We consider the problem of computing persistent homology (PH) for large-scale Euclidean point cloud data, aimed at downstream machine learning tasks, where the exponential growth of the most widely-used Vietoris-Rips complex imposes serious computational limitations. Although more scalable alternatives such as the Alpha complex or sparse Rips approximations exist, they often still result in a prohibitively large number of simplices. This poses challenges in the complex construction and in the subsequent PH computation, prohibiting their use on large-scale point clouds. To mitigate these issues, we introduce the Flood complex, inspired by the advantages of the Alpha and Witness complex constructions. Informally, at a given filtration value $r\geq 0$, the Flood complex contains all simplices from a Delaunay triangulation of a small subset of a point cloud $X$ that are fully covered by the union of balls of radius $r$ emanating from $X$, a process we call flooding. Our construction allows for efficient PH computation, possesses several desirable theoretical properties, and is amenable to GPU parallelization. Scaling experiments on 3D point cloud data show that we can compute PH of up to dimension 2 on several millions of points. Importantly, when evaluating object classification performance on real-world and synthetic data, we provide evidence that this scaling capability is needed, especially if objects are geometrically or topologically complex, yielding performance superior to other PH-based methods and neural networks for point cloud data.

Domain adaptation for LiDAR semantic segmentation remains challenging due to the complex structural properties of point cloud data. While mix-based paradigms have shown promise, they often fail to fully leverage the rich structural priors inherent in 3D LiDAR point clouds. In this paper, we identify three critical yet underexploited structural priors: permutation invariance, local consistency, and geometric consistency. We introduce BeyondMix, a novel framework that harnesses the capabilities of State Space Models (specifically Mamba) to construct and exploit these structural priors while modeling long-range dependencies that transcend the limited receptive fields of conventional voxel-based approaches. By employing space-filling curves to impose sequential ordering on point cloud data and implementing strategic spatial partitioning schemes, BeyondMix effectively captures domain-invariant representations. Extensive experiments on challenging LiDAR semantic segmentation benchmarks demonstrate that our approach consistently outperforms existing state-of-the-art methods, establishing a new paradigm for unsupervised domain adaptation in 3D point cloud understanding.

A key requirement for training an accurate 3D object detector is the availability of a large amount of LiDAR-based point cloud data. Unfortunately, labeling point cloud data is extremely challenging, as accurate 3D bounding boxes and semantic labels are required for each potential object. This paper proposes a unified active 3D object detection framework, for greatly reducing the labeling cost of training 3D object detectors. Our framework is based on a novel formulation of submodular optimization, specifically tailored to the problem of active 3D object detection. In particular, we address two fundamental challenges associated with active 3D object detection: data imbalance and the need to cover the distribution of the data, including LiDAR-based point cloud data of varying difficulty levels. Extensive experiments demonstrate that our method achieves state-of-the-art performance with high computational efficiency compared to existing active learning methods. The code is available at https://github.com/RuiyuM/STONE

Recently, 3D point cloud deep learning has been making remarkable strides in various domains, e.g.,

Explainable AI (XAI) is a rapidly growing domain with a myriad of proposed methods as well as metrics aiming to evaluate their efficacy.

Neural Information Processing Systems http://nips.cc/

There exist a handful of techniques to tackle geometric transformations of 3D point cloud data in the context of 3D object recognition.

Domain Adaptation (DA) approaches achieved significant improvements in a wide range of machine learning and computer vision tasks (i.e., classification, detection, and segmentation). However, as far as we are aware, there are few methods yet to achieve domain adaptation directly on 3D point cloud data. The unique challenge of point cloud data lies in its abundant spatial geometric information, and the semantics of the whole object is contributed by including regional geometric structures. Specifically, most general-purpose DA methods that struggle for global feature alignment and ignore local geometric information are not suitable for 3D domain alignment. In this paper, we propose a novel 3D Domain Adaptation Network for point cloud data (PointDAN).