Daily Papers

Mesh deformation plays a pivotal role in many 3D vision tasks including dynamic simulations, rendering, and reconstruction. However, defining an efficient discrepancy between predicted and target meshes remains an open problem. A prevalent approach in current deep learning is the set-based approach which measures the discrepancy between two surfaces by comparing two randomly sampled point-clouds from the two meshes with Chamfer pseudo-distance. Nevertheless, the set-based approach still has limitations such as lacking a theoretical guarantee for choosing the number of points in sampled point-clouds, and the pseudo-metricity and the quadratic complexity of the Chamfer divergence. To address these issues, we propose a novel metric for learning mesh deformation. The metric is defined by sliced Wasserstein distance on meshes represented as probability measures that generalize the set-based approach. By leveraging probability measure space, we gain flexibility in encoding meshes using diverse forms of probability measures, such as continuous, empirical, and discrete measures via varifold representation. After having encoded probability measures, we can compare meshes by using the sliced Wasserstein distance which is an effective optimal transport distance with linear computational complexity and can provide a fast statistical rate for approximating the surface of meshes. To the end, we employ a neural ordinary differential equation (ODE) to deform the input surface into the target shape by modeling the trajectories of the points on the surface. Our experiments on cortical surface reconstruction demonstrate that our approach surpasses other competing methods in multiple datasets and metrics.

Detecting aligned 3D keypoints is essential under many scenarios such as object tracking, shape retrieval and robotics. However, it is generally hard to prepare a high-quality dataset for all types of objects due to the ambiguity of keypoint itself. Meanwhile, current unsupervised detectors are unable to generate aligned keypoints with good coverage. In this paper, we propose an unsupervised aligned keypoint detector, Skeleton Merger, which utilizes skeletons to reconstruct objects. It is based on an Autoencoder architecture. The encoder proposes keypoints and predicts activation strengths of edges between keypoints. The decoder performs uniform sampling on the skeleton and refines it into small point clouds with pointwise offsets. Then the activation strengths are applied and the sub-clouds are merged. Composite Chamfer Distance (CCD) is proposed as a distance between the input point cloud and the reconstruction composed of sub-clouds masked by activation strengths. We demonstrate that Skeleton Merger is capable of detecting semantically-rich salient keypoints with good alignment, and shows comparable performance to supervised methods on the KeypointNet dataset. It is also shown that the detector is robust to noise and subsampling. Our code is available at https://github.com/eliphatfs/SkeletonMerger.

To characterize the location (mean, median) of a set of graphs, one needs a notion of centrality that is adapted to metric spaces, since graph sets are not Euclidean spaces. A standard approach is to consider the Frechet mean. In this work, we equip a set of graphs with the pseudometric defined by the norm between the eigenvalues of their respective adjacency matrix. Unlike the edit distance, this pseudometric reveals structural changes at multiple scales, and is well adapted to studying various statistical problems for graph-valued data. We describe an algorithm to compute an approximation to the sample Frechet mean of a set of undirected unweighted graphs with a fixed size using this pseudometric.

The shadow of an abstract simplicial complex K with vertices in R^N is a subset of R^N defined as the union of the convex hulls of simplices of K. The Vietoris--Rips complex of a metric space (S,d) at scale β is an abstract simplicial complex whose each k-simplex corresponds to (k+1) points of S within diameter β. In case Ssubsetmathbb R^2 and d(a,b)=|a-b| the standard Euclidean metric, the natural shadow projection of the Vietoris--Rips complex is already proved by Chambers et al. to induce isomorphisms on π_0 and π_1. We extend the result beyond the standard Euclidean distance on Ssubsetmathbb R^N to a family of path-based metrics, d^varepsilon_{S}. From the pairwise Euclidean distances of points in S, we introduce a family (parametrized by varepsilon) of path-based Vietoris--Rips complexes R^varepsilon_β(S) for a scale β>0. If SsubsetR^2 is Hausdorff-close to a planar Euclidean graph G, we provide quantitative bounds on scales β,varepsilon for the shadow projection map of the Vietoris--Rips complex of (S,d^varepsilon_S) at scale β to induce π_1-isomorphism. This paper first studies the homotopy-type recovery of Gsubsetmathbb R^N using the abstract Vietoris--Rips complex of a Hausdorff-close sample S under the d^varepsilon_S metric. Then, our result on the π_1-isomorphism induced by the shadow projection lends itself to providing also a geometrically close embedding for the reconstruction. Based on the length of the shortest loop and large-scale distortion of the embedding of G, we quantify the choice of a suitable sample density varepsilon and a scale β at which the shadow of R^varepsilon_β(S) is homotopy-equivalent and Hausdorff-close to G.

Encoding input coordinates with sinusoidal functions into multi-layer perceptrons (MLPs) has proven effective for implicit neural representations (INRs) of surfaces defined as zero-level sets. However, existing methods often struggle to balance training efficiency, rendering speed, and noise robustness: single-MLP approaches are expensive at inference, grid-based representations are fast but can limit surface smoothness and overfit input noise, and previous multiscale approaches frequently capture noise and produce artifacts due to hard spectral truncation. To address these limitations, we propose M-plicits, a multiscale framework that models surfaces as a residual sum of MLPs trained via a sequence of nested neighborhoods. Unlike existing residual approaches that rely on standard domain-wide sampling and require costly mesh extraction for visualization, our method strictly localizes supervision to narrow bands around the previous zero-level sets. This nested design naturally provides robustness against noisy input data: the coarse network acts as a low-pass filter that establishes a clean geometric prior, while subsequent residuals progressively refine the geometry without fitting to high-frequency artifacts. We further introduce a multiscale sphere-tracing algorithm and a GEMM-based analytical normal computation that bypasses auto-differentiation entirely, yielding high-fidelity real-time rendering. On Stanford and Thingi32, M-plicits achieves the best mean Chamfer distance in the coarse configuration and the best median Chamfer distance and IoU in the fine configuration, with substantially better noise robustness than iNGP, BACON, and IDF, while using an order of magnitude fewer parameters than grid-based baselines. Code, models, and data are available at https://github.com/dsilvavinicius/m-plicits.

Diffusion models have shown strong potential for robot skill learning, yet their role in coverage path planning remains underexplored. In industrial surface processing (painting, polishing, spray coating), high coverage requires globally ordered, temporally coherent trajectories rather than stitching unordered local segments. We reformulate coverage path planning as conditional sequence generation and adopt a geometry-conditioned diffusion framework that synthesizes continuous trajectories directly from raw 3D point clouds. Our method produces temporally ordered trajectory chunks and avoids post-hoc heuristic ordering or stitching in prior learning-based methods via simple sequential concatenation, improving sequence-level consistency. A single shared policy generalizes across different geometries without category-specific architectures. Extensive benchmarks show substantial gains over prior learning-based baselines: 98.2\% lower point-wise Chamfer Distance (lower is better), 97.0\% lower jerk (smoother trajectories), and +67.5 percentage points overlapping surface coverage on average.

Neural radiance fields (NeRFs), 3D Gaussian Splatting (3DGS), and related novel-view synthesis methods are commonly evaluated under capture and reconstruction conditions cleaner than those encountered by robots, drones, and autonomous systems. Benchmarks often rely on reconstruction-friendly trajectories, optimized camera poses and intrinsics, and held-out views sampled from trajectories represented during training. These assumptions can obscure performance with measured poses, reusable camera calibration, and structurally different camera paths. We introduce PIVOT (Pose, Intrinsics and Viewpoint Oriented Testbed), a multi-trajectory dataset, processing pipeline, and evaluation framework for independently studying these factors. PIVOT captures each scene using diverse camera trajectories and retains, where available, both sensor-derived measured poses and COLMAP-optimized poses, together with calibrated and optimized camera intrinsics. It defines three benchmark families: (1) seen versus unseen trajectory novel-view generalization, (2) measured versus optimized pose sensitivity, and (3) calibrated versus optimized intrinsics sensitivity. We also introduce a directed pose-space Chamfer distance to quantify how well training poses cover an evaluation trajectory. PIVOT v1 contains five real-world scenes captured with a DJI Mini 4 Pro and provides an open processing and Nerfstudio-based evaluation toolchain. Benchmark results show a consistent quality gap between held-out views on represented trajectories and unseen trajectories, as well as substantial sensitivity to pose source and camera intrinsics.