Preserving Topological and Geometric Embeddings for Point Cloud Recovery

TL;DR

This paper introduces TopGeoFormer, an end-to-end architecture that preserves topological and geometric features for improved point cloud sampling and recovery, outperforming existing methods.

Contribution

The paper presents a novel architecture with InterTwining Attention and specialized loss functions to better maintain topological and geometric properties during point cloud processing.

Findings

Significantly outperforms existing sampling and recovery methods.

Effectively preserves topological and geometric attributes in point clouds.

Demonstrates improved geometric detail reconstruction.

Abstract

Recovering point clouds involves the sequential process of sampling and restoration, yet existing methods struggle to effectively leverage both topological and geometric attributes. To address this, we propose an end-to-end architecture named \textbf{TopGeoFormer}, which maintains these critical properties throughout the sampling and restoration phases. First, we revisit traditional feature extraction techniques to yield topological embedding using a continuous mapping of relative relationships between neighboring points, and integrate it in both phases for preserving the structure of the original space. Second, we propose the \textbf{InterTwining Attention} to fully merge topological and geometric embeddings, which queries shape with local awareness in both phases to form a learnable 3D shape context facilitated with point-wise, point-shape-wise, and intra-shape features. Third, we introduce a full geometry loss and a topological constraint loss to optimize the embeddings in both Euclidean and topological spaces. The geometry loss uses inconsistent matching between coarse-to-fine generations and targets for reconstructing better geometric details, and the constraint loss limits embedding variances for better approximation of the topological space. In experiments, we comprehensively analyze the circumstances using the conventional and learning-based sampling/upsampling/recovery algorithms. The quantitative and qualitative results demonstrate that our method significantly outperforms existing sampling and recovery methods.