Related papers: Hilbert curves for efficient exploratory landscape…
The goal of load balancing (grid partitioning) is to minimize overall computations and communications, and to make sure that all processors have a similar workload. Geometric methods divide a grid by using a location of a cell while…
Space-filling curves like the Hilbert-curve, Peano-curve and Z-order map natural or real numbers from a two or higher dimensional space to a one dimensional space preserving locality. They have numerous applications like search structures,…
Based on the seminal work on Array-RQMC methods and rank-1 lattice sequences by Pierre L'Ecuyer and collaborators, we introduce efficient deterministic algorithms for image synthesis. Enumerating a low discrepancy sequence along the Hilbert…
The paper presents a systematic strategy for implementing Hilbert's space filling curve for use in online exploration tasks and addresses its application in scenarios wherein the space to be searched obstacles (or holes) whose locations are…
This paper addresses the problem of exploring a region using the Hilbert's space-filling curve in the presence of obstacles. No prior knowledge of the region being explored is assumed. An online algorithm is proposed which can implement…
Hilbert's two-dimensional space-filling curve is appreciated for its good locality-preserving properties and easy implementation for many applications. However, Hilbert did not describe how to generalize his construction to higher…
Curve-based representations, particularly integral curves, are often used to represent large-scale computational fluid dynamic simulations. Processing and analyzing curve-based vector field data sets often involves searching for neighboring…
Hyperspectral measurements from long range sensors can give a detailed picture of the items, materials, and chemicals in a scene but analysis can be difficult, slow, and expensive due to high spatial and spectral resolutions of…
Computer vision has become a major source of information for autonomous navigation of robots of various types, self-driving cars, military robots and mars/lunar rovers are some examples. Nevertheless, the majority of methods focus on…
Severe background clutter is challenging in many computer vision tasks, including large-scale image retrieval. Global descriptors, that are popular due to their memory and search efficiency, are especially prone to corruption by such a…
In this paper we introduce an algorithm of construction of cyclic space-filling curves. One particular construction provides a family of space-filling curves in all dimensions (H-curves). They are compared here with the Hilbert curve in the…
Curve samplers are sampling algorithms that proceed by viewing the domain as a vector space over a finite field, and randomly picking a low-degree curve in it as the sample. Curve samplers exhibit a nice property besides the sampling…
We report our participation in the SISAP 2025 Indexing Challenge using a novel indexing technique called the Hilbert forest. The method is based on the fast Hilbert sort algorithm, which efficiently orders high-dimensional points along a…
The recent developments of basis pursuit and compressed sensing seek to extract information from as few samples as possible. In such applications, since the number of samples is restricted, one should deploy the sampling points wisely. We…
Space filling curves are widely used in Computer Science. In particular Hilbert curves and their generalisations to higher dimension are used as an indexing method because of their nice locality properties. This article generalises this…
Identifying the underlying models in a set of data points contaminated by noise and outliers, leads to a highly complex multi-model fitting problem. This problem can be posed as a clustering problem by the projection of higher order…
Sampling-based algorithms solve the path planning problem by generating random samples in the search-space and incrementally growing a connectivity graph or a tree. Conventionally, the sampling strategy used in these algorithms is biased…
Given a set of vectors (the data) in a Hilbert space H, we prove the existence of an optimal collection of subspaces minimizing the sum of the square of the distances between each vector and its closest subspace in the collection. This…
Salient object detection aims to locate objects that capture human attention within images. Previous approaches often pose this as a problem of image contrast analysis. In this work, we model an image as a hypergraph that utilizes a set of…
Sparse polynomial approximation has become indispensable for approximating smooth, high- or infinite-dimensional functions from limited samples. This is a key task in computational science and engineering, e.g., surrogate modelling in…