It is a long-standing goal of computer vision to achieve a holistic understanding of a visual scene: that is, to decompose it into meaningful elements that together explain the full visual inputhartley2003multiple . This goal is also at the heart of representation learning, which is concerned with extracting representations from data that generalize well for multiple tasks zamir2018taskonomy ; xu2018PAD-Net
. For example, a representation that was trained for object detection will invariably ignore details that are crucial for other tasks that are not object-centric, such as monocular depth estimation. As such, it is desirable to learn models that are not narrowly-scoped to a single taskcaruana1997multitask , though it is not always clear how to do so without an increased annotation burden for each additional task.
. It cleverly combines two predictions (i.e. tasks), relative camera pose estimation and depth estimation, to re-render an image from another point-of-view. By synthesizing a source frame from a video into another target frame, we obtain the supervision necessary (by comparing the synthetic and the real image) to enable end-to-end learning.
It is natural to ask if more tasks can be integrated into this framework, and intuitively the answer is yes. Each additional task that contributes to the image synthesis, by capturing an additional element of the visual world, should increase the fidelity of the model and achieve a lower reconstruction error. In this work, we propose to add the unsupervised tasks of object segmentation, and object 6D motion estimation. Since our primary interest is still the recovery of 3D geometry and motion, however, we do not seek, as done by some prior work casser2019depth ; tosi2020distilled ; guizilini2020semantically , “semantic” objects. Instead, we decompose the image into regions that are likely to be characterized by a well defined rigid motion, and learn those automatically, by optimizing for the same view synthesis objective. Our technical contribution is a locally-rigid model that supports crisp object boundaries through segmentation, and its efficient implementation by reusing a commonly-available but underused “tiling” operator. This results in an efficient lightweight model that transforms the original rigid-world model (where changes between frames are characterized only by a relative camera pose and depths) zhou2017unsupervised to a non-rigid model (where moving objects are also taken into account).
Experiments show that our proposed model is much more expressive, by making predictions that are outside the capabilities of the original model (namely segment moving objects and calculate their 6D motions). We show qualitative results of our neural networks successfully learning to segment non-rigid objects (hands and household objects), and recover accurate depth maps, in EPIC-KitchensDamen2020Collection , a large-scale indoors dataset that has not been used in this context before due to its challenging nature. We also demonstrate that the unsupervised segmentation cues and non-rigid model are beneficial for the previously-considered tasks. Our model achieves a new state-of-the-art result on KITTI Geiger2013IJRR in monocular depth estimation (88.9% accuracy at ), as well as visual odometry (0.011/0.010 ATE), from purely unsupervised data (see sec. 5 for details).
2 Related work
Self-supervised learningcaruana1997promoting ; self-supervised-survey2019
has gathered significant attention recently, since it promises to achieve unsupervised learning by reusing standard elements from supervised learning (e.g. architectures, loss functions), in relatively intuitive configurations. It can generally be described as the task of predicting one part of the input data given only another part. Successful examples include predicting the spatial relationship between two image regionsdoersch2015unsupervised zhang2016colorful , predicting audio from video nagrani2018seeing ; owens2016ambient , and predicting inertial measurement unit (IMU) data (odometry) from video agrawal2015learning . A related approach is to use synthetic transformations, such as predicting the rotation of an image gidaris2018unsupervised or whether a video is played in reverse wei2018learning . Given the large body of literature on self-supervised learning, we refer interested readers to a recent survey self-supervised-survey2019 . Within self-supervised learning, video prediction is a relatively popular task. It consists of generating a subset of a video given the remaining video. Several works have focused on video generation with neural networks srivastava2015unsupervised , by proposing multiple-hypothesis loss functions rupprecht2017learning , causal convolutions such as the PixelCNN for video kalchbrenner2017video , and generative models such as adversarial networks or variational auto-encoders videogen2019 . While successful, these approaches often produce blurry or physically-implausible predictions, and the image generation models are not interpretable.
Approaching this problem by view synthesis zhou2017unsupervised is relatively recent, but draws from traditional works in visual geometry and Simultaneous Location And Mapping (SLAM) scaramuzza2011visual ; davison2007monoslam ; Sheng2019Unsupervised . Instead of using a neural network for generation, it uses a differentiable warp (image deformation) to transform a source frame into a target frame, minimizing the reconstruction error. The task of the neural network is then to predict physically-interpretable quantities, such as 3D geometry, depth and poses, that are used to compute the image warp. This physical model of the world is useful in itself, and can be used for downstream tasks (such as visual odometry or 3D reconstruction). This line of work was pioneered by Garg et al. garg2016unsupervised , who considered stereo pairs or pairs of frames with known pose. This was further developed to include predicted poses by Zhou et al. zhou2017unsupervised (SfMLearner), and concurrently by Vijayanarasimhan et al. sfmnet2017 (SfM-Net), who also considered multiple layers to account for objects. The SfMLearner emphasized no supervision (as opposed to mixed modes of supervision like SfM-Net), and a simple architecture, so it forms the basis of our work. We describe it in detail in sec. 3. Further developments include improving the pose estimate by a direct visual odometry method (essentially second-order gradient descent) wang2018learning , and adding a FlowNet that can refine the image warp by fine-grained optical flow estimates yin2018geonet . Other proposed improvements are stereo inputs godard2017unsupervised ; li2018undeepvo and probabilistic outputs klodt2018supervising , bundle adjustment to warp stored key frames instead of recent frames yang2018deep , adversarial training pilzer2018unsupervised , and feature computation in 3D space guizilini2019packnet .
3 Unsupervised learning by view synthesis
We begin by describing the canonical self-supervised setup for learning monocular depth estimation, inspired by early methods such as SfMLearner zhou2017unsupervised (sec. 2). Assume that we are given a pair of images , respectively the source and target, usually extracted as nearby frames from a video. If the scene is Lambertian and unchanged between frames (rigid-world assumption) and if we discount occlusions, the target image can be predicted from knowledge of the source image , the depth map , and the relative camera pose between the two views:
Synthesizing the target image amounts to using projective geometry hartley2003multiple to find which pixels correspond in the two views and then transport their intensities from source to target. Namely, the synthesis function
is a warp that linearly interpolates each pixel ofat coordinates to according to the projective equations:
where is the camera intrinsics matrix, retrieves the depth at pixels , and is the transformation matrix that translates any input 3D point along the axis by this depth. We can extract a supervisory signal for depth and pose by comparing the measured and predicted target image:
where is a training dataset of image pairs, is a mask that tells which pixels can be explained by the model and , i.e. the norm weighted by a mask .
Of course, the pose , depth and mask must be obtained somehow. This is the role of the pose, depth and mask networks:
with parameters . The last layer of the mask network is a sigmoid, to constrain outputs to the range. Back-propagating the error in eq. 3 to the networks’ parameters is what allows end-to-end learning. Since predicting is a trivial minimum of eq. 3, a regularization term is added, penalizing the distance between and a target of 1:111The regularization loss used in zhou2017unsupervised was the cross-entropy, which is not a material difference.
The overall objective is then , with a regularization weight .
Although this is the main objective, Zhou et al. zhou2017unsupervised mention a few details that improve performance: (1) a smoothness loss (TV-norm), which penalizes the L1 norm of the second-order gradients of the depth maps ; (2) repeating the objective for multiple scales of the input image; (3) using several source images to predict their poses jointly, instead of one at a time.
4 Proposed method
is that it assumes a rigid world. Our main goal then is to augment it to also account for freely-moving, potentially non-rigid objects. Note that since most pixels in common scenes correspond to a static background, it is undesirable to have a fully non-rigid model, as that would afford too many degrees-of-freedom and thus be prone to overfitting (a hypothesis that we verify in sec.5). For this reason, we segment the pixels into 2 categories: background (with a global rigid model), and objects (with a local, non-rigid model). Together, they fully explain all pixels of the image. The required segmentation network is trained unsupervised as part of the overall objective, and so object segmentation is obtained “for free”. We will now describe these three elements: non-rigid and rigid models, and segmentation.
4.1 Locally-rigid scene model
The starting point for our method is the simple fact that, although a scene is not globally rigid, it usually is locally rigid. It is always possible to make the rigid-world assumption essentially correct, by narrowing down the view to a rigid region (e.g. background, a rigid object, or a smaller region within a non-rigid object). This seems to suggest that the previous method (sec. 3) can express a non-rigid model, by focusing on smaller regions of the image at a time instead of full images. We can then predict a different relative pose prediction for each region, instead of a single pose . We thus propose to average the objective (eq. 3) over a set of regions , extracted with a sliding window:
where we element-wise multiply () the mask with an indicator function , which is 1 inside the region and 0 outside of it. denotes the corresponding pose, extracted from a pose map at the center of the region. The dense map of pose predictions fits naturally into the CNN-based architecture, in the same way as the depth predictions .
While it achieves our goal of a locally-rigid model, eq. 6 is very inefficient (by summing over many zeros), and an efficient implementation would require customizing the differentiable warp operator . However, we can ensure an easy implementation with no modification to by using an operator that extracts patches in a sliding window, and concatenates them as samples before they are passed on to . This tiling operator, also known as im2row, is used in some implementations of convolutions.222unfold operation. We can write it succinctly, for an input with channels and spatial dimensions , as :
is the tensor slice operator, the patches are
, and the stride is. Eq. 6 then becomes:
which effectively amounts to applying the tiling operator to all image-sized inputs of the original rigid-model objective (eq. 3
), and vectorizing the pose mapso that the spatial dimensions correspond to the batch dimension (). Since the kernel size is unknown, in practice we repeat the objective for several values of , corresponding to different object sizes. Our proposed inclusion of the tiling operators is illustrated in fig. 1.
4.2 Object segmentation
As discussed in sec. 4, a fully non-rigid model contains too many degrees-of-freedom. Another issue is that regions defined by square sliding windows (eq. 6) are too coarse to accurately delineate objects’ boundaries. We propose to solve both issues at once by using the predicted mask to partition the pixels into moving objects () and static background ():
where is the background pose, obtained by averaging the pose of all background pixels. Unfortunately, since the non-rigid model is more expressive than the rigid one, assigning all pixels to the former will always attain a lower error. To prevent this trivial solution, we modify the regularization term (eq. 3) to encourage a constant area of foreground pixels in a training batch. We consider that the top 10% of the predictions correspond to pixels with moving objects (), and the rest to background (), penalizing the distance to these target values:
where sort operates in descending order, and is a vector where the first 10% of the elements are 1 and the rest are 0. This “constant area” soft constraint is inspired by a similar approach used for visualizing salient regions in deep network interpretability fong2019understanding , and we found it to be an effective strategy to ensure a correct proportion of object and background pixels. Our overall objective is then , in analogy to sec. 3. An illustration of the objective is shown in fig. 1.
We conducted a series of experiments to validate the effectiveness of our approach. The tasks we focused on were visual odometry, monocular depth estimation, and 6D motion segmentation.
We evaluate the proposed approach on two different large-scale datasets. The first one is the challenging autonomous driving benchmark KITTI Geiger2013IJRR . For the depth estimation, we use the training split defined by Eigen et al. eigen2014depth . For evaluating the performance of the visual odometry, we use the KITTI Odometry dataset, training on sequences and testing on . For the second dataset, we used EPIC-Kitchens Damen2020Collection , which is collected under various indoor kitchen scenarios, and is the largest dataset for egocentric vision. It contains 32 kitchens crossing 4 cities, totalling 55 hours of video. It captures rich non-rigid dynamic motions. Some examples are shown in Fig. 4. As the original frame rate of the videos is 60 FPS, to reduce the redundancy, we sample the dataset at every 4 frames, resulting in a dataset of around 120k images. Among them, 100k images are used for training, and the rest for testing. The dataset does not provide ground-truth depth, camera poses and intrinsics. We learn to recover all of them by unsupervised end-to-end learning.
Our training procedure is exactly the same as for the SfMLearner zhou2017unsupervised , except with the non-rigid model we propose (sec. 4). We used a ResNet-50 as the backbone CNN, and apply the same TV-norm (sec. 3) to both depth () and pose () maps. The only other improvements are depth mean normalizaton and backbone initialization according to Gordon et al. gordon2019depth , as well as disabling the multi-scale prediction, which does not seem beneficial. For brevity, we do not describe the full setup here, but a self-contained description can be found in the supp. material (Appendix A).
Pose estimation performance.
Our sequential pose estimation (visual odometry) performance is reported in table 3. We compare our method with a traditional monocular SLAM system, ORB-SLAM (full) mur2015orb , as well as its local version, ORB-SLAM (short), which uses -frame snippets. We also compare with the SfMLearner zhou2017unsupervised and several recent proposals zou2018df ; mahjourian2018unsupervised ; yin2018geonet ; bian2019unsupervised ; klodt2018supervising ; ranjan2019competitive . As can be seen in table 3, our method outperforms all the other methods. This includes a traditional SLAM pipeline that draws from many years of careful engineering and manual tuning (ORB-SLAM). It is worth mentioning that our method is not explicitly trained for visual odometry, yet it is a useful by-product of training. Regarding the deep learning based approaches, our camera motion estimator outperforms the original SfMLearner zhou2017unsupervised
by a large margin, and recent competing approaches by narrower but still significant margins. We include the standard deviations over several runs in table3 for additional context.
Qualitative results on visual odometry.
We visualize the predicted camera trajectories in fig. 3a and 3b, for several algorithms, on two KITTI test sequences (09 and 10, respectively). All trajectories are registered w.r.t. the ground truth as standard zhan2018unsupervised . It is apparent that the trajectory predicted by our method very accurately follows the ground truth. While other methods can also get close to the ground truth trajectory (SC-SFM in fig. 3a and ORB-SLAM in 3b), no other can achieve the same performance simultaneously on both settings.
Depth estimation performance.
We report the result for depth estimation in table 2. The columns are relative error and its square, root-mean-squared error (RMSE) and its logarithm, as well as the accuracy at 3 given depth thresholds. We include several state-of-the-art approaches in the comparison, including supervised methods eigen2014depth ; liu2015deep and unsupervised stereo-based methods godard2017unsupervised ; garg2016unsupervised , which are not comparable but present an informative upper bound on performance. We do not include in the comparison works with significantly different protocols, such as 3DPackNet guizilini2019packnet which uses higher-resolution images and 3D CNNs, and other works with higher amounts of supervision. These interesting developments are complementary to ours, and thus outside of the scope of this paper. All methods are compared with raw ground truth depth, following recent protocols gordon2019depth ; guizilini2019packnet . We can observe that our method achieves the best performance out of all unsupervised methods, even beating several supervised ones, on almost all metrics. We show two variants of our method, using ResNet-18 and ResNet-50 backbone CNNs, which highlights that the performance gains are not solely due to an increase in capacity, since most methods have comparable backbones. On the other hand, it also reveals that our model is expressive enough to afford some gains when increasing the capacity to ResNet-50. More importantly, our method achieves clearly better results compared with two recent works, i.e. Struct2Depth casser2019depth and Tosi et al. tosi2020distilled , which use explicit semantic labels to guide the learning of object motion, demonstrating the benefits of unsupervised segmentation.
|rel||sq rel||rmse||rmse (log)|
|Eigen et al. eigen2014depth||M + D||0.203||1.548||6.307||0.282||0.702||0.890||0.958|
|Liu et al. liu2015deep||M + D||0.202||1.614||6.523||0.275||0.678||0.895||0.965|
|Garg et al. garg2016unsupervised||S||0.169||1.080||5.104||0.273||0.740||0.904||0.962|
|Zhan et al. zhan2018unsupervised||S||0.144||1.391||5.869||0.241||0.803||0.933||0.971|
|MS-CRF xu2018monocular||M + D||0.125||0.899||4.685||-||0.816||0.951||0.983|
|Godard et al. et al. godard2017unsupervised||S||0.124||1.076||5.311||0.219||0.847||0.942||0.973|
|Kuznietsov et al. kuznietsov2017semi||S + D||0.113||0.741||4.621||0.189||0.862||0.960||0.986|
|Zhou et al. zhou2017unsupervised||M + V||0.208||1.768||6.858||0.283||0.678||0.885||0.957|
|Yang et al. yang2018unsupervised||M + V||0.182||1.481||6.501||0.267||0.725||0.906||0.963|
|Mahjourian mahjourian2018unsupervised||M + V||0.163||1.240||6.220||0.250||0.762||0.916||0.968|
|Geonet (ResNet) yin2018geonet||M + V||0.155||1.296||5.857||0.233||0.793||0.931||0.973|
|Wang et al. wang2017learning||M + V||0.151||1.257||5.583||0.228||0.810||0.936||0.974|
|DF-Net zou2018df||M + V||0.150||1.124||5.507||0.223||0.806||0.933||0.973|
|Struct2Depth casser2019depth||M + V||0.141||1.026||5.291||0.215||0.816||0.945||0.979|
|CC (ResNet) ranjan2019competitive||M + V||0.140||1.070||5.326||0.217||0.826||0.941||0.975|
|Bian et al. bian2019unsupervised||M + V||0.128||1.047||5.234||0.208||0.846||0.947||0.976|
|Gordon et al. gordon2019depth||M + V||0.128||0.959||5.230||–||–||–||–|
|Tosi et al. tosi2020distilled||M + V||0.125||0.805||4.795||0.195||0.849||0.955||0.983|
|Monodepth2 gordon2019depth||M + V||0.115||0.882||4.701||0.190||0.879||0.961||0.982|
|Ours (ResNet-18)||M + V||0.105||0.889||4.780||0.182||0.884||0.961||0.982|
|Ours (ResNet-50)||M + V||0.103||0.881||4.763||0.179||0.889||0.964||0.984|
Qualitative results on depth.
Fig. 2 shows a direct comparison of the depth estimates from our method, the most comparable baseline by Zhou et al. zhou2017unsupervised , and a stereo-based method garg2016unsupervised . Our method recovers much finer details, compared to a rigid-world model (4th column). It is also interesting to compare the level of detail with the stereo method (3rd column), which achieves better error metrics (table 2), but has relatively inconsistent fine details. Ours seems to strike a good balance between capturing the high-level layout and small-scale features. We also show qualitative results of our method in EPIC-Kitchens, for which there is no ground truth, in fig. 4. Despite the challenges of the quick camera and object motions in this setting, the quality of the recovered depths is apparent, making it possible to identify individual small objects and fine geometry.
Qualitative results on object discovery and motion prediction.
Since our proposed method can predict relative poses (6D motion) densely for the whole image and separate foreground pixels (with independent motions) from static background pixels (with a single coherent motion), it should be able to discover moving objects in the image automatically. We validate this idea by binarizing the mask(with a threshold of 0.7), and overlaying it on the original data. The resulting segmentations in EPIC-Kitchens can be visualized in fig. 5, along with the projected 3D geometry. We can observe the correct segmentation and clustering of the hands, and of objects as they are being held. We show more visualizations of the motion prediction in the suppl. material (Appendix B).
Although our model adds relatively few elements to view synthesis, it is important to know their relative impact on performance. We show the performance of our system with the addition of each element in tables 5-5. It is apparent that the biggest boost comes from adding our non-rigid model, especially in visual odometry performance. We also show a similar breakdown, but adding our improvements to the original SfMLearner system zhou2017unsupervised , which has a weaker backbone CNN and no depth normalization (see Appendix A for details). This shows that the benefits of our non-rigid model are complementary to other improvements, yet very significant.
We have proposed a simple approach to view synthesis for self-supervised learning, which leverages a successful rigid-world model and augments it with a locally-rigid model instead. This is done by strategic placement of tiling operators within the network, which is both efficient and produces highly consistent depth and pose estimates. Our change enables unsupervised object discovery by motion segmentation, and allows associating 3D pose and 6D motion to different objects in the scene. We also demonstrated a new state-of-the-art in unsupervised visual odometry and monocular depth estimation over comparable baselines. We hope that our contribution enables a new class of non-rigid SLAM algorithms, that continue the trend towards truly holistic scene understanding.
7 Broader impact
Our contributions improve the automatic understanding of 3D geometry, including camera and object motions through space. The most widespread applications of this technology nowadays are self-driving vehicles and robots meant to navigate human spaces (including indoors), which have a positive impact for society.
Given that the kind of perception we study has little semantic content, focusing instead on geometry, there is limited potential for harmful biases. It is conceivable that machines intended to cause harm on purpose could be built using computer vision technology, and that 3D environment perception would be one small part of such devices. This is a problem that we strongly believe that society as a whole needs to work through with appropriate regulations, and that in the case of 3D perception, the benefits (e.g. self-driving vehicle technology) outweigh the avoidable risks.
As for unintentional failure cases, we must point out that monocular depth estimation systems are inherently dependent on past experience to make accurate predictions in a given environment. As such, it is important that safety-critical systems (e.g. collision avoidance) do not depend solely on monocular estimates of depth since they may fail in unfamiliar situations; redundant systems (e.g. stereo, other sensors) are necessary.
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