Zero-Shot Image Feature Consensus with Deep Functional Maps

Correspondences emerge from large-scale vision models trained for generative and discriminative tasks. This has been revealed and benchmarked by computing correspondence maps between pairs of images, using nearest neighbors on the feature grids. Existing work has attempted to improve the quality of these correspondence maps by carefully mixing features from different sources, such as by combining the features of different layers or networks. We point out that a better correspondence strategy is available, which directly imposes structure on the correspondence field: the functional map. Wielding this simple mathematical tool, we lift the correspondence problem from the pixel space to the function space and directly optimize for mappings that are globally coherent. We demonstrate that our technique yields correspondences that are not only smoother but also more accurate, with the possibility of better reflecting the knowledge embedded in the large-scale vision models that we are studying. Our approach sets a new state-of-the-art on various dense correspondence tasks. We also demonstrate our effectiveness in keypoint correspondence and affordance map transfer.

SAGE: Bridging Semantic and Actionable Parts for GEneralizable Articulated-Object Manipulation under Language Instructions

Generalizable manipulation of articulated objects remains a challenging problem in many real-world scenarios, given the diverse object structures, functionalities, and goals. In these tasks, both semantic interpretations and physical plausibilities are crucial for a policy to succeed. To address this problem, we propose SAGE, a novel framework that bridges the understanding of semantic and actionable parts of articulated objects to achieve generalizable manipulation under language instructions. Given a manipulation goal specified by natural language, an instruction interpreter with Large Language Models (LLMs) first translates them into programmatic actions on the object's semantic parts. This process also involves a scene context parser for understanding the visual inputs, which is designed to generate scene descriptions with both rich information and accurate interaction-related facts by joining the forces of generalist Visual-Language Models (VLMs) and domain-specialist part perception models. To further convert the action programs into executable policies, a part grounding module then maps the object semantic parts suggested by the instruction interpreter into so-called Generalizable Actionable Parts (GAParts). Finally, an interactive feedback module is incorporated to respond to failures, which greatly increases the robustness of the overall framework. Experiments both in simulation environments and on real robots show that our framework can handle a large variety of articulated objects with diverse language-instructed goals. We also provide a new benchmark for language-guided articulated-object manipulation in realistic scenarios.

Rethinking Directional Integration in Neural Radiance Fields

Recent works use the Neural radiance field (NeRF) to perform multi-view 3D reconstruction, providing a significant leap in rendering photorealistic scenes. However, despite its efficacy, NeRF exhibits limited capability of learning view-dependent effects compared to light field rendering or image-based view synthesis. To that end, we introduce a modification to the NeRF rendering equation which is as simple as a few lines of code change for any NeRF variations, while greatly improving the rendering quality of view-dependent effects. By swapping the integration operator and the direction decoder network, we only integrate the positional features along the ray and move the directional terms out of the integration, resulting in a disentanglement of the view-dependent and independent components. The modified equation is equivalent to the classical volumetric rendering in ideal cases on object surfaces with Dirac densities. Furthermore, we prove that with the errors caused by network approximation and numerical integration, our rendering equation exhibits better convergence properties with lower error accumulations compared to the classical NeRF. We also show that the modified equation can be interpreted as light field rendering with learned ray embeddings. Experiments on different NeRF variations show consistent improvements in the quality of view-dependent effects with our simple modification.

Make a Donut: Language-Guided Hierarchical EMD-Space Planning for Zero-shot Deformable Object Manipulation

Deformable object manipulation stands as one of the most captivating yet formidable challenges in robotics. While previous techniques have predominantly relied on learning latent dynamics through demonstrations, typically represented as either particles or images, there exists a pertinent limitation: acquiring suitable demonstrations, especially for long-horizon tasks, can be elusive. Moreover, basing learning entirely on demonstrations can hamper the model's ability to generalize beyond the demonstrated tasks. In this work, we introduce a demonstration-free hierarchical planning approach capable of tackling intricate long-horizon tasks without necessitating any training. We employ large language models (LLMs) to articulate a high-level, stage-by-stage plan corresponding to a specified task. For every individual stage, the LLM provides both the tool's name and the Python code to craft intermediate subgoal point clouds. With the tool and subgoal for a particular stage at our disposal, we present a granular closed-loop model predictive control strategy. This leverages Differentiable Physics with Point-to-Point correspondence (DiffPhysics-P2P) loss in the earth mover distance (EMD) space, applied iteratively. Experimental findings affirm that our technique surpasses multiple benchmarks in dough manipulation, spanning both short and long horizons. Remarkably, our model demonstrates robust generalization capabilities to novel and previously unencountered complex tasks without any preliminary demonstrations. We further substantiate our approach with experimental trials on real-world robotic platforms.

SparseDFF: Sparse-View Feature Distillation for One-Shot Dexterous Manipulation

Humans excel at transferring manipulation skills across diverse object shapes, poses, and appearances due to their understanding of semantic correspondences between different instances. To endow robots with a similar high-level understanding, we develop a Distilled Feature Field (DFF) for 3D scenes, leveraging large 2D vision models to distill semantic features from multiview images. While current research demonstrates advanced performance in reconstructing DFFs from dense views, the development of learning a DFF from sparse views is relatively nascent, despite its prevalence in numerous manipulation tasks with fixed cameras. In this work, we introduce SparseDFF, a novel method for acquiring view-consistent 3D DFFs from sparse RGBD observations, enabling one-shot learning of dexterous manipulations that are transferable to novel scenes. Specifically, we map the image features to the 3D point cloud, allowing for propagation across the 3D space to establish a dense feature field. At the core of SparseDFF is a lightweight feature refinement network, optimized with a contrastive loss between pairwise views after back-projecting the image features onto the 3D point cloud. Additionally, we implement a point-pruning mechanism to augment feature continuity within each local neighborhood. By establishing coherent feature fields on both source and target scenes, we devise an energy function that facilitates the minimization of feature discrepancies w.r.t. the end-effector parameters between the demonstration and the target manipulation. We evaluate our approach using a dexterous hand, mastering real-world manipulations on both rigid and deformable objects, and showcase robust generalization in the face of object and scene-context variations.

EquivAct: SIM(3)-Equivariant Visuomotor Policies beyond Rigid Object Manipulation

If a robot masters folding a kitchen towel, we would also expect it to master folding a beach towel. However, existing works for policy learning that rely on data set augmentations are still limited in achieving this level of generalization. Our insight is to add equivariance to both the visual object representation and policy architecture. We propose EquivAct which utilizes SIM(3)-equivariant network structures that guarantee generalization across all possible object translations, 3D rotations, and scales by construction. Training of EquivAct is done in two phases. We first pre-train a SIM(3)-equivariant visual representation on simulated scene point clouds. Then, we learn a SIM(3)-equivariant visuomotor policy on top of the pre-trained visual representation using a small amount of source task demonstrations. We demonstrate that after training, the learned policy directly transfers to objects that substantially differ in scale, position and orientation from the source demonstrations. In simulation, we evaluate our method in three manipulation tasks involving deformable and articulated objects thereby going beyond the typical rigid object manipulation tasks that prior works considered. We show that our method outperforms prior works that do not use equivariant architectures or do not use our contrastive pre-training procedure. We also show quantitative and qualitative experiments on three real robot tasks, where the robot watches twenty demonstrations of a tabletop task and transfers zero-shot to a mobile manipulation task in a much larger setup. Project website: https://equivact.github.io

Banana: Banach Fixed-Point Network for Pointcloud Segmentation with Inter-Part Equivariance

Equivariance has gained strong interest as a desirable network property that inherently ensures robust generalization. However, when dealing with complex systems such as articulated objects or multi-object scenes, effectively capturing inter-part transformations poses a challenge, as it becomes entangled with the overall structure and local transformations. The interdependence of part assignment and per-part group action necessitates a novel equivariance formulation that allows for their co-evolution. In this paper, we present Banana, a Banach fixed-point network for equivariant segmentation with inter-part equivariance by construction. Our key insight is to iteratively solve a fixed-point problem, where point-part assignment labels and per-part SE(3)-equivariance co-evolve simultaneously. We provide theoretical derivations of both per-step equivariance and global convergence, which induces an equivariant final convergent state. Our formulation naturally provides a strict definition of inter-part equivariance that generalizes to unseen inter-part configurations. Through experiments conducted on both articulated objects and multi-object scans, we demonstrate the efficacy of our approach in achieving strong generalization under inter-part transformations, even when confronted with substantial changes in pointcloud geometry and topology.

NAP: Neural 3D Articulation Prior

We propose Neural 3D Articulation Prior (NAP), the first 3D deep generative model to synthesize 3D articulated object models. Despite the extensive research on generating 3D objects, compositions, or scenes, there remains a lack of focus on capturing the distribution of articulated objects, a common object category for human and robot interaction. To generate articulated objects, we first design a novel articulation tree/graph parameterization and then apply a diffusion-denoising probabilistic model over this representation where articulated objects can be generated via denoising from random complete graphs. In order to capture both the geometry and the motion structure whose distribution will affect each other, we design a graph-attention denoising network for learning the reverse diffusion process. We propose a novel distance that adapts widely used 3D generation metrics to our novel task to evaluate generation quality, and experiments demonstrate our high performance in articulated object generation. We also demonstrate several conditioned generation applications, including Part2Motion, PartNet-Imagination, Motion2Part, and GAPart2Object.

EFEM: Equivariant Neural Field Expectation Maximization for 3D Object Segmentation Without Scene Supervision

We introduce Equivariant Neural Field Expectation Maximization (EFEM), a simple, effective, and robust geometric algorithm that can segment objects in 3D scenes without annotations or training on scenes. We achieve such unsupervised segmentation by exploiting single object shape priors. We make two novel steps in that direction. First, we introduce equivariant shape representations to this problem to eliminate the complexity induced by the variation in object configuration. Second, we propose a novel EM algorithm that can iteratively refine segmentation masks using the equivariant shape prior. We collect a novel real dataset Chairs and Mugs that contains various object configurations and novel scenes in order to verify the effectiveness and robustness of our method. Experimental results demonstrate that our method achieves consistent and robust performance across different scenes where the (weakly) supervised methods may fail. Code and data available at https://www.cis.upenn.edu/~leijh/projects/efem

NeRDi: Single-View NeRF Synthesis with Language-Guided Diffusion as General Image Priors

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.