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3D generative modeling is accelerating as the technology allowing the capture of geometric data is developing. However, the acquired data is often inconsistent, resulting in unregistered meshes or point clouds. Many generative learning…
The curse of dimensionality is a phenomenon frequently observed in machine learning (ML) and knowledge discovery (KD). There is a large body of literature investigating its origin and impact, using methods from mathematics as well as from…
This paper proposes a new high dimensional regression method by merging Gaussian process regression into a variational autoencoder framework. In contrast to other regression methods, the proposed method focuses on the case where output…
Diffusion maps are a commonly used kernel-based method for manifold learning, which can reveal intrinsic structures in data and embed them in low dimensions. However, as with most kernel methods, its implementation requires a heavy…
Voronoi constellations (VCs) are finite sets of vectors of a coding lattice enclosed by the translated Voronoi region of a shaping lattice, which is a sublattice of the coding lattice. In conventional VCs, the shaping lattice is a scaled-up…
In this work, we present a general, efficient, and provably robust representation for intrinsic triangulations. These triangulations have emerged as a powerful tool for robust geometry processing of surface meshes, taking a low-quality mesh…
All that structure from motion algorithms "see" are sets of 2D points. We show that these impoverished views of the world can be faked for the purpose of reconstructing objects in challenging settings, such as from a single image, or from a…
From descent theory to higher geometry, the idea of gluing has been embedded in many elegant and powerful techniques, proving instrumental for the solution of many problems. In this paper, we introduce a framework that allows to link…
With more satellite and model precipitation data becoming available, new analytical methods are needed that can take advantage of emerging data patterns to make well informed predictions in many hydrological applications. We propose a new…
The lecture notes describe the Delaunay Tessellation Field Estimator for Cosmic Web analysis. The high sensitivity of Voronoi/Delaunay tessellations to the local point distribution is used to obtain estimates of density and related…
Density modeling is notoriously difficult for high dimensional data. One approach to the problem is to search for a lower dimensional manifold which captures the main characteristics of the data. Recently, the Gaussian Process Latent…
This tutorial provides an exposition of a flexible geometric framework for high dimensional estimation problems with constraints. The tutorial develops geometric intuition about high dimensional sets, justifies it with some results of…
In this work, a cut high-dimensional model representation (cut-HDMR) expansion based on multiple anchors is constructed via the clustering method. Specifically, a set of random input realizations is drawn from the parameter space and…
Cross-view geo-spatial learning consists of two important tasks: Cross-View Geo-Localization (CVGL) and Cross-View Image Synthesis (CVIS), both of which rely on establishing geometric correspondences between ground and aerial views. Recent…
Advances in deep learning have led to remarkable success in augmented microscopy, enabling us to obtain high-quality microscope images without using expensive microscopy hardware and sample preparation techniques. However, current deep…
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…
Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of…
Any solid object can be decomposed into a collection of convex polytopes (in short, convexes). When a small number of convexes are used, such a decomposition can be thought of as a piece-wise approximation of the geometry. This…
Deep learning-based approaches, particularly graph neural networks (GNNs), have gained prominence in simulating flexible deformations and contacts of solids, due to their ability to handle unstructured physical fields and nonlinear…
Neural models learn representations of high-dimensional data on low-dimensional manifolds. Multiple factors, including stochasticities in the training process, model architectures, and additional inductive biases, may induce different…