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Topological data analysis (TDA) is a rapidly developing collection of methods for studying the shape of point cloud and other data types. One popular approach, designed to be robust to noise and outliers, is to first use a smoothing…

The ever-increasing 3D application makes the point cloud compression unprecedentedly important and needed. In this paper, we propose a patch-based compression process using deep learning, focusing on the lossy point cloud geometry…

Great progress has been made in point cloud classification with learning-based methods. However, complex scene and sensor inaccuracy in real-world application make point cloud data suffer from corruptions, such as occlusion, noise and…

There has been a growing interest in statistical inference from data satisfying the so-called manifold hypothesis, assuming data points in the high-dimensional ambient space to lie in close vicinity of a submanifold of much lower dimension.…

Robotic manipulation systems benefit from complementary sensing modalities, where each provides unique environmental information. Point clouds capture detailed geometric structure, while RGB images provide rich semantic context. Current…

We propose a novel approach to self-supervised learning of point cloud representations by differentiable neural rendering. Motivated by the fact that informative point cloud features should be able to encode rich geometry and appearance…

For highly skewed or fat-tailed distributions, mean or median-based methods often fail to capture the central tendencies in the data. Despite being a viable alternative, estimating the conditional mode given certain covariates (or mode…

Contemporary deep neural networks offer state-of-the-art results when applied to visual reasoning, e.g., in the context of 3D point cloud data. Point clouds are important datatype for precise modeling of three-dimensional environments, but…

In healthcare, accurately classifying medical images is vital, but conventional methods often hinge on medical data with a consistent grid structure, which may restrict their overall performance. Recent medical research has been focused on…

Data augmentation is widely used to train deep learning models to address data scarcity. However, traditional data augmentation (TDA) typically relies on simple geometric transformation, such as random rotation and rescaling, resulting in…

Multilinear Discriminant Analysis (MDA) is a powerful dimension reduction method specifically formulated to deal with tensor data. Precisely, the goal of MDA is to find mode-specific projections that optimally separate tensor data from…

In this paper, we study linear regression applied to data structured on a manifold. We assume that the data manifold is smooth and is embedded in a Euclidean space, and our objective is to reveal the impact of the data manifold's extrinsic…

Compressing massive LiDAR point clouds in real-time is critical to autonomous machines such as drones and self-driving cars. While most of the recent prior work has focused on compressing individual point cloud frames, this paper proposes a…

Persistence diagrams have been widely recognized as a compact descriptor for characterizing multiscale topological features in data. When many datasets are available, statistical features embedded in those persistence diagrams can be…

We consider the problem of propagating the uncertainty from a possibly large number of random inputs through a computationally expensive model. Stratified sampling is a well-known variance reduction strategy, but its application, thus far,…

Although unsupervised feature learning has demonstrated its advantages to reducing the workload of data labeling and network design in many fields, existing unsupervised 3D learning methods still cannot offer a generic network for various…

Over the last decade, deep learning has shown great success at performing computer vision tasks, including classification, super-resolution, and style transfer. Now, we apply it to data compression to help build the next generation of…

Modern information processing relies on the axiom that high-dimensional data lie near low-dimensional geometric structures. This paper revisits the problem of data-driven learning of these geometric structures and puts forth two new…

Autonomous vehicles need to have a semantic understanding of the three-dimensional world around them in order to reason about their environment. State of the art methods use deep neural networks to predict semantic classes for each point in…

In contrast to supervised backpropagation-based feature learning in deep neural networks (DNNs), an unsupervised feedforward feature (UFF) learning scheme for joint classification and segmentation of 3D point clouds is proposed in this…