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Convex hulls are useful as tight bounding proxies for a variety of tasks including collision detection, ray intersection, and distance computation. Unfortunately, the complexity of polyhedral convex hulls grows linearly with their input. We…
Simulations have become an indispensable tool for accurate modelling of observables measured in galaxy surveys, but can be expensive if very large dynamic range in scale is required. We describe how to combine Lagrangian perturbation theory…
Embedding tree-like data, from hierarchies to ontologies and taxonomies, forms a well-studied problem for representing knowledge across many domains. Hyperbolic geometry provides a natural solution for embedding trees, with vastly superior…
We present here the first systematic treatment of the problems posed by the visualization and analysis of large-scale, parallel adaptive mesh refinement (AMR) simulations on an Eulerian grid. When compared to those obtained by constructing…
Deep convolutional neural networks (ConvNets) of 3-dimensional kernels allow joint modeling of spatiotemporal features. These networks have improved performance of video and volumetric image analysis, but have been limited in size due to…
We study the problem of partitioning a set of $n$ objects in a metric space into $k$ clusters $V_1,\dots,V_k$. The quality of the clustering is measured by considering the vector of cluster costs and then minimizing some monotone symmetric…
The large-scale structure in cosmology is highly non-Gaussian at late times and small length scales, making it difficult to describe analytically. Parameter inference, data reconstruction, and data generation tasks in cosmology are greatly…
Contours may be viewed as the 2D outline of the image of an object. This type of data arises in medical imaging as well as in computer vision and can be modeled as data on a manifold and can be studied using statistical shape analysis.…
We describe a method to parse a complex, cluttered indoor scene into primitives which offer a parsimonious abstraction of scene structure. Our primitives are simple convexes. Our method uses a learned regression procedure to parse a scene…
Clouds frequently cover the Earth's surface and pose an omnipresent challenge to optical Earth observation methods. The vast majority of remote sensing approaches either selectively choose single cloud-free observations or employ a…
We present an algorithm to extend subhalo merger trees in a low-resolution dark-matter-only simulation by conditionally matching them to those in a high-resolution simulation. The algorithm is general and can be applied to simulation data…
Parallel surrogate optimization algorithms have proven to be efficient methods for solving expensive noisy optimization problems. In this work we develop a new parallel surrogate optimization algorithm (ProSRS), using a novel tree-based…
Plane arrangements are a useful tool for surface and volume modelling. However, their main drawback is poor scalability. We introduce two key novelties that enable the construction of plane arrangements for complex objects and entire…
We present several modifications to the previously proposed MSPP algorithm that can speed-up its execution considerably. The MSPP algorithm leverages a multiscale representation of the environment in $n$ dimensions. The information of the…
Boltzmann samplers and the recursive method are prominent algorithmic frameworks for the approximate-size and exact-size random generation of large combinatorial structures, such as maps, tilings, RNA sequences or various tree-like…
Being able to learn an effective semantic representation directly on raw point clouds has become a central topic in 3D understanding. Despite rapid progress, state-of-the-art encoders are restrictive to canonicalized point clouds, and have…
Measuring the complexity of tree structures can be beneficial in areas that use tree data structures for storage, communication, and processing purposes. This complexity can then be used to compress tree data structures to their…
Motivated by applications in robotics and computer vision, we study problems related to spatial reasoning of a 3D environment using sublevel sets of polynomials. These include: tightly containing a cloud of points (e.g., representing an…
Tubular tree structures such as blood vessels and lung airways are central to many clinical tasks, including diagnosis, treatment planning, and surgical navigation. Accurate centerline extraction with correct topology is essential, as…
In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees…