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Semantic shape completion is a challenging problem in 3D computer vision where the task is to generate a complete 3D shape using a partial 3D shape as input. We propose a learning-based approach to complete incomplete 3D shapes through…

In 2D image processing, some attempts decompose images into high and low frequency components for describing edge and smooth parts respectively. Similarly, the contour and flat area of 3D objects, such as the boundary and seat area of a…

Steady states are invaluable in the study of dynamical systems. High-dimensional dynamical systems, due to a separation of time-scales, often evolve towards a lower dimensional manifold $M$. We introduce an approach to locate saddle points…

Generative neural networks have a well recognized ability to estimate underlying manifold structure of high dimensional data. However, if a single latent space is used, it is not possible to faithfully represent a manifold with topology…

This paper considers optimization problems on Riemannian manifolds and analyzes iteration-complexity for gradient and subgradient methods on manifolds with non-negative curvature. By using tools from the Riemannian convex analysis and…

Meta-learning, or "learning to learn," aims to enable models to quickly adapt to new tasks with minimal data. While traditional methods like Model-Agnostic Meta-Learning (MAML) optimize parameters in Euclidean space, they often struggle to…

This paper advocates a novel framework for segmenting a dataset in a Riemannian manifold $M$ into clusters lying around low-dimensional submanifolds of $M$. Important examples of $M$, for which the proposed clustering algorithm is…

Generative adversarial networks (GANs) have emerged as a powerful unsupervised method to model the statistical patterns of real-world data sets, such as natural images. These networks are trained to map random inputs in their latent space…

Machine learning for point clouds has been attracting much attention, with many applications in various fields, such as shape recognition and material science. For enhancing the accuracy of such machine learning methods, it is often…

The emergence of digital avatars has raised an exponential increase in the demand for human point clouds with realistic and intricate details. The compression of such data becomes challenging with overwhelming data amounts comprising…

Capsule Networks (CapsNets) show exceptional graph representation capacity via dynamic routing and vectorized hierarchical representations, but they model the complex geometries of real\-world graphs poorly by fixed\-curvature space due to…

This paper focuses on minimizing a smooth function combined with a nonsmooth regularization term on a compact Riemannian submanifold embedded in the Euclidean space under a decentralized setting. Typically, there are two types of approaches…

This paper proposes a generalized framework with joint normalization which learns lower-dimensional subspaces with maximum discriminative power by making use of the Riemannian geometry. In particular, we model the similarity/dissimilarity…

We present a learning framework for abstracting complex shapes by learning to assemble objects using 3D volumetric primitives. In addition to generating simple and geometrically interpretable explanations of 3D objects, our framework also…

Several important algorithms for machine learning and data analysis use pairwise distances as input. On Riemannian manifolds these distances may be prohibitively costly to compute, in particular for large datasets. To tackle this problem,…

Point cloud learning often rests on the premise that observed samples are noisy traces of an underlying geometric object, such as a manifold embedded in a high-dimensional feature space. Yet much of this geometry is not captured directly by…

Clustering and dimensionality reduction have been crucial topics in machine learning and computer vision. Clustering high-dimensional data has been challenging for a long time due to the curse of dimensionality. For that reason, a more…

In real-world applications, data often reside in restricted domains with unknown boundaries, or as high-dimensional point clouds lying on a lower-dimensional, nontrivial, unknown manifold. Traditional Gaussian Processes (GPs) struggle to…

This paper tries to address a fundamental question in point cloud self-supervised learning: what is a good signal we should leverage to learn features from point clouds without annotations? To answer that, we introduce a point cloud…

Fitting an unknown number of hyperplanes to data is a fundamental yet challenging problem in machine learning, characterized by its non-convexity, non-differentiability, and unknown model order. Existing approaches often struggle with local…