Learning Canonical Embeddings for Unsupervised Shape Correspondence with Locally Linear Transformations

• URL: http://arxiv.org/abs/2209.02152v2
• Date: Wed, 7 Sep 2022 03:31:28 GMT
• Title: Learning Canonical Embeddings for Unsupervised Shape Correspondence with Locally Linear Transformations
• Authors: Pan He, Patrick Emami, Sanjay Ranka, Anand Rangarajan
• Abstract summary: We make the first attempt to adapt the classical locally linear embedding algorithm (LLE) for shape correspondence. We demonstrate that learning the embedding using a new LLE-inspired point cloud reconstruction objective results in accurate shape correspondences.
• Score: 11.69144204466843
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a new approach to unsupervised shape correspondence learning between pairs of point clouds. We make the first attempt to adapt the classical locally linear embedding algorithm (LLE) -- originally designed for nonlinear dimensionality reduction -- for shape correspondence. The key idea is to find dense correspondences between shapes by first obtaining high-dimensional neighborhood-preserving embeddings of low-dimensional point clouds and subsequently aligning the source and target embeddings using locally linear transformations. We demonstrate that learning the embedding using a new LLE-inspired point cloud reconstruction objective results in accurate shape correspondences. More specifically, the approach comprises an end-to-end learnable framework of extracting high-dimensional neighborhood-preserving embeddings, estimating locally linear transformations in the embedding space, and reconstructing shapes via divergence measure-based alignment of probabilistic density functions built over reconstructed and target shapes. Our approach enforces embeddings of shapes in correspondence to lie in the same universal/canonical embedding space, which eventually helps regularize the learning process and leads to a simple nearest neighbors approach between shape embeddings for finding reliable correspondences. Comprehensive experiments show that the new method makes noticeable improvements over state-of-the-art approaches on standard shape correspondence benchmark datasets covering both human and nonhuman shapes.

Related papers

• Curvy: A Parametric Cross-section based Surface Reconstruction [2.1165011830664677]
  We present a novel approach for reconstructing shape point clouds using planar sparse cross-sections with the help of generative modeling. We use a compact parametric polyline representation using adaptive splitting to represent the cross-sections and perform learning using a Graph Neural Network to reconstruct the underlying shape.
  arXiv  Detail & Related papers  (2024-09-01T20:15:08Z)
• Spectral Meets Spatial: Harmonising 3D Shape Matching and Interpolation [50.376243444909136]
  We present a unified framework to predict both point-wise correspondences and shape between 3D shapes. We combine the deep functional map framework with classical surface deformation models to map shapes in both spectral and spatial domains.
  arXiv  Detail & Related papers  (2024-02-29T07:26:23Z)
• Geometrically Consistent Partial Shape Matching [50.29468769172704]
  Finding correspondences between 3D shapes is a crucial problem in computer vision and graphics. An often neglected but essential property of matching geometrics is consistency. We propose a novel integer linear programming partial shape matching formulation.
  arXiv  Detail & Related papers  (2023-09-10T12:21:42Z)
• Bending Graphs: Hierarchical Shape Matching using Gated Optimal Transport [80.64516377977183]
  Shape matching has been a long-studied problem for the computer graphics and vision community. We investigate a hierarchical learning design, to which we incorporate local patch-level information and global shape-level structures. We propose a novel optimal transport solver by recurrently updating features on non-confident nodes to learn globally consistent correspondences between the shapes.
  arXiv  Detail & Related papers  (2022-02-03T11:41:46Z)
• Learning Canonical Embedding for Non-rigid Shape Matching [36.85782408336389]
  This paper provides a novel framework that learns canonical embeddings for non-rigid shape matching. Our framework is trained end-to-end and thus avoids instabilities and constraints associated with the commonly-used Laplace-Beltrami basis.
  arXiv  Detail & Related papers  (2021-10-06T18:09:13Z)
• Representing Shape Collections with Alignment-Aware Linear Models [17.635846912560627]
  We revisit the classical representation of 3D point clouds as linear shape models. Our key insight is to leverage deep learning to represent a collection of shapes as affine transformations.
  arXiv  Detail & Related papers  (2021-09-03T16:28:34Z)
• Learning to generate shape from global-local spectra [0.0]
  We build our method on top of recent advances on the so called shape-from-spectrum paradigm. We consider the spectrum as a natural and ready to use representation to encode variability of the shapes. Our results confirm the improvement of the proposed approach in comparison to existing and alternative methods.
  arXiv  Detail & Related papers  (2021-08-04T16:39:56Z)
• Deep Magnification-Flexible Upsampling over 3D Point Clouds [103.09504572409449]
  We propose a novel end-to-end learning-based framework to generate dense point clouds. We first formulate the problem explicitly, which boils down to determining the weights and high-order approximation errors. Then, we design a lightweight neural network to adaptively learn unified and sorted weights as well as the high-order refinements.
  arXiv  Detail & Related papers  (2020-11-25T14:00:18Z)
• Mapping in a cycle: Sinkhorn regularized unsupervised learning for point cloud shapes [47.49826669394906]
  We propose an unsupervised learning framework for finding dense correspondences between point cloud shapes. In order to learn discriminative pointwise features from point cloud data, we incorporate in the formulation a regularization term based on Sinkhorn normalization. We show that the learned pointwise features can be leveraged by supervised methods to improve the part segmentation performance.
  arXiv  Detail & Related papers  (2020-07-19T05:21:33Z)
• Manifold Learning via Manifold Deflation [105.7418091051558]
  dimensionality reduction methods provide a valuable means to visualize and interpret high-dimensional data. Many popular methods can fail dramatically, even on simple two-dimensional Manifolds. This paper presents an embedding method for a novel, incremental tangent space estimator that incorporates global structure as coordinates. Empirically, we show our algorithm recovers novel and interesting embeddings on real-world and synthetic datasets.
  arXiv  Detail & Related papers  (2020-07-07T10:04:28Z)
• Neural Subdivision [58.97214948753937]
  This paper introduces Neural Subdivision, a novel framework for data-driven coarseto-fine geometry modeling. We optimize for the same set of network weights across all local mesh patches, thus providing an architecture that is not constrained to a specific input mesh, fixed genus, or category. We demonstrate that even when trained on a single high-resolution mesh our method generates reasonable subdivisions for novel shapes.
  arXiv  Detail & Related papers  (2020-05-04T20:03:21Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.