The latest advancements in multi-modal large language models (MLLMs) have spurred a strong renewed interest in end-to-end motion planning approaches for autonomous driving. Many end-to-end approaches rely on human annotations to learn intermediate perception and prediction tasks, while purely self-supervised approaches—which directly learn from sensor inputs to generate planning trajectories without human annotations—often underperform the state of the art. We observe a key gap in the input representation space: end-to-end approaches built on MLLMs are often pretrained with reasoning tasks in 2D image space rather than the native 3D space in which autonomous vehicles plan. To this end, we propose S4-Driver, a scalable self-supervised motion planning algorithm with spatio-temporal visual representation, based on the popular PaLI [9] multimodal large language model. S4-Driver uses a novel sparse volume strategy to seamlessly transform the strong visual representation of MLLMs from perspective view to 3D space without the need to finetune the vision encoder. This representation aggregates multi-view and multi-frame visual inputs and enables better prediction of planning trajectories in 3D space. To validate our method, we run experiments on both nuScenes and Waymo Open Motion Dataset (with in-house camera data). Results show that S4-Driver performs favorably against existing supervised multi-task approaches while requiring no human annotations. It also demonstrates great scalability when pretrained on large volumes of unannotated driving logs.

The goal of traffic simulation is to augment a potentially limited amount of manually-driven miles that is available for testing and validation, with a much larger amount of simulated synthetic miles. The culmination of this vision would be a generative simulated city, where given a map of the city and an autonomous vehicle (AV) software stack, the simulator can seamlessly simulate the trip from point A to point B by populating the city around the AV and controlling all aspects of the scene, from animating the dynamic agents (e.g., vehicles, pedestrians) to controlling the traffic light states. We refer to this vision as CitySim, which requires an agglomeration of simulation technologies: scene generation to populate the initial scene, agent behavior modeling to animate the scene, occlusion reasoning, dynamic scene generation to seamlessly spawn and remove agents, and environment simulation for factors such as traffic lights. While some key technologies have been separately studied in various works, others such as dynamic scene generation and environment simulation have received less attention in the research community. We propose SceneDiffuser++, the first end-to-end generative world model trained on a single loss function capable of point A-to-B simulation on a city scale integrating all the requirements above. We demonstrate the city-scale traffic simulation capability of SceneDiffuser++ and study its superior realism under long simulation conditions. We evaluate the simulation quality on an augmented version of the Waymo Open Motion Dataset (WOMD) with larger map regions to support trip-level simulation.

Simulation is crucial for developing and evaluating autonomous vehicle (AV) systems. Recent literature builds on a new generation of generative models to synthesize highly realistic images for full-stack simulation. However, purely synthetically generated scenes are not grounded in reality and have difficulty in inspiring confidence in the relevance of its outcomes. Editing models, on the other hand, leverage source scenes from real driving logs, and enable the simulation of different traffic layouts, behaviors, and operating conditions such as weather and time of day. While image editing is an established topic in computer vision, it presents fresh sets of challenges in driving simulation: (1) the need for cross-camera 3D consistency, (2) learning “empty street” priors from driving data with foreground occlusions, and (3) obtaining paired image tuples of varied editing conditions while preserving consistent layout and geometry. To address these challenges, we propose SceneCrafter, a versatile editor for realistic 3D-consistent manipulation of driving scenes captured from multiple cameras. We build on recent advancements in multi-view diffusion models, using a fully controllable framework that scales seamlessly to multi-modality conditions like weather, time of day, agent boxes and high-definition maps. To generate paired data for supervising the editing model, we propose a novel framework on top of Prompt-to-Prompt [15] to generate geometrically consistent synthetic paired data with global edits. We also introduce an alpha-blending framework to synthesize data with local edits, leveraging a model trained on empty street priors through novel masked training and multi-view repaint paradigm. SceneCrafter demonstrates powerful editing capabilities and achieves state-of-the-art realism, controllability, 3D consistency, and scene editing quality compared to existing baselines.

Current autonomous driving systems rely on specialized models for perceiving and predicting motion, which demonstrate reliable performance in standard conditions. However, generalizing cost-effectively to diverse real-world scenarios remains a significant challenge. To address this, we propose Plug-and-Forecast (PnF), a plug-and-play approach that augments existing motion forecasting models with multimodal large language models (MLLMs). PnF builds on the insight that natural language provides a more effective way to describe and handle complex scenarios, enabling quick adaptation to targeted behaviors. We design prompts to extract structured scene understanding from MLLMs and distill this information into learnable embeddings to augment existing behavior prediction models. Our method leverages the zero-shot reasoning capabilities of MLLMs to achieve significant improvements in motion prediction performance, while requiring no fine-tuning—making it practical to adopt. We validate our approach on two state-of-the-art motion forecasting models using the Waymo Open Motion Dataset and the nuScenes Dataset, demonstrating consistent performance improvements across both benchmarks.

Recent advances in generative models have sparked exciting new possibilities in the field of autonomous vehicles. Specifically, video generation models are now being explored as controllable virtual testing environments. Simultaneously, end-to-end (E2E) driving models have emerged as a streamlined alternative to conventional modular autonomous driving systems, gaining popularity for their simplicity and scalability. However, the application of these techniques to simulation and planning raises important questions. First, while video generation models can generate increasingly realistic videos, can these videos faithfully adhere to the specified conditions and be realistic enough for E2E autonomous planner evaluation? Second, given that data is crucial for understanding and controlling E2E planners, how can we gain deeper insights into their biases and improve their ability to generalize to out-of-distribution scenarios? In this work, we bridge the gap between the driving models and generative world models (Drive&Gen) to address these questions. We propose novel statistical measures leveraging E2E drivers to evaluate the realism of generated videos. By exploiting the controllability of the video generation model, we conduct targeted experiments to investigate distribution gaps affecting E2E planner performance. Finally, we show that synthetic data produced by the video generation model offers a cost-effective alternative to real-world data collection. This synthetic data effectively improves E2E model generalization beyond existing Operational Design Domains, facilitating the expansion of autonomous vehicle services into new operational contexts.

Many existing motion prediction approaches rely on symbolic perception outputs to generate agent trajectories, such as bounding boxes, road graph information and traffic lights. This symbolic representation is a high-level abstraction of the real world, which may render the motion prediction model vulnerable to perception errors (e.g., failures in detecting open-vocabulary obstacles) while missing salient information from the scene context (e.g., poor road conditions). An alternative paradigm is end-to-end learning from raw sensors. However, this approach suffers from the lack of interpretability and requires significantly more training resources. In this work, we propose tokenizing the visual world into a compact set of scene elements and then leveraging pre-trained image foundation models and LiDAR neural networks to encode all the scene elements in an open-vocabulary manner. The image foundation model enables our scene tokens to encode the general knowledge of the open world while the LiDAR neural network encodes geometry information. Our proposed representation can efficiently encode the multi-frame multi-modality observations with a few hundred tokens and is compatible with most transformer-based architectures. To evaluate our method, we have augmented Waymo Open Motion Dataset with camera embeddings. Experiments over Waymo Open Motion Dataset show that our approach leads to significant performance improvements over the state-of-the-art.

Widely adopted motion forecasting datasets sub-stitute the observed sensory inputs with higher-level abstractions such as 3D boxes and polylines. These sparse shapes are inferred through annotating the original scenes with perception systems’ predictions. Such intermediate representations tie the quality of the motion forecasting models to the performance of computer vision models. Moreover, the human-designed explicit interfaces between perception and motion forecasting typically pass only a subset of the semantic information present in the original sensory input. To study the effect of these modular approaches, design new paradigms that mitigate these limitations, and accelerate the development of end-to-end motion forecasting models, we augment the Waymo Open Motion Dataset (WOMD) with large-scale, high-quality, diverse LiDAR data for the motion forecasting task.The new augmented dataset (WOMD-LiDAR)1consists of over 100,000 scenes that each spans 20 seconds, consisting of well-synchronized and calibrated high quality LiDAR point clouds captured across a range of urban and suburban geographies. Compared to Waymo Open Dataset (WOD), WOMDLiDAR dataset contains 100× more scenes. Furthermore, we integrate the LiDAR data into the motion forecasting model training and provide a strong baseline. Experiments show that the LiDAR data brings improvement in the motion forecasting task. We hope that WOMD-LiDAR will provide new opportunities for boosting end-to-end motion forecasting models.

The 3D Average Precision (3DAP) relies on the intersection over union between predictions and ground truth objects. However, camera-only detectors have limited depth accuracy, which may cause otherwise reasonable predictions that suffer from such longitudinal localization errors to be treated as false positives. We therefore propose variants of the 3DAP metric to be more permissive with respect to depth estimation errors. Specifically, our novel longitudinal error tolerant metrics, LET-3D-AP and LET-3D-APL, allow longitudinal localization errors of the prediction boxes up to a given tolerance. To evaluate the proposed metrics, we also construct a new test set for the Waymo Open Dataset, tailored to camera-only 3D detection methods. Surprisingly, we find that state-of-the-art camera-based detectors can outperform popular LiDAR-based detectors with our new metrics past at 10% depth error tolerance, suggesting that existing camera-based detectors already have the potential to surpass LiDAR-based detectors in downstream applications. We believe the proposed metrics and the new benchmark dataset will facilitate advances in the field of camera-only 3D detection by providing more informative signals that can better indicate the system-level performance.

3D object detectors for point clouds often rely on a pooling-based PointNet [20] to encode sparse points into grid-like voxels or pillars. In this paper, we identify that the common PointNet design introduces an information bottleneck that limits 3D object detection accuracy and scalability. To address this limitation, we propose PVTransformer: a transformer-based point-to-voxel architecture for 3D detection. Our key idea is to replace the PointNet pooling operation with an attention module, leading to a better point-to-voxel aggregation function. Our design respects the permutation invariance of sparse 3D points while being more expressive than the pooling-based PointNet. Experimental results show our PVTransformer achieves much better performance compared to the latest 3D object detectors. On the widely used Waymo Open Dataset, our PVTransformer achieves state-of-the-art 76.5 mAPH L2, outperforming the prior art of SWFormer [27] by +1.7 mAPH L2.

Simulation with realistic and interactive agents represents a key task for autonomous vehicle (AV) software development in order to test AV performance in prescribed, often long-tail scenarios. In this work, we propose SceneDiffuser, a scene-level diffusion prior for traffic simulation. We present a singular framework that unifies two key stages of simulation: scene initialization and scene rollout. Scene initialization refers to generating the initial layout for the traffic in a scene, and scene rollout refers to closed-loop simulation for the behaviors of the agents. While diffusion has been demonstrated to be effective in learning realistic, multimodal agent distributions, two open challenges remain: controllability and closed-loop inference efficiency and realism. To this end, to address controllability challenges, we propose generalized hard constraints, a generalized inference-time constraint mechanism that is simple yet effective. To improve closed-loop inference quality and efficiency, we propose amortized diffusion, a novel diffusion denoising paradigm that amortizes the physical cost of denoising over future simulation rollout steps, reducing the cost of per physical rollout step to a single denoising function evaluation, while dramatically reducing closed-loop errors. We demonstrate the effectiveness of our approach on the Waymo Open Dataset, where we are able to generate distributionally realistic scenes, while obtaining competitive performance in the Sim Agents Challenge, surpassing the state-of-the-art in many realism attributes.

2D-to-3D reconstruction is an ill-posed problem, yet humans are good at solving this problem due to their prior knowledge of the 3D world developed over years. Driven by this observation, we propose NeRDi, a single-view NeRF synthesis framework with general image priors from 2D diffusion models. Formulating single-view reconstruction as an image-conditioned 3D generation problem, we optimize the NeRF representations by minimizing a diffusion loss on its arbitrary view renderings with a pretrained image diffusion model under the input-view constraint. We leverage off-the-shelf vision-language models and introduce a two-section language guidance as conditioning inputs to the diffusion model. This is essentially helpful for improving multiview content coherence as it narrows down the general image prior conditioned on the semantic and visual features of the single-view input image. Additionally, we introduce a geometric loss based on estimated depth maps to regularize the underlying 3D geometry of the NeRF. Experimental results on the DTU MVS dataset show that our method can synthesize novel views with higher quality even compared to existing methods trained on this dataset. We also demonstrate our generalizability in zero-shot NeRF synthesis for in-the-wild images.

We present MotionDiffuser, a diffusion based representation for the joint distribution of future trajectories over multiple agents. Such representation has several key advantages: first, our model learns a highly multimodal distribution that captures diverse future outcomes. Second, the simple predictor design requires only a single L2 loss training objective, and does not depend on trajectory anchors. Third, our model is capable of learning the joint distribution for the motion of multiple agents in a permutation-invariant manner. Furthermore, we utilize a compressed trajectory representation via PCA, which improves model performance and allows for efficient computation of the exact sample log probability. Subsequently, we propose a general constrained sampling framework that enables controlled trajectory sampling based on differentiable cost functions. This strategy enables a host of applications such as enforcing rules and physical priors, or creating tailored simulation scenarios. MotionDiffuser can be combined with existing backbone architectures to achieve top motion forecasting results. We obtain state-of-the-art results for multi-agent motion prediction on the Waymo Open Motion Dataset.

Occluded and long-range objects are ubiquitous and challenging for 3D object detection. Point cloud sequence data provide unique opportunities to improve such cases, as an occluded or distant object can be observed from different viewpoints or gets better visibility over time. However, the efficiency and effectiveness in encoding longterm sequence data can still be improved. In this work, we propose MoDAR, using motion forecasting outputs as a type of virtual modality, to augment LiDAR point clouds. The MoDAR modality propagates object information from temporal contexts to a target frame, represented as a set of virtual points, one for each object from a waypoint on a forecasted trajectory. A fused point cloud of both raw sensor points and the virtual points can then be fed to any off-the-shelf point-cloud based 3D object detector. Evaluated on the Waymo Open Dataset, our method significantly improves prior art detectors by using motion forecasting from extra-long sequences (e.g. 18 seconds), achieving new state of the arts, while not adding much computation overhead.

Modeling the 3D world from sensor data for simulation is a scalable way of developing testing and validation environments for robotic learning problems such as autonomous driving. However, manually creating or recreating real-world-like environments is difficult, expensive, and not scalable. Recent generative model techniques have shown promising progress to address such challenges by learning 3D assets using only plentiful 2D images - but still suffer limitations as they leverage either human-curated image datasets or renderings from manually-created synthetic 3D environments. In this paper, we introduce GINA-3D, a generative model that uses real-world driving data from camera and LiDAR sensors to create realistic 3D implicit neural assets of diverse vehicles and pedestrians. Compared to the existing image datasets, the real-world driving setting poses new challenges due to occlusions, lighting-variations and longtail distributions. GINA-3D tackles these challenges by decoupling representation learning and generative modeling into two stages with a learned triplane latent structure, inspired by recent advances in generative modeling of images. To evaluate our approach, we construct a large-scale object-centric dataset containing over 520K images of vehicles and pedestrians from the Waymo Open Dataset, and a new set of 80K images of longtail instances such as construction equipment, garbage trucks, and cable cars. We compare our model with existing approaches and demonstrate that it achieves state-of-the-art performance in quality and diversity for both generated images and geometries.

Training a 3D human keypoint detector from point clouds in a supervised manner requires large volumes of high quality labels. While it is relatively easy to capture large amounts of human point clouds, annotating 3D key-points is expensive, subjective, error prone and especially difficult for long-tail cases (pedestrians with rare poses, scooterists, etc.). In this work, we propose GC-KPL - Geometry Consistency inspired Key Point Leaning, an approach for learning 3D human joint locations from point clouds without human labels. We achieve this by our novel unsupervised loss formulations that account for the structure and movement of the human body. We show that by training on a large training set from Waymo Open Dataset [21] without any human annotated keypoints, we are able to achieve reasonable performance as compared to the fully supervised approach. Further, the backbone benefits from the unsupervised training and is useful in downstream few-shot learning of keypoints, where fine-tuning on only 10 percent of the labeled training data gives comparable performance to fine-tuning on the entire set. We demonstrated that GC-KPL outperforms by a large margin over SoTA when trained on entire dataset and efficiently leverages large volumes of unlabeled data.

Closed-set 3D perception models trained on only a predefined set of object categories can be inadequate for safety critical applications such as autonomous driving where new object types can be encountered after deployment. In this paper, we present a multi-modal auto labeling pipeline capable of generating amodal 3D bounding boxes and tracklets for training models on open-set categories without 3D human labels. Our pipeline exploits motion cues inherent in point cloud sequences in combination with the freely available 2D image-text pairs to identify and track all traffic participants. Compared to the recent studies in this domain, which can only provide class-agnostic auto labels limited to moving objects, our method can handle both static and moving objects in the unsupervised manner and is able to output open-vocabulary semantic labels thanks to the proposed vision-language knowledge distillation. Experiments on the Waymo Open Dataset show that our approach outperforms the prior work by significant margins on various unsupervised 3D perception tasks.

Data augmentations are important for training high-performance 3D object detectors that use point clouds. Despite recent efforts on designing new data augmentations, perhaps surprisingly, most current state-of-the-art 3D detectors only rely on a few simple data augmentations. In particular, different from 2D image data augmentations, 3D data augmentations need to account for different representations of input data and require being customized for different models, which introduces significant overhead. In this paper, we propose LidarAugment, a practical and effective data augmentation strategy for 3D object detection. Unlike previous methods, which require tuning all augmentation policies in an exponentially large search space, we propose to factorize and align the search space of each data augmentation, which cuts down the 20+ hyperparameters to 2, and significantly reduces the search complexity. We show LidarAugment can be easily adapted to different model architectures with different input representations by a simple 2D grid search, and consistently improve a range of detectors including both convolution-based UPillars/StarNet/RSN and transformer-based SWFormer. Furthermore, Lidar Augment mitigates overfitting and enables 3D detectors to scale up to larger capacities. When combined with the latest 3D detectors, Lidar Augment achieves a new state-of-the-art 74.8 mAPH L2 on the Waymo Open Dataset.

We propose a late-to-early recurrent feature fusion scheme for 3D object detection using temporal LiDAR point clouds. Our main motivation is fusing object-aware latent embeddings into the early stages of a 3D object detector. This feature fusion strategy enables the model to better capture the shapes and poses for challenging objects, compared with learning from raw points directly. Our method conducts late-to-early feature fusion in a recurrent manner. This is achieved by enforcing window-based attention blocks upon temporally calibrated and aligned sparse pillar tokens. Leveraging bird's eye view foreground pillar segmentation, we reduce the number of sparse history features that our model needs to fuse into its current frame by 10x. We also propose a stochastic-length FrameDrop training technique, which generalizes the model to variable frame lengths at inference for improved performance without retraining. We evaluate our method on the widely adopted Waymo Open Dataset and demonstrate improvement on 3D object detection against the baseline model, especially for the challenging category of large objects.

Imitation learning (IL) is a simple and powerful way to use high-quality human driving data, which can be collected at scale, to produce human-like behavior. However, policies based on imitation learning alone often fail to sufficiently account for safety and reliability concerns. In this paper, we show how imitation learning combined with reinforcement learning using simple rewards can substan-tially improve the safety and reliability of driving policies over those learned from imitation alone. In particular, we train a policy on over lOOk miles of urban driving data, and measure its effectiveness in test scenarios grouped by different levels of collision likelihood. Our analysis shows that while imitation can perform well in low-difficulty scenarios that are well-covered by the demonstration data, our proposed approach significantly improves robustness on the most challenging scenarios (over 38 % reduction in failures). To our knowledge, this is the first application of a combined imitation and reinforcement learning approach in autonomous driving that utilizes large amounts of real- world human driving data.

Simulation is an essential tool to develop and benchmark autonomous vehicle planning software in a safe and cost-effective manner. However, realistic simulation requires accurate modeling of multi-agent interactive behaviors to be trustworthy, behaviors which can be highly nuanced and complex. To address these challenges, we introduce Waymax, a new data-driven simulator for autonomous driving in multi-agent scenes, designed for large-scale simulation and testing. Waymax uses publicly-released, real-world driving data (e.g., the Waymo Open Motion Dataset) to initialize or play back a diverse set of multi-agent simulated scenarios. It runs entirely on hardware accelerators such as TPUs/GPUs and supports in-graph simulation for training, making it suitable for modern large-scale, distributed machine learning workflows. To support online training and evaluation, Waymax includes several learned and hard-coded behavior models that allow for realistic interaction within simulation. To supplement Waymax, we benchmark a suite of popular imitation and reinforcement learning algorithms with ablation studies on different design decisions, where we highlight the effectiveness of routes as guidance for planning agents and the ability of RL to overfit against simulated agents.

Simulation with realistic, interactive agents represents a key task for autonomous vehicle software development. In this work, we introduce the Waymo Open Sim Agents Challenge (WOSAC). WOSAC is the first public challenge to tackle this task and propose corresponding metrics. The goal of the challenge is to stimulate the design of realistic simulators that can be used to evaluate and train a behavior model for autonomous driving. We outline our evaluation methodology, present results for a number of different baseline simulation agent methods, and analyze several submissions to the 2023 competition which ran from March 16, 2023 to May 23, 2023. The WOSAC evaluation server remains open for submissions and we discuss open problems for the task.

Lidars are depth measuring sensors widely used in autonomous driving and augmented reality. However, the large volume of data produced by lidars can lead to high costs in data storage and transmission. While lidar data can be represented as two interchangeable representations: 3D point clouds and range images, most previous work focus on compressing the generic 3D point clouds. In this work, we show that directly compressing the range images can leverage the lidar scanning pattern, compared to compressing the unprojected point clouds. We propose a novel datadriven range image compression algorithm, named RIDDLE (Range Image Deep DeLta Encoding). At its core is a deep model that predicts the next pixel value in a raster scanning order, based on contextual laser shots from both the current and past scans (represented as a 4D point cloud of spherical coordinates and time). The deltas between predictions and original values can then be compressed by entropy encoding. Evaluated on the Waymo Open Dataset and KITTI, our method demonstrates significant improvement in the compression rate (under the same distortion) compared to widely used point cloud and range image compression algorithms as well as recent deep methods.

Simulation is a crucial tool for accelerating the development of autonomous vehicles. Making simulation realistic requires models of the human road users who interact with such cars. Such models can be obtained by applying learning from demonstration (LfD) to trajectories observed by cars already on the road. However, existing LfD methods are typically insufficient, yielding policies that frequently collide or drive off the road. To address this problem, we propose Symphony, which greatly improves realism by combining conventional policies with a parallel beam search. The beam search refines these policies on the fly by pruning branches that are unfavourably evaluated by a discriminator. However, it can also harm diversity, i.e., how well the agents cover the entire distribution of realistic behaviour, as pruning can encourage mode collapse. Symphony addresses this issue with a hierarchical approach, factoring agent behaviour into goal generation and goal conditioning. The use of such goals ensures that agent diversity neither disappears during adversarial training nor is pruned away by the beam search. Experiments on both proprietary and open Waymo datasets confirm that Symphony agents learn more realistic and diverse behaviour than several baselines.

Monocular image-based 3D perception has become an active research area in recent years owing to its applications in autonomous driving. Approaches to monocular 3D perception including detection and tracking, however, often yield inferior performance when compared to LiDAR-based techniques. Through systematic analysis, we identified that per-object depth estimation accuracy is a major factor bounding the performance. Motivated by this observation, we propose a multi-level fusion method that combines different representations (RGB and pseudo-LiDAR) and temporal information across multiple frames for objects (tracklets) to enhance per-object depth estimation. Our proposed fusion method achieves the state-of-the-art performance of per-object depth estimation on the Waymo Open Dataset, the KITTI detection dataset, and the KITTI MOT dataset. We further demonstrate that by simply replacing estimated depth with fusion-enhanced depth, we can achieve significant improvements in monocular 3D perception tasks, including detection and tracking.

We introduce a motion forecasting (behavior prediction) method that meets the latency requirements for autonomous driving in dense urban environments without sacrificing accuracy. A whole-scene sparse input representation allows StopNet to scale to predicting trajectories for hundreds of road agents with reliable latency. In addition to predicting trajectories, our scene encoder lends itself to predicting whole-scene probabilistic occupancy grids, a complementary output representation suitable for busy urban environments. Occupancy grids allow the AV to reason collectively about the behavior of groups of agents without processing their individual trajectories. We demonstrate the effectiveness of our sparse input representation and our model in terms of computation and accuracy over three datasets. We further show that co-training consistent trajectory and occupancy predictions improves upon state-of-the-art performance under standard metrics.

Predicting the future behavior of road users is one of the most challenging and important problems in autonomous driving. Applying deep learning to this problem requires fusing heterogeneous world state in the form of rich perception signals and map information, and inferring highly multi-modal distributions over possible futures. In this paper, we present MultiPath++, a future prediction model that achieves state-of-the-art performance on popular benchmarks. MultiPath++ improves the MultiPath architecture [34] by revisiting many design choices. The first key design difference is a departure from dense image-based encoding of the input world state in favor of a sparse encoding of heterogeneous scene elements: MultiPath++ consumes compact and efficient polylines to describe road features, and raw agent state information directly (e.g., position, velocity, acceleration). We propose a context-aware fusion of these elements and develop a reusable multi-context gating fusion component. Second, we reconsider the choice of pre-defined static anchors, and develop a way to learn latent anchor embeddings end-to-end in the model. Lastly, we explore ensembling and output aggregation techniques—common in other ML domains—and find effective variants for our probabilistic multimodal output representation. We perform an extensive ablation on these design choices, and show that our proposed model achieves state-of-the-art performance on the Argoverse Motion Forecasting Competition [10] and the Waymo Open Dataset Motion Prediction Challenge [13].

While multi-class 3D detectors are needed in many robotics applications, training them with fully labeled datasets can be expensive in labeling cost. An alternative approach is to have targeted single-class labels on disjoint data samples. In this paper, we are interested in training a multi-class 3D object detection model, while using these single-class labeled data. We begin by detailing the unique stance of our “Single-Class Supervision” (SCS) setting with respect to related concepts such as partial supervision and semi supervision. Then, based on the case study of training the multi-class version of Range Sparse Net (RSN), we adapt a spectrum of algorithms - from supervised learning to pseudo-labeling - to fully exploit the properties of our SCS setting, and perform extensive ablation studies to identify the most effective algorithm and practice. Empirical experiments on the Waymo Open Dataset show that proper training under SCS can approach or match full supervision training while saving labeling costs.

We demonstrate the first large-scale application of model-based generative adversarial imitation learning (MGAIL) to the task of dense urban self-driving. We augment standard MGAIL using a hierarchical model to enable generalization to arbitrary goal routes, and measure performance using a closed-loop evaluation framework with simulated interactive agents. We train policies from expert trajectories collected from real vehicles driving over 100,000 miles in San Francisco, and demonstrate a steerable policy that can navigate robustly even in a zero-shot setting, generalizing to synthetic scenarios with novel goals that never occurred in real-world driving. We also demonstrate the importance of mixing closed-loop MGAIL losses with open-loop behavior cloning losses, and show our best policy approaches the performance of the expert. We evaluate our imitative model in both average and challenging scenarios, and show how it can serve as a useful prior to plan successful trajectories.

3D object detection is vital for many robotics applications. For tasks where a 2D perspective range image exists, we propose to learn a 3D representation directly from this range image view. To this end, we designed a 2D convolutional network architecture that carries the 3D spherical coordinates of each pixel throughout the network. Its layers can consume any arbitrary convolution kernel in place of the default inner product kernel and exploit the underlying local geometry around each pixel. We outline four such kernels: a dense kernel according to the bag-of-words paradigm, and three graph kernels inspired by recent graph neural network advances: the Transformer, the PointNet, and the Edge Convolution. We also explore cross-modality fusion with the camera image, facilitated by operating in the perspective range image view. Our method performs competitively on the Waymo Open Dataset and improves the state-of-the-art AP for pedestrian detection from 69.7% to 75.5%. It is also efficient in that our smallest model, which still outperforms the popular PointPillars in quality, requires 180 times fewer FLOPS and model parameters.

High Definition (HD) maps are maps with precise definitions of road lanes with rich semantics of the traffic rules. They are critical for several key stages in an autonomous driving system, including motion forecasting and planning. However, there are only a small amount of real-world road topologies and geometries, which significantly limits our ability to test out the self-driving stack to generalize onto new unseen scenarios. To address this issue, we introduce a new challenging task to generate HD maps. In this work, we explore several autoregressive models using different data representations, including sequence, plain graph, and hierarchical graph. We propose HDMapGen, a hierarchical graph generation model capable of producing high-quality and diverse HD maps through a coarse-to-fine approach. Experiments on the Argoverse dataset and an inhouse dataset show that HDMapGen significantly outperforms baseline methods. Additionally, we demonstrate that HDMapGen achieves high scalability and efficiency.

While current 3D object recognition research mostly focuses on the real-time, onboard scenario, there are many offboard use cases of perception that are largely underexplored, such as using machines to automatically generate high-quality 3D labels. Existing 3D object detectors fail to satisfy the high-quality requirement for offboard uses due to the limited input and speed constraints. In this paper, we propose a novel offboard 3D object detection pipeline using point cloud sequence data. Observing that different frames capture complementary views of objects, we design the offboard detector to make use of the temporal points through both multi-frame object detection and novel objectcentric refinement models. Evaluated on the Waymo Open Dataset, our pipeline named 3D Auto Labeling shows significant gains compared to the state-of-the-art onboard detectors and our offboard baselines. Its performance is even on par with human labels verified through a human label study. Further experiments demonstrate the application of auto labels for semi-supervised learning and provide extensive analysis to validate various design choices.

The detection of 3D objects from LiDAR data is a critical component in most autonomous driving systems. Safe, high speed driving needs larger detection ranges, which are enabled by new LiDARs. These larger detection ranges require more efficient and accurate detection models. Towards this goal, we propose Range Sparse Net (RSN) – a simple, efficient, and accurate 3D object detector – in order to tackle real time 3D object detection in this extended detection regime. RSN predicts foreground points from range images and applies sparse convolutions on the selected foreground points to detect objects. The lightweight 2D convolutions on dense range images results in significantly fewer selected foreground points, thus enabling the later sparse convolutions in RSN to efficiently operate. Combining features from the range image further enhance detection accuracy. RSN runs at more than 60 frames per second on a 150m × 150m detection region on Waymo Open Dataset (WOD) while being more accurate than previously published detectors. As of 11/2020, RSN is ranked first in the WOD leaderboard based on the APH/LEVEL_1 metrics for LiDAR-based pedestrian and vehicle detection, while being several times faster than alternatives.

As autonomous driving systems mature, motion forecasting has received increasing attention as a critical requirement for planning. Of particular importance are interactive situations such as merges, unprotected turns, etc., where predicting individual object motion is not sufficient. Joint predictions of multiple objects are required for effective route planning. There has been a critical need for high-quality motion data that is rich in both interactions and annotation to develop motion planning models. In this work, we introduce the most diverse interactive motion dataset to our knowledge, and provide specific labels for interacting objects suitable for developing joint prediction models. With over 100,000 scenes, each 20 seconds long at 10 Hz, our new dataset contains more than 570 hours of unique data over 1750 km of roadways. It was collected by mining for interesting interactions between vehicles, pedestrians, and cyclists across six cities within the United States. We use a high-accuracy 3D auto-labeling system to generate high quality 3D bounding boxes for each road agent, and provide corresponding high definition 3D maps for each scene. Furthermore, we introduce a new set of metrics that provides a comprehensive evaluation of both single agent and joint agent interaction motion forecasting models. Finally, we provide strong baseline models for individual-agent prediction and joint-prediction. We hope that this new large-scale interactive motion dataset will provide new opportunities for advancing motion forecasting models.

In autonomous driving, a LiDAR-based object detector should perform reliably at different geographic locations and under various weather conditions. While recent 3D detection research focuses on improving performance within a single domain, our study reveals that the performance of modern detectors can drop drastically cross-domain. In this paper, we investigate unsupervised domain adaptation (UDA) for LiDAR-based 3D object detection. On the Waymo Domain Adaptation [49] dataset, we identify the deteriorating point cloud quality as the root cause of the performance drop. To address this issue, we present Semantic Point Generation (SPG), a general approach to enhance the reliability of LiDAR detectors against domain shifts. Specifically, SPG generates semantic points at the predicted fore-ground regions and faithfully recovers missing parts of the foreground objects, which are caused by phenomena such as occlusions, low reflectance, or weather interference. By merging the semantic points with the original points, we obtain an augmented point cloud, which can be directly consumed by modern LiDAR-based detectors. To validate the wide applicability of SPG, we experiment with two representative detectors, PointPillars [22] and PV-RCNN [45]. On the UDA task, SPG significantly improves both detectors across all object categories of interest and at all difficulty levels. SPG can also benefit object detection in the original domain. On the Waymo Open Dataset [49] and KITTI [17], SPG improves 3D detection results of these two methods across all categories. Combined with PV-RCNN [45], SPG achieves state-of-the-art 3D detection results on KITTI.

Interactive driving scenarios, such as lane changes, merges and unprotected turns, are some of the most challenging situations for autonomous driving. Planning in interactive scenarios requires accurately modeling the reactions of other agents to different future actions of the ego agent. We develop end-to-end models for conditional behavior prediction (CBP) that take as an input a query future trajectory for an ego-agent, and predict distributions over future trajectories for other agents conditioned on the query. Leveraging such a model, we develop a general-purpose agent interactivity score derived from probabilistic first principles. The interactivity score allows us to find interesting interactive scenarios for training and evaluating behavior prediction models. We further demonstrate that the proposed score is effective for agent prioritization under computational budget constraints.

3D object detection is a key module for safety-critical robotics applications such as autonomous driving. For these applications, we care most about how the detections affect the ego-agent’s behavior and safety (the egocentric perspective). Intuitively, we seek more accurate descriptions of object geometry when it’s more likely to interfere with the ego-agent’s motion trajectory. However, current detection metrics, based on box Intersection-over-Union (IoU), are object-centric and aren’t designed to capture the spatio-temporal relationship between objects and the ego-agent. To address this issue, we propose a new egocentric measure to evaluate 3D object detection, namely Support Distance Error (SDE). Our analysis based on SDE reveals that the egocentric detection quality is bounded by the coarse geometry of the bounding boxes. Given the insight that SDE would benefit from more accurate geometry descriptions, we propose to represent objects as amodal contours, specifically amodal star-shaped polygons, and devise a simple model, StarPoly, to predict such contours. Our experiments on the large-scale Waymo Open Dataset show that SDE better reflects the impact of detection quality on the ego-agent’s safety compared to IoU; and the estimated contours from StarPoly consistently improve the egocentric detection quality over recent 3D object detectors.

Behavior prediction in dynamic, multi-agent systems is an important problem in the context of self-driving cars, due to the complex representations and interactions of road components, including moving agents (e.g. pedestrians and vehicles) and road context information (e.g. lanes, traffic lights). This paper introduces VectorNet, a hierarchical graph neural network that first exploits the spatial locality of individual road components represented by vectors and then models the high-order interactions among all components. In contrast to most recent approaches, which render trajectories of moving agents and road context information as bird-eye images and encode them with convolutional neural networks (ConvNets), our approach operates on the primitive vector representation. By operating on the vectorized high definition (HD) maps and agent trajectories, we avoid lossy rendering and computationally intensive ConvNet encoding steps. To further boost VectorNet's capability in learning context features, we propose a novel auxiliary task to recover the randomly masked out map entities and agent trajectories based on their context. We evaluate VectorNet on our in-house behavior prediction benchmark and the recently released Argoverse forecasting dataset. Our method achieves on par or better performance than the competitive rendering approach on both benchmarks while saving over 70% of the model parameters with an order of magnitude reduction in FLOPs. It also obtains state-of-the-art performance on the Argoverse dataset.

The research community has increasing interest in autonomous driving research, despite the resource intensity of obtaining representative real world data. Existing self-driving datasets are limited in the scale and variation of the environments they capture, even though generalization within and between operating regions is crucial to the over-all viability of the technology. In an effort to help align the research community’s contributions with real-world self-driving problems, we introduce a new large scale, high quality, diverse dataset. Our new dataset consists of 1150 scenes that each span 20 seconds, consisting of well synchronized and calibrated high quality LiDAR and camera data captured across a range of urban and suburban geographies. It is 15x more diverse than the largest camera+LiDAR dataset available based on our proposed diversity metric. We exhaustively annotated this data with 2D (camera image) and 3D (LiDAR) bounding boxes, with consistent identifiers across frames. Finally, we provide strong baselines for 2D as well as 3D detection and tracking tasks. We further study the effects of dataset size and generalization across geographies on 3D detection methods. Find data, code and more up-to-date information at http://www.waymo.com/open.

Autonomous driving system development is critically dependent on the ability to replay complex and diverse traffic scenarios in simulation. In such scenarios, the ability to accurately simulate the vehicle sensors such as cameras, lidar or radar is hugely helpful. However, current sensor simulators leverage gaming engines such as Unreal or Unity, requiring manual creation of environments, objects, and material properties. Such approaches have limited scalability and fail to produce realistic approximations of camera, lidar, and radar data without significant additional work. In this paper, we present a simple yet effective approach to generate realistic scenario sensor data, based only on a limited amount of lidar and camera data collected by an autonomous vehicle. Our approach uses texture-mapped surfels to efficiently reconstruct the scene from an initial vehicle pass or set of passes, preserving rich information about object 3D geometry and appearance, as well as the scene conditions. We then leverage a SurfelGAN network to reconstruct realistic camera images for novel positions and orientations of the self-driving vehicle and moving objects in the scene. We demonstrate our approach on the Waymo Open Dataset and show that it can synthesize realistic camera data for simulated scenarios. We also create a novel dataset that contains cases in which two self-driving vehicles observe the same scene at the same time. We use this dataset to provide additional evaluation and demonstrate the usefulness of our SurfelGAN model.

Detecting pedestrians and predicting future trajectories for them are critical tasks for numerous applications, such as autonomous driving. Previous methods either treat the detection and prediction as separate tasks or simply add a trajectory regression head on top of a detector. In this work, we present a novel end-to-end two-stage network: Spatio-Temporal-Interactive Network (STINet). In addition to 3D geometry modeling of pedestrians, we model the temporal information for each of the pedestrians. To do so, our method predicts both current and past locations in the first stage, so that each pedestrian can be linked across frames and the comprehensive spatio-temporal information can be captured in the second stage. Also, we model the interaction among objects with an interaction graph, to gather the information among the neighboring objects. Comprehensive experiments on the Lyft Dataset and the recently released large-scale Waymo Open Dataset for both object detection and future trajectory prediction validate the effectiveness of the proposed method. For the Waymo Open Dataset, we achieve a bird-eyes-view (BEV) detection AP of 80.73 and trajectory prediction average displacement error (ADE) of 33.67cm for pedestrians, which establish the state-of-the-art for both tasks.

The vast majority of deep models use multiple gradient signals, typically corresponding to a sum of multiple loss terms, to update a shared set of trainable weights. However, these multiple updates can impede optimal training by pulling the model in conflicting directions. We present Gradient Sign Dropout (GradDrop), a probabilistic masking procedure which samples gradients at an activation layer based on their level of consistency. GradDrop is implemented as a simple deep layer that can be used in any deep net and synergizes with other gradient balancing approaches. We show that GradDrop outperforms the state-of-the-art multiloss methods within traditional multitask and transfer learning settings, and we discuss how GradDrop reveals links between optimal multiloss training and gradient stochasticity.

We present PointFusion, a generic 3D object detection method that leverages both image and 3D point cloud information. Unlike existing methods that either use multistage pipelines or hold sensor and dataset-specific assumptions, PointFusion is conceptually simple and application-agnostic. The image data and the raw point cloud data are independently processed by a CNN and a PointNet architecture, respectively. The resulting outputs are then combined by a novel fusion network, which predicts multiple 3D box hypotheses and their confidences, using the input 3D points as spatial anchors. We evaluate PointFusion on two distinctive datasets: the KITTI dataset that features driving scenes captured with a lidar-camera setup, and the SUN-RGBD dataset that captures indoor environments with RGB-D cameras. Our model is the first one that is able to perform better or on-par with the state-of-the-art on these diverse datasets without any dataset-specific model tuning.

We present a method for 3D object detection and pose estimation from a single image. In contrast to current techniques that only regress the 3D orientation of an object, our method first regresses relatively stable 3D object properties using a deep convolutional neural network and then combines these estimates with geometric constraints provided by a 2D object bounding box to produce a complete 3D bounding box. The first network output estimates the 3D object orientation using a novel hybrid discrete-continuous loss, which significantly outperforms the L2 loss. The second output regresses the 3D object dimensions, which have relatively little variance compared to alternatives and can often be predicted for many object types. These estimates, combined with the geometric constraints on translation imposed by the 2D bounding box, enable us to recover a stable and accurate 3D object pose. We evaluate our method on the challenging KITTI object detection benchmark [2] both on the official metric of 3D orientation estimation and also on the accuracy of the obtained 3D bounding boxes. Although conceptually simple, our method outperforms more complex and computationally expensive approaches that leverage semantic segmentation, instance level segmentation and flat ground priors [4] and sub-category detection [23][24]. Our discrete-continuous loss also produces state of the art results for 3D viewpoint estimation on the Pascal 3D+ dataset[26].

This paper introduces self-taught object localization, a novel approach that leverages deep convolutional networks trained for whole-image recognition to localize objects in images without additional human supervision, i.e., without using any ground-truth bounding boxes for training. The key idea is to analyze the change in the recognition scores when artificially masking out different regions of the image. The masking out of a region that includes the object typically causes a significant drop in recognition score. This idea is embedded into an agglomerative clustering technique that generates self-taught localization hypotheses. Our object localization scheme outperforms existing proposal methods in both precision and recall for small number of subwindow proposals (e.g., on ILSVRC-2012 it produces a relative gain of 23.4% over the state-of-the-art for top-1 hypothesis). Furthermore, our experiments show that the annotations automatically-generated by our method can be used to train object detectors yielding recognition results remarkably close to those obtained by training on manually-annotated bounding boxes.

We propose a deep convolutional neural network architecture codenamed Inception that achieves the new state of the art for classification and detection in the ImageNet Large-Scale Visual Recognition Challenge 2014 (ILSVRC14). The main hallmark of this architecture is the improved utilization of the computing resources inside the network. By a carefully crafted design, we increased the depth and width of the network while keeping the computational budget constant. To optimize quality, the architectural decisions were based on the Hebbian principle and the intuition of multi-scale processing. One particular incarnation used in our submission for ILSVRC14 is called GoogLeNet, a 22 layers deep network, the quality of which is assessed in the context of classification and detection.

Deep convolutional neural networks have recently achieved state-of-the-art performance on a number of image recognition benchmarks, including the ImageNet Large-Scale Visual Recognition Challenge (ILSVRC-2012). The winning model on the localization sub-task was a network that predicts a single bounding box and a confidence score for each object category in the image. Such a model captures the whole-image context around the objects but cannot handle multiple instances of the same object in the image without naively replicating the number of outputs for each instance. In this work, we propose a saliency-inspired neural network model for detection, which predicts a set of class-agnostic bounding boxes along with a single score for each box, corresponding to its likelihood of containing any object of interest. The model naturally handles a variable number of instances for each class and allows for cross-class generalization at the highest levels of the network. We are able to obtain competitive recognition performance on VOC2007 and ILSVRC2012, while using only the top few predicted locations in each image and a small number of neural network evaluations.

We argue that object subcategories follow a long-tail distribution: a few subcategories are common, while many are rare. We describe distributed algorithms for learning large- mixture models that capture long-tail distributions, which are hard to model with current approaches. We introduce a generalized notion of mixtures (or subcategories) that allow for examples to be shared across multiple subcategories. We optimize our models with a discriminative clustering algorithm that searches over mixtures in a distributed, "brute-force" fashion. We used our scalable system to train tens of thousands of deformable mixtures for VOC objects. We demonstrate significant performance improvements, particularly for object classes that are characterized by large appearance variation.

We introduce a method for fast and accurate registration of multiple horizontal laser scans obtained by a mobile robot. The method is based on novel representation of the scene geometry called a latent map, which consists of a set of piecewise linear functions defined over a spatial grid covering the scene. The latent map representation is designed to handle the noise, outliers and limited spatial resolution of laser scan data in a principled manner. The main idea of our algorithm is to iterate between optimizing the latent map, and optimizing the alignment between the latent map and the input scans. In order to handle large datasets containing tens of thousands of scans, we introduce a multi-resolution pose estimation procedure, which applies our scan alignment algorithm at multiple resolutions and combines the results. We demonstrate our novel scan matching technique on several challenging data sets, where we obtain state of the art pose and map reconstructions that are markedly superior to what pairwise scan matching methods can achieve.

We present a novel “hybrid Hessian” six-degrees-of-freedom simultaneous localization and mapping (SLAM) algorithm. Our method allows for the smooth trade-off of accuracy for efficiency and for the incorporation of GPS measurements during real-time operation, thereby offering significant advantages over other SLAM solvers. Like other stochastic SLAM methods, such as SGD and TORO, our technique is robust to local minima and eliminates the need for costly relinearizations of the map. Unlike other stochastic methods, but similar to exact solvers, such as iSAM, our technique is able to process position-only constraints, such as GPS measurements, without introducing systematic distortions in the map. We present results from the Google Street View database, and compare our method with results from TORO. We show that our solver is able to achieve higher accuracy while operating within real-time bounds. In addition, as far as we are aware, this is the first stochastic SLAM solver capable of processing GPS constraints in real-time.

This paper presents an algorithm for measuring hair and face appearance in 2D images. Our approach starts by using learned mixture models of color and location information to suggest the hypotheses of the face, hair, and background regions. In turn, the image gradient information is used to generate the likely suggestions in the neighboring image regions. Either Graph-Cut or Loopy Belief Propagation algorithm is then applied to optimize the resulting Markov network in order to obtain the most likely hair and face segmentation from the background. We demonstrate that our algorithm can precisely identify the hair and face regions from a large dataset of face images automatically detected by the state-of-the-art face detector.

We present an efficient probabilistic method for identity recognition in personal photo albums. Personal photos are usually taken under uncontrolled conditions -the captured faces exhibit significant variations in pose, expression and illumination that limit the success of traditional face recognition algorithms. We show how to improve recognition rates by incorporating additional cues present in personal photo collections, such as clothing appearance and information about when the photo was taken. This is done by constructing a Markov random field (MRF) that effectively combines all available contextual cues in a principled recognition framework. Performing inference in the MRF produces markedly improved recognition results in a challenging dataset consisting of the personal photo collections of multiple people. At the same time, the computational cost of our approach remains comparable to that of standard face recognition approaches.

We address the problem of detecting complex articulated objects and their pose in 3D range scan data. This task is very difficult when the orientation of the object is unknown, and occlusion and clutter are present in the scene. To address the problem, we design an efficient probabilistic framework, based on the articulated model of an object, which combines multiple information sources. Our framework enforces that the surfaces and edge discontinuities of model parts are matched well in the scene while respecting the rules of occlusion, that joint constraints and angles are maintained, and that object parts don’t intersect. Our approach starts by using low-level detectors to suggest part placement hypotheses. In a hypothesis enrichment phase, these original hypotheses are used to generate likely placement suggestions for their neighboring parts. The probabilities over the possible part placement configurations are computed using efficient OpenGL rendering. Loopy belief propagation is used to optimize the resulting Markov network to obtain the most likely object configuration, which is additionally refined using an Iterative Closest Point algorithm adapted for articulated models. Our model is tested on several datasets, where we demonstrate successful pose detection for models consisting of 15 parts or more, even when the object is seen from different viewpoints, and various occluding objects and clutter are present in the scene.

We address the problem of segmenting 3D scan data into objects or object classes. Our segmentation framework is based on a subclass of Markov random fields (MRFs) which support efficient graph-cut inference. The MRF models incorporate a large set of diverse features and enforce the preference that adjacent scan points have the same classification label. We use a recently proposed maximum-margin framework to discriminatively train the model from a set of labeled scans; as a result we automatically learn the relative importance of the features for the segmentation task. Performing graph-cut inference in the trained MRF can then be used to segment new scenes very efficiently. We test our approach on three large-scale datasets produced by different kinds of 3D sensors, showing its applicability to both outdoor and indoor environments containing diverse objects.

We introduce the SCAPE method (Shape Completion and Animation for PEople)---a data-driven method for building a human shape model that spans variation in both subject shape and pose. The method is based on a representation that incorporates both articulated and non-rigid deformations. We learn a pose deformation model that derives the non-rigid surface deformation as a function of the pose of the articulated skeleton. We also learn a separate model of variation based on body shape. Our two models can be combined to produce 3D surface models with realistic muscle deformation for different people in different poses, when neither appear in the training set. We show how the model can be used for shape completion --- generating a complete surface mesh given a limited set of markers specifying the target shape. We present applications of shape completion to partial view completion and motion capture animation. In particular, our method is capable of constructing a high-quality animated surface model of a moving person, with realistic muscle deformation, using just a single static scan and a marker motion capture sequence of the person.

We describe a probabilistic framework for detection and modeling of doors from sensor data acquired in corridor environments with mobile robots. The framework captures shape, color, and motion properties of door and wall objects. The probabilistic model is optimized with a version of the expectation maximization algorithm, which segments the environment into door and wall objects and learns their properties. The framework allows the robot to generalize the properties of detected object instances to new object instances. We demonstrate the algorithm on real-world data acquired by a Pioneer robot equipped with a laser range finder and an omni-directional camera. Our results show that our algorithm reliably segments the environment into walls and doors, finding both doors that move and doors that do not move. We show that our approach achieves better results than models that only capture behavior, or only capture appearance.

We present an unsupervised algorithm for registering 3D surface scans of an object undergoing significant deformations. Our algorithm does not need markers, nor does it assume prior knowledge about object shape, the dynamics of its deformation, or scan alignment. The algorithm registers two meshes by optimizing a joint probabilistic model over all point-to- point correspondences between them. This model enforces preservation of local mesh geometry, as well as more global constraints that capture the preservation of geodesic distance between corresponding point pairs. The algorithm applies even when one of the meshes is an incomplete range scan; thus, it can be used to automatically fill in the remaining sur- faces for this partial scan, even if those surfaces were previously only seen in a different configuration. We evaluate the algorithm on several real-world datasets, where we demonstrate good results in the presence of significant movement of articulated parts and non-rigid surface defor- mation. Finally, we show that the output of the algorithm can be used for compelling computer graphics tasks such as interpolation between two scans of a non-rigid object and automatic recovery of articulated object models. 1 Introduction The construction of 3D object models is a key task for many graphics applications. It is becoming increasingly common to acquire these models from a range scan of a physical object. This paper deals with an important subproblem of this acquisition task -- the problem of registering two deforming surfaces corresponding to different configurations of the same non-rigid object. The main difficulty in the 3D registration problem is determining the correspondences of points on one surface to points on the other. Local regions on the surface are rarely distinc- tive enough to determine the correct correspondence, whether because of noise in the scans, or because of symmetries in the object shape. Thus, the set of candidate correspondences to a given point is usually large. Determining the correspondence for all object points results in a combinatorially large search problem. The existing algorithms for deformable surface A results video is available at http://robotics.stanford.edu/drago/cc/video.mp4 Figure 1: A) Registration results for two meshes. Nonrigid ICP and its variant augmented with spin images get stuck in local maxima. Our CC algorithm produces a largely correct registration, although with an artifact in the right shoulder (inset). B) Illustration of the link deformation process C) The CC algorithm which uses only deformation potentials can violate mesh geometry. Near regions can map to far ones (segment AB) and far regions can map to near ones (points C,D). registration make the problem tractable by assuming significant prior knowledge about the objects being registered. Some rely on the presence of markers on the object [1, 20], while others assume prior knowledge about the object dynamics [16], or about the space of non- rigid deformations [15, 5]. Algorithms that make neither restriction [18, 12] simplify the problem by decorrelating the choice of correspondences for the different points in the scan. However, this approximation is only good in the case when the object deformation is small; otherwise, it results in poor local maxima as nearby points in one scan are allowed to map to far-away points in the other. Our algorithm defines a joint probabilistic model over all correspondences, which ex- plicitly model the correlations between them -- specifically, that nearby points in one mesh should map to nearby points in the other. Importantly, the notion of "nearby" used in our model is defined in terms of geodesic distance over the mesh. We define a probabilistic model over the set of correspondences, that encodes these geodesic distance constraints as well as penalties for link twisting and stretching, and high-level local surface features [14]. We then apply loopy belief propagation [21] to this model, in order to solve for the entire set of correspondences simultaneously. The result is a registration that respects the surface geometry. To the best of our knowledge, the algorithm we present in this paper is the first algorithm which allows the registration of 3D surfaces of an object where the object config- urations can vary significantly, there is no prior knowledge about object shape or dynamics of deformation, and nothing whatsoever is known about the object alignment. Moreover, unlike many methods, our algorithm can be used to register a partial scan to a complete model, greatly increasing its applicability. We apply our approach to three datasets containing 3D scans of a wooden puppet, a human arm and entire human bodies in different configurations. We demonstrate good registration results for scan pairs exhibiting articulated motion, non-rigid deformations, or both. We also describe three applications of our method. In our first application, we show how a partial scan of an object can be registered onto a fully specified model in a dif- ferent configuration. The resulting registration allows us to use the model to "complete" the partial scan in a way that preserves the local surface geometry. In the second, we use the correspondences found by our algorithm to smoothly interpolate between two different poses of an object. In our final application, we use a set of registered scans of the same object in different positions to recover a decomposition of the object into approximately rigid parts, and recover an articulated skeleton linking the parts. All of these applications are done in an unsupervised way, using only the output of our Correlated Correspondence algorithm applied to pairs of poses with widely varying deformations, and unknown initial alignments. These results demonstrate the value of a high-quality solution to the registra- tion problem to a range of graphics tasks. 2 Previous Work Surface registration is a fundamental building block in computer graphics. The classical so- lution for registering rigid surfaces is the Iterative Closest Point algorithm (ICP) [4, 6, 17]. Recently, there has been work extending ICP to non-rigid surfaces [18, 8, 12, 1]. These algorithms treat one of the scans (usually a complete model of the surface) as a deformable template. The links between adjacent points on the surface can be thought of as springs, which are allowed to deform at a cost. Similarly to ICP, these algorithms iterate between two subproblems -- estimating the non-rigid transformation and estimating the set of correspondences C between the scans. The step estimating the correspondences assumes that a good estimate of the nonrigid transformation is available. Under this assumption, the assignments to the correspondence variables become decorrelated: each point in the second scan is associated with the nearest point (in the Euclidean distance sense) in the deformed template scan. However, the decomposition also induces the algorithm's main limitation. By assigning points in the second scan to points on the deformed model inde- pendently, nearby points in the scan can get associated to remote points in the model if the estimate of is poor (Fig. 1A). While several approaches have been proposed to address this problem of incorrect correspondences, their applicability is largely limited to problems where the deformation is local, and the initial alignment is approximately correct. Another line of related work is the work on deformable template matching in the com- puter vision community. In the 3D case, this framework is used for detection of articulated object models in images [13, 22, 19]. The algorithms assume the decomposition of the object into a relatively small number of parts is known, and that a detector for each object part is available. Template matching approaches have also been applied to deformable 2D objects, where very efficient solutions exist [9, 11]. However, these methods do not extend easily to the case of 3D surfaces. 3 The Correlated Correspondence Algorithm The input to the algorithm is a set of two meshes (surfaces tessellated into polygons). The model mesh X = (V X , EX ) is a complete model of the object, in a particular pose. V X = (x1, . . . , xN ) denotes the mesh points, while EX is the set of links between adjacent points on the mesh surface. The data mesh Z = (V Z , EZ ) is either a complete model or a partial view of the object in a different configuration. Each data mesh point zk is associated with a correspondence variable ck, specifying the corresponding model mesh point. The task of registration is one of estimating the set of all correspondences C and a non-rigid transformation which aligns the corresponding points. 3.1 Probabilistic Model We formulate the registration problem as one of finding an embedding of the data mesh Z into the model mesh X, which is encoded as an assignment to all correspondence vari- ables C = (c1, . . . , cK ). The main idea behind our approach is to preserve the consis- tency of the embedding by explicitly correlating the assignments to the correspondence variables. We define a joint distribution over the correspondence variables c1, . . . , cK , rep- resented as a Markov network. For each pair of adjacent data mesh points zk, zl, we want to define a probabilistic potential (ck, cl) that constrains this pair of correspondences to reasonable and consistent. This gives rise to a joint probability distribution of the form p(C) = 1 (c (c Z k k ) k,l k , cl) which contains only single and pairwise potentials. Performing probabilistic inference to find the most likely joint assignment to the entire set of correspondence variables C should yield a good and consistent registration. Deformation Potentials. We want our model to encode a preference for embeddings of mesh Z into mesh X, which minimize the amount of deformation induced by the embedding. In order to quantify the amount of deformation , applied to the model, we will follow the ideas of Hahnel et al. [12] and treat the links in the set EX as springs, which resist stretching and twisting at their endpoints. Stretching is easily quantified by looking at changes in the link length induced by the transformation . Link twisting, however, is ill- specified by looking only at the Cartesian coordinates of the points alone. Following [12], we attach an imaginary local coordinate system to each point on the model. This local coordinate system allows us to quantify the "twist" of a point xj relative to a neighbor xi. A non-rigid transformation defines, for each point xi, a translation of its coordinates and a rotation of its local coordinate system. To evaluate the deformation penalty, we parameterize each link in the model in terms of its length and its direction relative to its endpoints (see Fig. 1B). Specifically, we define li,j to be the distance between xi and xj; dij is a unit vector denoting the direction of the point xj in the coordinate system of xi (and vice versa). We use ei,j to denote the set of edge parameters (li,j, dij, dji). It is now straightforward to specify the penalty for model deformations. Let be a transformation, and let ~ ei,j denote the triple of parameters associated with the link between xi and xj after applying . Our model penalizes twisting and stretching, using a separate zero-mean Gaussian noise model for each: P (~ ei,j | ei,j) = P (~li,j | li,j) P ( ~ dij | dij) P ( ~ dji | dji) (1) In the absence of prior information, we assume that all links are equally likely to deform. In order to quantify the deformation induced by an embedding C, we need to include a potential d(ck, cl) for each link eZ EZ . Every probability k,l d(ck = i, cl = j) corresponds to the deformation penalty incurred by deforming model link ei,j to generate link eZ and is defined in (1). We do not restrict ourselves to the set of links in EX , since k,l the original mesh tessellation is sparse and local. Any two points in X are allowed to implicitly define a link. Unfortunately, we cannot directly estimate the quantity P (eZ | e k,l i,j ), since the link pa- rameters eZ depend on knowing the nonrigid transformation, which is not given as part k,l of the input. The key issue is estimating the (unknown) relative rotation of the link end- points. In effect, this rotation is an additional latent variable, which must also be part of the probabilistic model. To remain within the realm of discrete Markov networks, allowing the application of standard probabilistic inference algorithms, we discretize the space of the possible rotations, and fold it into the domains of the correspondence variables. For each possible value of the correspondence variable ck = i we select a small set of candidate rotations, consistent with local geometry. We do this by aligning local patches around the points xi and zk using rigid ICP. We extend the domain of each correspondence variables ck, where each value encodes a matching point and a particular rotation from the precom- puted set for that point. Now the edge parameters eZ are fully determined and so is the k,l probabilistic potential. Geodesic Distances. Our proposed approach raises the question as to what constitutes the best constraint between neighboring correspondence variables. The literature on scan registration -- for rigid and non-rigid models alike -- relies on the preserving Euclidean distance. While Euclidean distance is meaningful for rigid objects, it is very sensitive to de- formations, especially those induced by moving parts. For example, in Fig. 1C, we see that the two legs in one configuration of our puppet are fairly close together, allowing the algo- rithm to map two adjacent points in the data mesh to the two separate legs, with minimal deformation penalty. In the complementary situation, especially when object symmetries are present, two distant yet similar points in one scan might get mapped to the same region in the other. For example, in the same figure, we see that points in both an arm and a leg in the data mesh get mapped to a single leg in the model mesh. We therefore want to enforce constraints preserving distance along the mesh surface (geodesic distance). Our probabilistic framework easily incorporate such constraints as correlations between pairs of correspondence variables. We encode a nearness preservation Figure 2: A) Automatic interpolation between two scans of an arm and a wooden puppet. B) Regis- tration results on two scans of the same man sitting and standing up (select points were displayed) C) Registration results on scans of a larger man and a smaller woman. The algorithm is robust to small changes in object scale. constraint which prevents adjacent points in mesh Z to be mapped to distant points in X in the geodesic distance sense. For adjacent points zk, zl in the data mesh, we define the following potential: 0 dist Geodesic (xi, xj ) > n(ck = i, cl = j) = (2) 1 otherwise where is the data mesh resolution and is some constant, chosen to be 3.5. The farness preservation potentials encode the complementary constraint. For every pair of points zk, zl whose geodesic distance is more than 5 on the data mesh, we have a potential: 0 dist Geodesic(xi, xj ) < f (ck = i, cl = j) = (3) 1 otherwise where is also a constant, chosen to be 2 in our implementation. The intuition behind this constraint is fairly clear: if zk, zl are far apart on the data mesh, then their corresponding points must be far apart on the model mesh. Local Surface Signatures. Finally, we encode a set of potentials that correspond to the preservation of local surface properties between the model mesh and data mesh. The use of local surface signatures is important, because it helps to guide the optimization in the exponential space of assignments. We use spin images [14] compressed with prin- cipal component analysis to produce a low-dimensional signature sx of the local surface geometry around a point x. When data and model points correspond, we expect their lo- cal signatures to be similar. We introduce a potential whose values s(ck) = i enforce a zero-mean Gaussian penalty for discrepancies between sx and s . i zk 3.2 Optimization In the previous section, we defined a Markov network, which encodes a joint probability distribution over the correspondence variables as a product of single and pairwise poten- tials. Our goal is to find a joint assignment to these variables that maximizes this proba- bility. This problem is one of standard probabilistic inference over the Markov network. However, the Markov network is quite large, and contains a large number of loops, so that exact inference is computationally infeasible. We therefore apply an approximate inference method known as loopy belief propagation (LBP)[21], which has been shown to work in a wide variety of applications. Running LBP until convergence results in a set of probabilis- tic assignments to the different correspondence variables, which are locally consistent. We then simply extract the most likely assignment for each variable to obtain a correspondence. One remaining complication arises from the form of our farness preservation constraints. In general, most pairs of points in the mesh are not close, so that the total number of such potentials grows as O(M 2), where M is the number of points in the data mesh. However, rather than introducing all these potentials into the Markov net from the start, we introduce them as needed. First, we run LBP without any farness preservation potentials. If the solution violates a set of farness preservation constraints, we add it and rerun BP. In practice, this approach adds a very small number of such constraints. 4 Experimental Results Basic Registration. We applied our registration algorithm to three different datasets, containing meshes of a human arm, wooden puppet and the CAESAR dataset of whole human bodies [1], all acquired by a 3D range scanner. The meshes were not complete surfaces, but several techniques exist for filling the holes (e.g., [10]). We ran the Correlated Correspondence algorithm using the same probabilistic model and the same parameters on all data sets. We use a coarse-to-fine strategy, using the result of a coarse sub-sampling of the mesh surface to constrain the correspondences at a finer-grained level. The resulting set of correspondences were used as markers to initialize the non-rigid ICP algorithm of Hahnel et al. [12]. The Correlated Correspondence algorithm successfully aligned all mesh pairs in our hu- man arm data set containing 7 arms. In the puppet data set we registered one of the meshes to the remaining 6 puppets. The algorithm correctly registered 4 out of 6 data meshes to the model mesh. In the two remaining cases, the algorithm produced a registration where the torso was flipped, so that the front was mapped to the back. This problem arises from am- biguities induced by the puppet symmetry, whose front and back are almost identical. Im- portantly, our probabilistic model assigns a higher likelihood score to the correct solution, so that the incorrect registration is a consequence of local maxima in the LBP algorithm. This fact allows us to address the issue in an unsupervised way simply by running loopy BP several times, with different initialization. For details on the unsupervised initialization scheme we used, please refer to our technical report [2]. We ran the modified algorithm to register one puppet mesh to the remaining 6 meshes in the dataset, obtaining the correct registration in all cases. In particular, as shown in Fig. 1A, we successfully deal with the case on which the straightforward nonrigid ICP algorithm failed. The modified algorithm was applied to the CAESAR dataset and produced very good registration for challenging cases exhibiting both articulated motion and deformation (Fig. 2B), or exhibiting deforma- tion and a (small) change in object scale (Fig. 2C). Overall, the algorithm performed robustly, producing a close-to-optimal registrations even for pairs of meshes that involve large deformations, articulated motion or both. The registration is accomplished in an unsupervised way, without any prior knowledge about object shape, dynamics, or alignment. Partial view completion. The Correlated Correspondence algorithm allows us to register a data mesh containing only a partial scan of an object to a known complete surface model of the object, which serves as a template. We can then transform the template mesh to the partial scan, a process which leaves undisturbed the links that are not involved in the partial mesh. The result is a mesh that matches the data on the observed points, while completing the unknown portion of the surface using the template. We take a partial mesh, which is missing the entire back part of the puppet in a particular pose. The resulting partial model is displayed in Fig. 3B-1; for comparison, the correct complete model in this configuration (which was not available to the algorithm), is shown in Fig. 3B-2. We register the partial mesh to models of the object in a different pose (Fig. 3B- 3), and compare the completions we obtain (Fig. 3B-4), to the ground truth represented in Fig. 3B-2. The result demonstrates a largely correct reconstruction of the complete surface geometry from the partial scan and the deformed template. We report additional shape completion results in [2]. Interpolation. Current research [20] shows that if a nonrigid transformation between the poses is available, believable animation can be produced by linear interpolation be- Figure 3: A) The results produced by the CC algorithm were used for unsupervised recovery of articulated models. 15 puppet parts and 4 arm parts, as well as the articulated object skeletons, were recovered. B) Partial view completion results. The missing parts of the surface were estimated by registering the partial view to a complete model of the object in a different configuration. tween the model mesh and the transformed model mesh. The interpolation is performed in the space of local link parameters (li,j, dij, dji), We demonstrate that transforma- tion estimates produced by our algorithm can be used to automatically generate believable animation sequences between fairly different poses, as shown in Fig. 2A. Recovering Articulated Models. Articulated object models have a number of appli- cations in animation and motion capture, and there has been work on recovering them automatically from 3D data [7, 3]. We show that our unsupervised registration capability can greatly assist articulated model recovery. In particular, the algorithm in [3] requires an estimate of the correspondences between a template mesh and the remaining meshes in the dataset. We supplied it with registration computed with the Correlated Correspondence algorithm. As a result we managed to recover in a completely unsupervised way all 15 rigid parts of the puppet, as well as the joints between them (Fig. 3A). We demonstrate successful articulation recovery even for objects which are not purely rigid, as is the case with the human arm (see Fig. 3A).

In recent years, there has been a lot of interest in the database community in mining time series data.Surprisingly, little work has been done on verifying which measures are most suitable for mining of a given class of data sets.Such work is of crucial importance, since it enables us to identify similarity measures which are useful in a given context and therefore for which efficient algorithms should be further investigated.Moreover, an accurate evaluation of the performance of even existing algorithms is not possible without a good understanding of the data sets occurring in practice.In this work we attempt to fill this gap by studying similarity measures for clustering of similar stocks (which, of course, is an interesting problem on its own).Our approach is to cluster the stocks according to various measures (including several novel ones) and compare the results to the "groundtruth" clustering based on the Standard and Poor 500 Index.Our experiments reveal several interesting facts about the similarity measures used for stock-market data.