View-Consistent Hierarchical 3D SegmentationUsing Ultrametric Feature Fields

Large-scale vision foundation models such as Segment Anything (SAM) demonstrate impressive performance in zero-shot image segmentation at multiple levels of granularity. However, these zero-shot predictions are rarely 3D-consistent. As the camera viewpoint changes in a scene, so do the segmentation predictions, as well as the characterizations of ``coarse" or ``fine" granularity. In this work, we address the challenging task of lifting multi-granular and view-inconsistent image segmentations into a hierarchical and 3D-consistent representation. We learn a novel feature field within a Neural Radiance Field (NeRF) representing a 3D scene, whose segmentation structure can be revealed at different scales by simply using different thresholds on feature distance. Our key idea is to learn an ultrametric feature space, which unlike a Euclidean space, exhibits transitivity in distance-based grouping, naturally leading to a hierarchical clustering. Put together, our method takes view-inconsistent multi-granularity 2D segmentations as input and produces a hierarchy of 3D-consistent segmentations as output. We evaluate our method and several baselines on synthetic datasets with multi-view images and multi-granular segmentation, showcasing improved accuracy and viewpoint-consistency. We additionally provide qualitative examples of our model's 3D hierarchical segmentations in real world scenes.\footnote{The code and dataset are available at:

ActAnywhere: Subject-Aware Video Background Generation

Generating video background that tailors to foreground subject motion is an important problem for the movie industry and visual effects community. This task involves synthesizing background that aligns with the motion and appearance of the foreground subject, while also complies with the artist's creative intention. We introduce ActAnywhere, a generative model that automates this process which traditionally requires tedious manual efforts. Our model leverages the power of large-scale video diffusion models, and is specifically tailored for this task. ActAnywhere takes a sequence of foreground subject segmentation as input and an image that describes the desired scene as condition, to produce a coherent video with realistic foreground-background interactions while adhering to the condition frame. We train our model on a large-scale dataset of human-scene interaction videos. Extensive evaluations demonstrate the superior performance of our model, significantly outperforming baselines. Moreover, we show that ActAnywhere generalizes to diverse out-of-distribution samples, including non-human subjects. Please visit our project webpage at https://actanywhere.github.io.

Refining Pre-Trained Motion Models

Given the difficulty of manually annotating motion in video, the current best motion estimation methods are trained with synthetic data, and therefore struggle somewhat due to a train/test gap. Self-supervised methods hold the promise of training directly on real video, but typically perform worse. These include methods trained with warp error (i.e., color constancy) combined with smoothness terms, and methods that encourage cycle-consistency in the estimates (i.e., tracking backwards should yield the opposite trajectory as tracking forwards). In this work, we take on the challenge of improving state-of-the-art supervised models with self-supervised training. We find that when the initialization is supervised weights, most existing self-supervision techniques actually make performance worse instead of better, which suggests that the benefit of seeing the new data is overshadowed by the noise in the training signal. Focusing on obtaining a ``clean'' training signal from real-world unlabelled video, we propose to separate label-making and training into two distinct stages. In the first stage, we use the pre-trained model to estimate motion in a video, and then select the subset of motion estimates which we can verify with cycle-consistency. This produces a sparse but accurate pseudo-labelling of the video. In the second stage, we fine-tune the model to reproduce these outputs, while also applying augmentations on the input. We complement this boot-strapping method with simple techniques that densify and re-balance the pseudo-labels, ensuring that we do not merely train on ``easy'' tracks. We show that our method yields reliable gains over fully-supervised methods in real videos, for both short-term (flow-based) and long-range (multi-frame) pixel tracking.

Towards Learning Geometric Eigen-Lengths Crucial for Fitting Tasks

Some extremely low-dimensional yet crucial geometric eigen-lengths often determine the success of some geometric tasks. For example, the height of an object is important to measure to check if it can fit between the shelves of a cabinet, while the width of a couch is crucial when trying to move it through a doorway. Humans have materialized such crucial geometric eigen-lengths in common sense since they are very useful in serving as succinct yet effective, highly interpretable, and universal object representations. However, it remains obscure and underexplored if learning systems can be equipped with similar capabilities of automatically discovering such key geometric quantities from doing tasks. In this work, we therefore for the first time formulate and propose a novel learning problem on this question and set up a benchmark suite including tasks, data, and evaluation metrics for studying the problem. We focus on a family of common fitting tasks as the testbed for the proposed learning problem. We explore potential solutions and demonstrate the feasibility of learning eigen-lengths from simply observing successful and failed fitting trials. We also attempt geometric grounding for more accurate eigen-length measurement and study the reusability of the learned eigen-lengths across multiple tasks. Our work marks the first exploratory step toward learning crucial geometric eigen-lengths and we hope it can inspire future research in tackling this important yet underexplored problem.

PointOdyssey: A Large-Scale Synthetic Dataset for Long-Term Point Tracking

We introduce PointOdyssey, a large-scale synthetic dataset, and data generation framework, for the training and evaluation of long-term fine-grained tracking algorithms. Our goal is to advance the state-of-the-art by placing emphasis on long videos with naturalistic motion. Toward the goal of naturalism, we animate deformable characters using real-world motion capture data, we build 3D scenes to match the motion capture environments, and we render camera viewpoints using trajectories mined via structure-from-motion on real videos. We create combinatorial diversity by randomizing character appearance, motion profiles, materials, lighting, 3D assets, and atmospheric effects. Our dataset currently includes 104 videos, averaging 2,000 frames long, with orders of magnitude more correspondence annotations than prior work. We show that existing methods can be trained from scratch in our dataset and outperform the published variants. Finally, we introduce modifications to the PIPs point tracking method, greatly widening its temporal receptive field, which improves its performance on PointOdyssey as well as on two real-world benchmarks. Our data and code are publicly available at: https://pointodyssey.com

Learning a Diffusion Prior for NeRFs

Neural Radiance Fields (NeRFs) have emerged as a powerful neural 3D representation for objects and scenes derived from 2D data. Generating NeRFs, however, remains difficult in many scenarios. For instance, training a NeRF with only a small number of views as supervision remains challenging since it is an under-constrained problem. In such settings, it calls for some inductive prior to filter out bad local minima. One way to introduce such inductive priors is to learn a generative model for NeRFs modeling a certain class of scenes. In this paper, we propose to use a diffusion model to generate NeRFs encoded on a regularized grid. We show that our model can sample realistic NeRFs, while at the same time allowing conditional generations, given a certain observation as guidance.

Physics-informed PointNet: On how many irregular geometries can it solve an inverse problem simultaneously? Application to linear elasticity

Regular physics-informed neural networks (PINNs) predict the solution of partial differential equations using sparse labeled data but only over a single domain. On the other hand, fully supervised learning models are first trained usually over a few thousand domains with known solutions (i.e., labeled data) and then predict the solution over a few hundred unseen domains. Physics-informed PointNet (PIPN) is primarily designed to fill this gap between PINNs (as weakly supervised learning models) and fully supervised learning models. In this article, we demonstrate that PIPN predicts the solution of desired partial differential equations over a few hundred domains simultaneously, while it only uses sparse labeled data. This framework benefits fast geometric designs in the industry when only sparse labeled data are available. Particularly, we show that PIPN predicts the solution of a plane stress problem over more than 500 domains with different geometries, simultaneously. Moreover, we pioneer implementing the concept of remarkable batch size (i.e., the number of geometries fed into PIPN at each sub-epoch) into PIPN. Specifically, we try batch sizes of 7, 14, 19, 38, 76, and 133. Additionally, the effect of the PIPN size, symmetric function in the PIPN architecture, and static and dynamic weights for the component of the sparse labeled data in the loss function are investigated.

CurveCloudNet: Processing Point Clouds with 1D Structure

Modern depth sensors such as LiDAR operate by sweeping laser-beams across the scene, resulting in a point cloud with notable 1D curve-like structures. In this work, we introduce a new point cloud processing scheme and backbone, called CurveCloudNet, which takes advantage of the curve-like structure inherent to these sensors. While existing backbones discard the rich 1D traversal patterns and rely on Euclidean operations, CurveCloudNet parameterizes the point cloud as a collection of polylines (dubbed a "curve cloud"), establishing a local surface-aware ordering on the points. Our method applies curve-specific operations to process the curve cloud, including a symmetric 1D convolution, a ball grouping for merging points along curves, and an efficient 1D farthest point sampling algorithm on curves. By combining these curve operations with existing point-based operations, CurveCloudNet is an efficient, scalable, and accurate backbone with low GPU memory requirements. Evaluations on the ShapeNet, Kortx, Audi Driving, and nuScenes datasets demonstrate that CurveCloudNet outperforms both point-based and sparse-voxel backbones in various segmentation settings, notably scaling better to large scenes than point-based alternatives while exhibiting better single object performance than sparse-voxel alternatives.

SceneHGN: Hierarchical Graph Networks for 3D Indoor Scene Generation with Fine-Grained Geometry

3D indoor scenes are widely used in computer graphics, with applications ranging from interior design to gaming to virtual and augmented reality. They also contain rich information, including room layout, as well as furniture type, geometry, and placement. High-quality 3D indoor scenes are highly demanded while it requires expertise and is time-consuming to design high-quality 3D indoor scenes manually. Existing research only addresses partial problems: some works learn to generate room layout, and other works focus on generating detailed structure and geometry of individual furniture objects. However, these partial steps are related and should be addressed together for optimal synthesis. We propose SCENEHGN, a hierarchical graph network for 3D indoor scenes that takes into account the full hierarchy from the room level to the object level, then finally to the object part level. Therefore for the first time, our method is able to directly generate plausible 3D room content, including furniture objects with fine-grained geometry, and their layout. To address the challenge, we introduce functional regions as intermediate proxies between the room and object levels to make learning more manageable. To ensure plausibility, our graph-based representation incorporates both vertical edges connecting child nodes with parent nodes from different levels, and horizontal edges encoding relationships between nodes at the same level. Extensive experiments demonstrate that our method produces superior generation results, even when comparing results of partial steps with alternative methods that can only achieve these. We also demonstrate that our method is effective for various applications such as part-level room editing, room interpolation, and room generation by arbitrary room boundaries.

Equivalence Between SE(3) Equivariant Networks via Steerable Kernels and Group Convolution

A wide range of techniques have been proposed in recent years for designing neural networks for 3D data that are equivariant under rotation and translation of the input. Most approaches for equivariance under the Euclidean group $\mathrm{SE}(3)$ of rotations and translations fall within one of the two major categories. The first category consists of methods that use $\mathrm{SE}(3)$-convolution which generalizes classical $\mathbb{R}^3$-convolution on signals over $\mathrm{SE}(3)$. Alternatively, it is possible to use \textit{steerable convolution} which achieves $\mathrm{SE}(3)$-equivariance by imposing constraints on $\mathbb{R}^3$-convolution of tensor fields. It is known by specialists in the field that the two approaches are equivalent, with steerable convolution being the Fourier transform of $\mathrm{SE}(3)$ convolution. Unfortunately, these results are not widely known and moreover the exact relations between deep learning architectures built upon these two approaches have not been precisely described in the literature on equivariant deep learning. In this work we provide an in-depth analysis of both methods and their equivalence and relate the two constructions to multiview convolutional networks. Furthermore, we provide theoretical justifications of separability of $\mathrm{SE}(3)$ group convolution, which explain the applicability and success of some recent approaches. Finally, we express different methods using a single coherent formalism and provide explicit formulas that relate the kernels learned by different methods. In this way, our work helps to unify different previously-proposed techniques for achieving roto-translational equivariance, and helps to shed light on both the utility and precise differences between various alternatives. We also derive new TFN non-linearities from our equivalence principle and test them on practical benchmark datasets.