Recent advancements in language models have demonstrated its capacity of context understanding and generative representations. Leveraged by these developments, we propose a novel multimodal trajectory predictor based on a vision-language model, named VLMTraj, which fully takes advantage of the prior knowledge of multimodal large language models and the human-like reasoning across diverse modality information. The key idea of our model is to reframe the trajectory prediction task into a visual question answering format, using historical information as context and instructing the language model to make predictions in a conversational manner. Specifically, we transform all the inputs into a natural language style: historical trajectories are converted into text prompts, and scene images are described through image captioning. Additionally, visual features from input images are also transformed into tokens via a modality encoder and connector. The transformed data is then formatted to be used in a language model. Next, in order to guide the language model in understanding and reasoning high-level knowledge, such as scene context and social relationships between pedestrians, we introduce an auxiliary multi-task question and answers. For training, we first optimize a numerical tokenizer with the prompt data to effectively separate integer and decimal parts, allowing us to capture correlations between consecutive numbers in the language model. We then train our language model using all the visual question answering prompts. During model inference, we implement both deterministic and stochastic prediction methods through beam-search-based most-likely prediction and temperature-based multimodal generation. Our VLMTrajvalidates that the language-based model can be a powerful pedestrian trajectory predictor, and outperforms existing numerical-based predictor methods. Extensive experiments show that VLMTrajcan successfully understand social relationships and accurately extrapolate the multimodal futures on public pedestrian trajectory prediction benchmarks.

Modeling and reproducing crowd behaviors are important in various domains including psychology, robotics, transport engineering and virtual environments. Conventional methods have focused on synthesizing momentary scenes, which have difficulty in replicating the continuous nature of real-world crowds. In this paper, we introduce a novel method for automatically generating continuous, realistic crowd trajectories with heterogeneous behaviors and interactions among individuals. We first design a crowd emitter model. To do this, we obtain spatial layouts from single input images, including a segmentation map, appearance map, population density map and population probability, prior to crowd generation. The emitter then continually places individuals on the time-line by assigning independent behavior characteristics such as agents’ type, pace, and start/end positions using diffusion models. Next, our crowd simulator produces their long-term locomotions. To simulate diverse actions, it can augment their behaviors based on a Markov chain. As a result, our overall framework populates the scenes with heterogeneous crowd behaviors by alternating between the proposed emitter and simulator. Note that all the components in the proposed framework are user-controllable. Lastly, we propose a benchmark protocol to evaluate the realism and quality of the generated crowds in terms of the scene-level population dynamics and the individual-level trajectory accuracy. We demonstrate that our approach effectively models diverse crowd behavior patterns and generalizes well across different geographical environments. Code is publicly available at https://github.com/InhwanBae/CrowdES.

Language models have demonstrated impressive ability in context understanding and generative performance. Inspired by the recent success of language foundation models, in this paper, we propose LMTraj (Language-based Multimodal Trajectory predictor), which recasts the trajectory prediction task into a sort of question-answering problem. Departing from traditional numerical regression models, which treat the trajectory coordinate sequence as continuous signals, we consider them as discrete signals like text prompts. Specially, we first transform an input space for the trajectory coordinate into the natural language space. Here, the entire timeseries trajectories of pedestrians are converted into a text prompt, and scene images are described as text information through image captioning. The transformed numerical and image data are then wrapped into the question-answering template for use in a language model. Next, to guide the language model in understanding and reasoning high-level knowledge, such as scene context and social relationships between pedestrians, we introduce an auxiliary multi-task question and answering. We then train a numerical tokenizer with the prompt data. We encourage the tokenizer to separate the integer and decimal parts well, and leverage it to capture correlations between the consecutive numbers in the language model. Lastly, we train the language model using the numerical tokenizer and all of the question-answer prompts. Here, we propose a beam-search-based most-likely prediction and a temperature-based multimodal prediction to implement both deterministic and stochastic inferences. Applying our LMTraj, we show that the language-based model can be a powerful pedestrian trajectory predictor, and outperforms existing numerical-based predictor methods. Extensive experiments show that our LMTraj can successfully understand social relationships and accurately extrapolate the multimodal futures on the public pedestrian trajectory prediction benchmark. Code is publicly available at https://github.com/inhwanbae/LMTrajectory.

There are five types of trajectory prediction tasks: deterministic, stochastic, domain adaptation, momentary observation, and few-shot. These associated tasks are defined by various factors, such as the length of input paths, data split and pre-processing methods. Interestingly, even though they commonly take sequential coordinates of observations as input and infer future paths in the same coordinates as output, designing specialized architectures for each task is still necessary. For the other task, generality issues can lead to sub-optimal performances. In this paper, we propose SingularTrajectory, a diffusion-based universal trajectory prediction framework to reduce the performance gap across the five tasks. The core of SingularTrajectory is to unify a variety of human dynamics representations on the associated tasks. To do this, we first build a Singular space to project all types of motion patterns from each task into one embedding space. We next propose an adaptive anchor working in the Singular space. Unlike traditional fixed anchor methods that sometimes yield unacceptable paths, our adaptive anchor enables correct anchors, which are put into a wrong location, based on a traversability map. Finally, we adopt a diffusion-based predictor to further enhance the prototype paths using a cascaded denoising process. Our unified framework ensures the generality across various benchmark settings such as input modality, and trajectory lengths. Extensive experiments on five public benchmarks demonstrate that SingularTrajectory substantially outperforms existing models, highlighting its effectiveness in estimating general dynamics of human movements. Code is publicly available at https://github.com/inhwanbae/SingularTrajectory.

Estimating neural radiance fields (NeRFs) is able to generate novel views of a scene from known imagery. Recent approaches have afforded dramatic progress on small bounded regions of the scene. For an unbounded scene where cameras point in any direction and contents exist at any distance, certain mapping functions are used to represent it within a bounded space, yet they either work in object-centric scenes or focus on objects close to the camera. The goal of this paper is to understand how to design a proper mapping function that considers per-scene optimization, which remains unexplored. We first present a geometric understanding of existing mapping functions that express the relation between the bounded and unbounded scenes. Here, we exploit a stereographic projection method to explain failures of the mapping functions, where input ray samples are too sparse to account for scene geometry in unbounded regions. To overcome the failures, we propose a novel mapping function based on a $p$-norm distance, allowing to adaptively sample the rays by adjusting the $p$-value according to scene geometry, even in unbounded regions. To take the advantage of our mapping function, we also introduce a new ray parameterization to properly allocate ray samples in the geometry of unbounded regions. Through the incorporation of both the novel mapping function and the ray parameterization within existing NeRF frameworks, our method achieves state-of-the-art novel view synthesis results on a variety of challenging datasets.

3D Gaussian Splatting has shown fast and high-quality rendering results in static scenes by leveraging dense 3D prior and explicit representations. Unfortunately, the benefits of the prior and representation do not involve novel view synthesis for dynamic motions. Ironically, this is because the main barrier is the reliance on them, which requires increasing training and rendering times to account for dynamic motions. In this paper, we design Explicit 4D Gaussian Splatting (Ex4DGS). Our key idea is to firstly separate static and dynamic Gaussians during training, and to explicitly sample positions and rotations of the dynamic Gaussians at sparse timestamps. The sampled positions and rotations are then interpolated to represent both spatially and temporally continuous motions of objects in dynamic scenes as well as reducing computational cost. Additionally, we introduce a progressive training scheme and a point-backtracking technique that improves Ex4DGS's convergence. We initially train Ex4DGS using short timestamps and progressively extend timestamps, which makes it work well with a few point clouds. The point-backtracking is used to quantify the cumulative error of each Gaussian over time, enabling the detection and removal of erroneous Gaussians in dynamic scenes. Comprehensive experiments on various scenes demonstrate the state-of-the-art rendering quality from our method, achieving fast rendering of 62 fps on a single 2080Ti GPU.

Predicting the trajectories of pedestrians in crowded conditions is an important task for applications like autonomous navigation systems. Previous studies have tackled this problem using two strategies. They (1) infer all future steps recursively, or (2) predict the potential destinations of pedestrians at once and interpolate the intermediate steps to arrive there. However, these strategies often suffer from the accumulated errors of the recursive inference, or restrictive assumptions about social relations in the intermediate path. In this paper, we present a graph convolutional network-based trajectory prediction. Firstly, we propose a control point prediction that divides the future path into three sections and infers the intermediate destinations of pedestrians to reduce the accumulated error. To do this, we construct multi-relational weighted graphs to account for their physical and complex social relations. We then introduce a trajectory refinement step based on a spatio-temporal and multi-relational graph. By considering the social interactions between neighbors, better prediction results are achievable. In experiments, the proposed network achieves state-of-the-art performance on various real-world trajectory prediction benchmarks.

Capturing high-dimensional social interactions and feasible futures is essential for predicting trajectories. To address this complex nature, several attempts have been devoted to reducing the dimensionality of the output variables via parametric curve fitting such as the Bézier curve and B-spline function. However, these functions, which originate in computer graphics fields, are not suitable to account for socially acceptable human dynamics. In this paper, we present EigenTrajectory ($\mathbb{E}\mathbb{T}$), a trajectory prediction approach that uses a novel trajectory descriptor to form a compact space, known here as $\mathbb{E}\mathbb{T}$ space, in place of Euclidean space, for representing pedestrian movements. We first reduce the complexity of the trajectory descriptor via a low-rank approximation. We transform the pedestrians' history paths into our $\mathbb{E}\mathbb{T}$ space represented by spatio-temporal principle components, and feed them into off-the-shelf trajectory forecasting models. The inputs and outputs of the models as well as social interactions are all gathered and aggregated in the corresponding $\mathbb{E}\mathbb{T}$ space. Lastly, we propose a trajectory anchor-based refinement method to cover all possible futures in the proposed $\mathbb{E}\mathbb{T}$ space. Extensive experiments demonstrate that our EigenTrajectory predictor can significantly improve both the prediction accuracy and reliability of existing trajectory forecasting models on public benchmarks, indicating that the proposed descriptor is suited to represent pedestrian behaviors. Code is publicly available at https://github.com/inhwanbae/EigenTrajectory.

Recent approaches to representation learning have successfully demonstrated the benefits in hyperbolic space, driven by an excellent ability to make hierarchical relationships. In this work, we demonstrate that the properties of hyperbolic geometry serve as a valuable alternative to learning hierarchical affinity for spatial propagation tasks. We propose a Hyperbolic Affinity learning Module (HAM) to learn spatial affinity by considering geodesic distance on the hyperbolic space. By simply incorporating our HAM into conventional spatial propagation tasks, we validate its effectiveness, capturing the pixel hierarchy of affinity maps in hyperbolic space. The proposed methodology can lead to performance improvements in explicit propagation processes such as depth completion and semantic segmentation.

Capturing multimodal natures is essential for stochastic pedestrian trajectory prediction, to infer a finite set of future trajectories. The inferred trajectories are based on observation paths and the latent vectors of potential decisions of pedestrians in the inference step. However, stochastic approaches provide varying results for the same data and parameter settings, due to the random sampling of the latent vector. In this paper, we analyze the problem by reconstructing and comparing probabilistic distributions from prediction samples and socially-acceptable paths, respectively. Through this analysis, we observe that the inferences of all stochastic models are biased toward the random sampling, and fail to generate a set of realistic paths from finite samples. The problem cannot be resolved unless an infinite number of samples is available, which is infeasible in practice. We introduce that the Quasi-Monte Carlo (QMC) method, ensuring uniform coverage on the sampling space, as an alternative to the conventional random sampling. With the same finite number of samples, the QMC improves all the multimodal prediction results. We take an additional step ahead by incorporating a learnable sampling network into the existing networks for trajectory prediction. For this purpose, we propose the Non-Probability Sampling Network (NPSN), a very small network (~5K parameters) that generates purposive sample sequences using the past paths of pedestrians and their social interactions. Extensive experiments confirm that NPSN can significantly improve both the prediction accuracy (up to 60%) and reliability of the public pedestrian trajectory prediction benchmark. Code is publicly available at https://github.com/inhwanbae/NPSN.

Pedestrian trajectory prediction is one of the important tasks required for autonomous navigation and social robots in human environments. Previous studies focused on estimating social forces among individual pedestrians. However, they did not consider the social forces of groups on pedestrians, which results in over-collision avoidance problems. To address this problem, we present a Disentangled Multi-Relational Graph Convolutional Network (DMRGCN) for socially entangled pedestrian trajectory prediction. We first introduce a novel disentangled multi-scale aggregation to better represent social interactions, among pedestrians on a weighted graph. For the aggregation, we construct the multi-relational weighted graphs based on distances and relative displacements among pedestrians. In the prediction step, we propose a global temporal aggregation to alleviate accumulated errors for pedestrians changing their directions. Finally, we apply DropEdge into our DMRGCN to avoid the over-fitting issue on relatively small pedestrian trajectory datasets. Through the effective incorporation of the three parts within an end-to-end framework, DMRGCN achieves state-of-the-art performances on a variety of challenging trajectory prediction benchmarks.