Scalar Function Topology Divergence: Comparing Topology of 3D Objects

• URL: http://arxiv.org/abs/2407.08364v3
• Date: Tue, 12 Nov 2024 10:56:38 GMT
• Title: Scalar Function Topology Divergence: Comparing Topology of 3D Objects
• Authors: Ilya Trofimov, Daria Voronkova, Eduard Tulchinskii, Evgeny Burnaev, Serguei Barannikov,
• Abstract summary: We propose a new topological tool for computer vision - Scalar Function Topology Divergence (SFTD) SFTD measures the dissimilarity of multi-scale topology between sublevel sets of two functions having a common domain. The proposed tool provides useful visualizations depicting areas where functions have topological dissimilarities.
• Score: 21.49200381462702
• License:
• Abstract: We propose a new topological tool for computer vision - Scalar Function Topology Divergence (SFTD), which measures the dissimilarity of multi-scale topology between sublevel sets of two functions having a common domain. Functions can be defined on an undirected graph or Euclidean space of any dimensionality. Most of the existing methods for comparing topology are based on Wasserstein distance between persistence barcodes and they don't take into account the localization of topological features. The minimization of SFTD ensures that the corresponding topological features of scalar functions are located in the same places. The proposed tool provides useful visualizations depicting areas where functions have topological dissimilarities. We provide applications of the proposed method to 3D computer vision. In particular, experiments demonstrate that SFTD as an additional loss improves the reconstruction of cellular 3D shapes from 2D fluorescence microscopy images, and helps to identify topological errors in 3D segmentation. Additionally, we show that SFTD outperforms Betti matching loss in 2D segmentation problems.

Related papers

• ParaPoint: Learning Global Free-Boundary Surface Parameterization of 3D Point Clouds [52.03819676074455]
  ParaPoint is an unsupervised neural learning pipeline for achieving global free-boundary surface parameterization. This work makes the first attempt to investigate neural point cloud parameterization that pursues both global mappings and free boundaries.
  arXiv  Detail & Related papers  (2024-03-15T14:35:05Z)
• SemanticTopoLoop: Semantic Loop Closure With 3D Topological Graph Based on Quadric-Level Object Map [0.8158530638728501]
  Loop closure is one of the crucial components in SLAM. Traditional appearance-based methods, such as bag-of-words models, are often limited by local 2D features and the volume of training data.
  arXiv  Detail & Related papers  (2023-11-06T02:30:30Z)
• Enforcing 3D Topological Constraints in Composite Objects via Implicit Functions [60.56741715207466]
  Medical applications often require accurate 3D representations of complex organs with multiple parts, such as the heart and spine. This paper introduces a novel approach to enforce topological constraints in 3D object reconstruction using deep implicit signed distance functions. We propose a sampling-based technique that effectively checks and enforces topological constraints between 3D shapes by evaluating signed distances at randomly sampled points throughout the volume.
  arXiv  Detail & Related papers  (2023-07-16T10:07:15Z)
• Euler Characteristic Transform Based Topological Loss for Reconstructing 3D Images from Single 2D Slices [9.646922337783137]
  We propose a novel topological loss function based on the Euler Characteristic Transform. This loss can be used as an inductive bias to aid the optimization of any neural network toward better reconstructions in the regime of limited data. We show the effectiveness of the proposed loss function by incorporating it into SHAPR, a state-of-the-art shape reconstruction model.
  arXiv  Detail & Related papers  (2023-03-08T02:12:17Z)
• Learning Topology-Preserving Data Representations [9.710409273484464]
  We propose a method for learning topology-preserving data representations (dimensionality reduction) The core of the method is the minimization of the Representation Topology Divergence (RTD) between original high-dimensional data and low-dimensional representation in latent space. The proposed method better preserves the global structure and topology of the data manifold than state-of-the-art competitors as measured by linear correlation, triplet distance ranking accuracy, and Wasserstein distance between persistence barcodes.
  arXiv  Detail & Related papers  (2023-01-31T22:55:04Z)
• Flattening-Net: Deep Regular 2D Representation for 3D Point Cloud Analysis [66.49788145564004]
  We present an unsupervised deep neural architecture called Flattening-Net to represent irregular 3D point clouds of arbitrary geometry and topology. Our methods perform favorably against the current state-of-the-art competitors.
  arXiv  Detail & Related papers  (2022-12-17T15:05:25Z)
• Homography Loss for Monocular 3D Object Detection [54.04870007473932]
  A differentiable loss function, termed as Homography Loss, is proposed to achieve the goal, which exploits both 2D and 3D information. Our method yields the best performance compared with the other state-of-the-arts by a large margin on KITTI 3D datasets.
  arXiv  Detail & Related papers  (2022-04-02T03:48:03Z)
• 3D Equivariant Graph Implicit Functions [51.5559264447605]
  We introduce a novel family of graph implicit functions with equivariant layers that facilitates modeling fine local details. Our method improves over the existing rotation-equivariant implicit function from 0.69 to 0.89 on the ShapeNet reconstruction task.
  arXiv  Detail & Related papers  (2022-03-31T16:51:25Z)
• Capturing Shape Information with Multi-Scale Topological Loss Terms for 3D Reconstruction [7.323706635751351]
  We propose to complement geometrical shape information by including multi-scale topological features, such as connected components, cycles, and voids, in the reconstruction loss. Our method calculates topological features from 3D volumetric data based on cubical complexes and uses an optimal transport distance to guide the reconstruction process. We demonstrate the utility of our loss by incorporating it into SHAPR, a model for predicting the 3D cell shape of individual cells based on 2D microscopy images.
  arXiv  Detail & Related papers  (2022-03-03T13:18:21Z)
• Cylindrical Convolutional Networks for Joint Object Detection and Viewpoint Estimation [76.21696417873311]
  We introduce a learnable module, cylindrical convolutional networks (CCNs), that exploit cylindrical representation of a convolutional kernel defined in the 3D space. CCNs extract a view-specific feature through a view-specific convolutional kernel to predict object category scores at each viewpoint. Our experiments demonstrate the effectiveness of the cylindrical convolutional networks on joint object detection and viewpoint estimation.
  arXiv  Detail & Related papers  (2020-03-25T10:24:58Z)

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.