Mathematical Supplement for the $\texttt{gsplat}$ Library

This report provides the mathematical details of the gsplat library, a modular toolbox for efficient differentiable Gaussian splatting, as proposed by Kerbl et al. It provides a self-contained reference for the computations involved in the forward and backward passes of differentiable Gaussian splatting. To facilitate practical usage and development, we provide a user friendly Python API that exposes each component of the forward and backward passes in rasterization at github.com/nerfstudio-project/gsplat .

Generative Proxemics: A Prior for 3D Social Interaction from Images

Social interaction is a fundamental aspect of human behavior and communication. The way individuals position themselves in relation to others, also known as proxemics, conveys social cues and affects the dynamics of social interaction. We present a novel approach that learns a 3D proxemics prior of two people in close social interaction. Since collecting a large 3D dataset of interacting people is a challenge, we rely on 2D image collections where social interactions are abundant. We achieve this by reconstructing pseudo-ground truth 3D meshes of interacting people from images with an optimization approach using existing ground-truth contact maps. We then model the proxemics using a novel denoising diffusion model called BUDDI that learns the joint distribution of two people in close social interaction directly in the SMPL-X parameter space. Sampling from our generative proxemics model produces realistic 3D human interactions, which we validate through a user study. Additionally, we introduce a new optimization method that uses the diffusion prior to reconstruct two people in close proximity from a single image without any contact annotation. Our approach recovers more accurate and plausible 3D social interactions from noisy initial estimates and outperforms state-of-the-art methods. See our project site for code, data, and model: muelea.github.io/buddi.

Decoupling Human and Camera Motion from Videos in the Wild

We propose a method to reconstruct global human trajectories from videos in the wild. Our optimization method decouples the camera and human motion, which allows us to place people in the same world coordinate frame. Most existing methods do not model the camera motion; methods that rely on the background pixels to infer 3D human motion usually require a full scene reconstruction, which is often not possible for in-the-wild videos. However, even when existing SLAM systems cannot recover accurate scene reconstructions, the background pixel motion still provides enough signal to constrain the camera motion. We show that relative camera estimates along with data-driven human motion priors can resolve the scene scale ambiguity and recover global human trajectories. Our method robustly recovers the global 3D trajectories of people in challenging in-the-wild videos, such as PoseTrack. We quantify our improvement over existing methods on 3D human dataset Egobody. We further demonstrate that our recovered camera scale allows us to reason about motion of multiple people in a shared coordinate frame, which improves performance of downstream tracking in PoseTrack. Code and video results can be found at https://vye16.github.io/slahmr.

Deformable Sprites for Unsupervised Video Decomposition

We describe a method to extract persistent elements of a dynamic scene from an input video. We represent each scene element as a \emph{Deformable Sprite} consisting of three components: 1) a 2D texture image for the entire video, 2) per-frame masks for the element, and 3) non-rigid deformations that map the texture image into each video frame. The resulting decomposition allows for applications such as consistent video editing. Deformable Sprites are a type of video auto-encoder model that is optimized on individual videos, and does not require training on a large dataset, nor does it rely on pre-trained models. Moreover, our method does not require object masks or other user input, and discovers moving objects of a wider variety than previous work. We evaluate our approach on standard video datasets and show qualitative results on a diverse array of Internet videos. Code and video results can be found at https://deformable-sprites.github.io

pixelNeRF: Neural Radiance Fields from One or Few Images

We propose pixelNeRF, a learning framework that predicts a continuous neural scene representation conditioned on one or few input images. The existing approach for constructing neural radiance fields involves optimizing the representation to every scene independently, requiring many calibrated views and significant compute time. We take a step towards resolving these shortcomings by introducing an architecture that conditions a NeRF on image inputs in a fully convolutional manner. This allows the network to be trained across multiple scenes to learn a scene prior, enabling it to perform novel view synthesis in a feed-forward manner from a sparse set of views (as few as one). Leveraging the volume rendering approach of NeRF, our model can be trained directly from images with no explicit 3D supervision. We conduct extensive experiments on ShapeNet benchmarks for single image novel view synthesis tasks with held-out objects as well as entire unseen categories. We further demonstrate the flexibility of pixelNeRF by demonstrating it on multi-object ShapeNet scenes and real scenes from the DTU dataset. In all cases, pixelNeRF outperforms current state-of-the-art baselines for novel view synthesis and single image 3D reconstruction. For the video and code, please visit the project website: https://alexyu.net/pixelnerf

Robust Guarantees for Perception-Based Control

Motivated by vision based control of autonomous vehicles, we consider the problem of controlling a known linear dynamical system for which partial state information, such as vehicle position, can only be extracted from high-dimensional data, such as an image. Our approach is to learn a perception map from high-dimensional data to partial-state observation and its corresponding error profile, and then design a robust controller. We show that under suitable smoothness assumptions on the perception map and generative model relating state to high-dimensional data, an affine error model is sufficiently rich to capture all possible error profiles, and can further be learned via a robust regression problem. We then show how to integrate the learned perception map and error model into a novel robust control synthesis procedure, and prove that the resulting perception and control loop has favorable generalization properties. Finally, we illustrate the usefulness of our approach on a synthetic example and on the self-driving car simulation platform CARLA.