Related papers: The Application of kd-tree in Astronomy
Neighborhood algorithms may take a considerable percentage of computer time in discrete element methods (DEM). While the sort-and-sweep algorithm is ideal in some ways, as it only deal with particles whose relative positions change in one…
An array of large observational programs using ground-based and space-borne telescopes is planned in the next decade. The forthcoming wide-field sky surveys are expected to deliver a sheer volume of data exceeding an exabyte. Processing the…
We present a ray-tracing technique for radiative transfer modeling of complex three-dimensional (3D) structures which include dense regions of high optical depth like in dense molecular clouds, circumstellar disks, envelopes of evolved…
Nearest neighbor (kNN) methods have been gaining popularity in recent years in light of advances in hardware and efficiency of algorithms. There is a plethora of methods to choose from today, each with their own advantages and…
We introduce a graph partitioning problem motivated by computational topology and propose two algorithms that produce approximate solutions. Specifically, given a weighted, undirected graph $G$ and a positive integer $k$, we desire to find…
Existing methods for retrieving k-nearest neighbours suffer from the curse of dimensionality. We argue this is caused in part by inherent deficiencies of space partitioning, which is the underlying strategy used by most existing methods. We…
Geometric Near-neighbor Access Tree (GNAT) is a metric space indexing method based on hierarchical hyperplane partitioning of the space. While GNAT is very efficient in proximity searching, it has a bad reputation of being a memory hog. We…
Ultrametric trees are trees whose leaves lie at the same distance from the root. They are used to model the genealogy of a population of particles co-existing at the same point in time. We show how the boundary of an ultrametric tree, like…
Airborne discrete return light detection and ranging (LiDAR) point clouds covering forested areas can be processed to segment individual trees and retrieve their morphological attributes. Segmenting individual trees in natural deciduous…
A common approach to implementing similarity search applications is the usage of distance functions, where small distances indicate high similarity. In the case of metric distance functions, metric index structures can be used to accelerate…
With histograms as its foundation, we develop Categorical Exploratory Data Analysis (CEDA) under the extreme-$K$ sample problem, and illustrate its universal applicability through four 1D categorical datasets. Given a sizable $K$, CEDA's…
We formalize the notion of sampling a function using k-d darts. A k-d dart is a set of independent, mutually orthogonal, k-dimensional subspaces called k-d flats. Each dart has d choose k flats, aligned with the coordinate axes for…
With the ever-growing complexity of models in the field of remote sensing (RS), there is an increasing demand for solutions that balance model accuracy with computational efficiency. Knowledge distillation (KD) has emerged as a powerful…
The Baire metric induces an ultrametric on a dataset and is of linear computational complexity, contrasted with the standard quadratic time agglomerative hierarchical clustering algorithm. We apply the Baire distance to spectrometric and…
Object cross-identification in multiple observations is often complicated by the uncertainties in their astrometric calibration. Due to the lack of standard reference objects, an image with a small field of view can have significantly…
A crucial ingredient for numerically solving the 3D radiative transfer problem is the choice of the grid that discretizes the transfer medium. Many modern radiative transfer codes, whether using Monte Carlo or ray tracing techniques, are…
In this paper, a sampling-based trajectory planning algorithm for a laboratory-scale 3D gantry crane in an environment with static obstacles and subject to bounds on the velocity and acceleration of the gantry crane system is presented. The…
High redshift sources suffer from magnification or demagnification due to weak gravitational lensing by large scale structure. One consequence of this is that the distance-redshift relation, in wide use for cosmological tests, suffers…
We present an algorithm for the fast computation of the general $N$-point spatial correlation functions of any discrete point set embedded within an Euclidean space of $\mathbb{R}^n$. Utilizing the concepts of kd-trees and graph databases,…
In this paper we present some new, practical, geometric optimization techniques for computing polygon partitions, 1D and 2D point, interval, square and rectangle covers, as well as 1D and 2D interval and rectangle K-centers. All the…