disparity predictions , we can estimate the plane parameter in closed-form via . With the estimated plane parameter, the fitted planar disparities can be computed as .
Our plane fitting loss then can be defined as
|Probabilistic fusion ||Stereo + Lidar||No||-||-||0.0591||-||-||99.6%|
|CNN Fusion ||Stereo + Lidar||Yes||-||-||0.0484||-||-||99.8%|
|Our method||Stereo + Lidar||No||0.0350||0.0287||0.0198||0.0126||0.9872||100.00%|
|(a) Input image||(b) Input lidar disparity||(c) Ground truth||(d) Ours|
|(e)S2D ||(f) SINet ||(g) Probabilistic fusion ||(h) CNN fusion |
We implemented our LidarStereoNet in Pytorch. All input images were randomly cropped toduring training phases while we used their original size in inference. The typical processing time of our net was about 0.5 fps on Titan XP. We used the Adam optimizer with a constant learning rate of 0.001 and a batch size of 1. We performed a series of experiments to evaluate our LidarStereoNet on both real-world and synthetic datasets. In addition to analyzing the accuracy of depth prediction in comparison to previous work, we also conducted a series of ablation studies on different sensor fusing architectures and investigate how each component of the proposed losses contributes to the performance.
5.1 KITTI Dataset
The KITTI dataset  is created to set a benchmark for autonomous driving visual systems. It captures depth information from a Velodyne HDL-64E Lidar and corresponding stereo images from a moving platform. They use a highly accurate inertial measurement unit to accumulate 20 frames of raw Lidar depth data in a reference frame and serves as ground truth for the stereo matching benchmark. In KITTI 2015 , they also take moving objects into consideration. The dynamic objects are first removed and then re-inserted by fitting CAD models to the point clouds, resulting in a clean and dense ground truth for depth evaluation.
After these processes, the raw Lidar points and the ground truth differ significantly in terms of outliers and density as shown in Fig.1. In raw data, due to the large displacement between the Lidar and the stereo cameras 
, boundaries of objects may not perfectly align when projecting Lidar points onto image planes. Also, since Lidar system scans depth in a line by line order, it will create a rolling shutter effect on the reference image, especially for a moving platform. Instead of heuristically removing measurements, our method is able to omit these outliers automatically which is evidently shown in Fig.1 and Fig. 2.
We used the KITTI VO dataset  as our training set. We sorted all 22 KITTI VO sequences and found 7 frames from sequence 17 and 20 having corresponding frames in the KITTI 2015 training set. Therefore we excluded these two sequences and used the remaining 20 stereo sequences as our training dataset. Our training dataset contains 42104 images with a typical image resolution of . To obtain sparse disparities inputs, we projected raw Lidar points onto left and right images using provided extrinsic and intrinsic parameters and converted the raw Lidar depths to disparities. Maddern et al.  also traced 141 frames from KITTI raw dataset that have corresponding frames in the KITTI 2015 dataset and reported their results on this subset. For consistency, we used the same subset to evaluate our performance and utilize the 6 frames from KITTI VO dataset as our validation set (we excluded 1 frame that overlaps the KITTI 141 subset from our validation).
Comparisons with State-of-the-Art
We compared our results with depth completion methods and Lidar-stereo fusion methods using depth metrics from  and bad pixel ratio disparity error from KITTI . We also provide a comparison of our method and stereo matching methods in the supplemental material.
For depth completion, we compared with S2D  and SINet . In our implementation of S2D and SINet, we trained them on KITTI depth completion dataset . From 151 training sequences, we excluded 28 sequences that overlaps with KITTI 141 dataset and used the remaining 123 sequences to train these networks from scratch in a supervised manner. As a reference, we computed the error rate of the input Lidar. It is worth noting that our method increases the disparity density from less than 7.3% to 100% while reducing the error rate by a half.
We also compared our method with two existing Lidar-Stereo fusion methods: Probabilistic fusion  and CNN fusion  and outperforms them with a large margin. Quantitative comparison between our method and the competing state-of-the-art methods is reported in Tab. 1. We can clearly see that our self-supervised LidarStereoNet achieves the best performance throughout all the metrics evaluated. Note that, our method even outperforms recent supervised CNN based fusion method  with a large margin. More qualitative evaluations of our method in challenging scenes are provided in Fig. 11. These results demonstrate the superiority of our method that can effectively leverage the complementary information between Lidar and stereo images.
On Input Sparsity
Thanks to the nature of deep network and sparsity invariant convolution, our LidarStereoNet can handle Lidar input of varying density, ranging from no Lidar input to 64 lines input. To see this trend, we downsampled the vertical and horizontal resolution of the Lidar points. As shown in Fig. 6, our method performs equally well when using 8 or more lines of Lidar points. Note that even when there are no Lidar points as input (in this case, the problem becomes a pure stereo matching problem), our method still outperforms SOTA stereo matching methods.
5.2 Ablation Study
In this section, we perform ablation studies to evaluate the importance of our feedback loop and proposed losses. Notably, all ablation studies on losses and fusion strategies are evaluated on Core Architecture only in order to reduce the randomness introduced by our feedback loop module.
Importance of the feedback loop
We evaluate the importance of the feedback loop in two aspects. One is to remove the error points from the back-end, i.e. the loss computation part. The other is to remove them from the input. In our baseline model (Type 1), we use raw Lidar as our input and compute the Lidar loss on them. For Type 2 model, we also use the raw Lidar as input but compute the Lidar loss only on cleaned Lidar points. Our full model uses clean Lidar points in both parts. As shown in Tab. 2, removing errors in the back-end can improve the performance by . However, using cleaned Lidar points as input can boost the performance in in metric, which demonstrates the importance of our feedback loop module.
Comparing different loss functions
Tab. 3 shows the performance gain with different losses. As we can see, when only using Lidar points as supervision, its performance is affected by the outliers in Lidar measurements. Adding a warping loss can reduce the error rate from to . Adding our proposed plane fitting loss can further reduce the metric from to . In the supplementary material, we further compare our soft slanted plane model and a hard plane fitting model. The soft one achieves better performance.
|+ + +||0.0468||0.0393||0.0276||0.0201|
Comparing different fusion strategies
Considering the problem of utilizing sparse depth information, one no-fusion approach will be directly using Lidar measurements for supervisions. As shown in Tab. 4, its performance is affected by the misaligned Lidar points and it has a relatively high error rate of . The second method is to leverage the depth as a fourth channel additionally to the RGB images. We term it an early fusion strategy. As shown in Tab. 4, it has the worst performance among the baselines. This may be due to the incompatible characteristics between RGB images and depth maps thus the network is unable to handle well within a common convolution layer. Our late fusion strategy achieves the best performance among them.
5.3 Generalizing to Other Datasets
To illustrate that our method can generalize to other datasets, we compare our method to several methods on the Synthia dataset . Synthia contains 5 sequences under different scenarios. And for each scenario, they capture images under different lighting and weather conditions such as Spring, Winter, Soft-rain, Fog and Night. We show quantitative results of experiments in Tab. 5 and qualitative results are provided in the supplementary material.
For sparse disparity inputs, we randomly selected 10% of full image resolution. As discussed before, projected Lidar points have misalignment with stereo images in KITTI dataset. To simulate the similar interference, we add various density levels of Gaussian noise to sparse disparity maps. As shown in Fig. 8, our proposed LidarStereoNet adapts well to the noisy input disparity maps, while S2D  fails to recover disparity information.
In this paper, we have proposed an unsupervised end-to-end learning based Lidar-Stereo fusion network “LidarStereoNet” for accurate 3D perception in real world scenarios. To effectively handle noisy Lidar points and misalignment between sensors, we presented a novel “Feedback Loop” to sort out clean measurements by comparing output stereo disparities and input Lidar points. We have also introduced a piecewise slanted plane fitting loss to enforce strong 3D structural regularization on generated disparity maps. Our LidarStereoNet does not need ground truth disparity maps for training and has good generalization capabilities. Extensive experiments demonstrate the superiority of our approach, which outperforms state-of-the-art stereo matching and depth completion methods with a large margin. Our approach can reliably work even when Lidar points are completely missing. In the future, we plan to extend our method to other depth perception and sensor fusion scenarios.
Acknowledgement Y. Dai (firstname.lastname@example.org) is the corresponding author. This research was supported in part by Australia Centre for Robotic Vision, Data61 CSIRO, the Natural Science Foundation of China grants (61871325, 61420106007) the Australian Research Council (ARC) grants (LE190100080, CE140100016, DP190102261, DE140100180). The authors are grateful to the GPUs donated by NVIDIA.
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1 Detailed Network Structure
The core architecture of our LidarStereoNet contains three blocks: 1) Feature extraction and fusion; 2) Feature matching, and 3) Disparity computing. We provide the detailed structure of the feature extraction and fusion block in Table 6. The feature matching block and disparity computing block share the same structures with PSMnet .
|Lidar feature extraction|
|layer||k , s||chns||input|
|Stereo feature extraction|
|layer||k , s||chns||input|
|[ 32/64 64/64 ]||conv1_3|
|[ 64/128 128/128 ]||conv2_16|
|lastconv + conv_mask|
2 Hard versus Soft Plane Fitting
There are two kinds of plane fitting constraints. Conventional CRF based methods use one slanted plane model to describe all disparities in one segment, i.e., disparities insides one segment exactly obeys one slanted plane model. We term it as “Hard” plane fitting constraint. Our method, on the other hand, only applies this term as part of the whole optimization target. In other words, we only require the recovered disparities to fit a plane in a segment if possible but it can still be balanced by other loss terms.
Fig. 9 illustrates the difference between our soft constraint and the CRF-style hard constraint in a recovered disparity map. As can be seen in Fig. 9, strictly applying the slanted plane model in recovered disparity map decreases its performance from to and it is very sensitive to segments as well. By switching segments from Stereo SLIC to SLIC, its performance further decreases from to .
|SLIC segments||Hard constraint result|
|Stereo SLIC segments||Hard constraint result|
|Ground truth disparity||Soft constraint result|
3 Comparisons with STOA stereo matching methods
For the sake of completeness, we provide qualitative and quantitative comparisons with state-of-the-art stereo matching methods. We choose SPS-ST , MC-CNN, PSMnet  and SsSMnet for reference. Note that the SPS-ST method is a traditional (non-deep) method, and its meta-parameters were tuned on KITTI dataset. For deep MC-CNN we used a model which was firstly trained on Middlebury dataset and for PSMnet we used the model that was trained on SceneFlow  dataset and the model (“-ft”) that we fine-tuned on KITTI VO dataset. We also compared our method with state-of-the-art self-supervised stereo matching network SsSMnet .
|Our method||Stereo + Lidar||No||0.0350||0.0287||0.0198||0.0126||0.9872||100.00%|
|(a) Input image||(b) Input lidar disparity||(c) Ground truth||(d) Ours|
|(e)SPS-ST ||(f) SsSMNet ||(g) MC-CNN ||(h) PSMnet |
4 Qualitative results on Synthia dataset
In Fig. 10, we show qualitative comparison results on Synthia dataset. Our method achieves the lowest bad pixel ratio.