Related papers: Resampling and averaging coordinates on data

Deep neural networks have achieved impressive results in many image classification tasks. However, since their performance is usually measured in controlled settings, it is important to ensure that their decisions remain correct when…

Reconstructing a continuous surface from an unoritented 3D point cloud is a fundamental task in 3D shape processing. In recent years, several methods have been proposed to address this problem using implicit neural representations (INRs).…

While generalizing well over natural inputs, neural networks are vulnerable to adversarial inputs. Existing defenses against adversarial inputs have largely been detached from the real world. These defenses also come at a cost to accuracy.…

Existing ordinal embedding methods usually follow a two-stage routine: outlier detection is first employed to pick out the inconsistent comparisons; then an embedding is learned from the clean data. However, learning in a multi-stage manner…

Point cloud upsampling is to densify a sparse point set acquired from 3D sensors, providing a denser representation for the underlying surface. Existing methods divide the input points into small patches and upsample each patch separately,…

Compression of point clouds has so far been confined to coding the positions of a discrete set of points in space and the attributes of those discrete points. We introduce an alternative approach based on volumetric functions, which are…

We develop a general framework for the probabilistic analysis of random finite point clouds in the context of topological data analysis. We extend the notion of a barcode of a finite point cloud to compact metric spaces. Such a barcode…

Most deep learning-based point cloud processing methods are supervised and require large scale of labeled data. However, manual labeling of point cloud data is laborious and time-consuming. Self-supervised representation learning can…

Graph representation learning is a fast-growing field where one of the main objectives is to generate meaningful representations of graphs in lower-dimensional spaces. The learned embeddings have been successfully applied to perform various…

Reconstruction of a continuous surface of two-dimensional manifold from its raw, discrete point cloud observation is a long-standing problem. The problem is technically ill-posed, and becomes more difficult considering that various sensing…

We show that geometric inference of a point cloud can be calculated by examining its kernel density estimate with a Gaussian kernel. This allows one to consider kernel density estimates, which are robust to spatial noise, subsampling, and…

We introduce a new approach for smoothing and improving the quality of word embeddings. We consider a method of fusing word embeddings that were trained on the same corpus but with different initializations. We project all the models to a…

Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…

Clustering high-dimensional datasets is hard because interpoint distances become less informative in high-dimensional spaces. We present a clustering algorithm that performs nonlinear dimensionality reduction and clustering jointly. The…

Deep representation learning has become one of the most widely adopted approaches for visual search, recommendation, and identification. Retrieval of such representations from a large database is however computationally challenging.…

This works extends the Random Embedding Bayesian Optimization approach by integrating a warping of the high dimensional subspace within the covariance kernel. The proposed warping, that relies on elementary geometric considerations, allows…

Three-dimensional geometric data offer an excellent domain for studying representation learning and generative modeling. In this paper, we look at geometric data represented as point clouds. We introduce a deep AutoEncoder (AE) network with…

The study of provable adversarial robustness has mostly been limited to classification tasks and models with one-dimensional real-valued outputs. We extend the scope of certifiable robustness to problems with more general and structured…

This study proposes a data condensation method for multivariate kernel density estimation by genetic algorithm. First, our proposed algorithm generates multiple subsamples of a given size with replacement from the original sample. The…

The learning and aggregation of multi-scale features are essential in empowering neural networks to capture the fine-grained geometric details in the point cloud upsampling task. Most existing approaches extract multi-scale features from a…