Related papers: Line Simplification
Inspired by cartographic generalization principles, we present a generalization technique for rendering line charts at different sizes, preserving the important semantics of the data at that display size. The algorithm automatically…
Simplification is one of the fundamental operations used in geoinformation science (GIS) to reduce size or representation complexity of geometric objects. Although different simplification methods can be applied depending on one's purpose,…
There are many practical applications that require simplification of polylines. Some of the goals are to reduce the amount of information necessary to store, improve processing time, or simplify editing. The simplification is usually done…
The continuous and rapid growth of highly interconnected datasets, which are both voluminous and complex, calls for the development of adequate processing and analytical techniques. One method for condensing and simplifying such datasets is…
The principal innovative idea in this paper is to transform the original complex nonlinear modeling problem into a combination of linear problem and very simple nonlinear problems. The key step is the generalized linearization of nonlinear…
The simplification of a multigraph into a simple graph can be abstracted to a more general comma category under some common conditions. When using the identity functor, the category of simple objects in a comma category generalizes the…
A fractal can be simply understood as a set or pattern in which there are far more small things than large ones, e.g., far more small geographic features than large ones on the earth surface, or far more large-scale maps than small-scale…
By generalizing the notion of linearization, a concept originally arising from microlocal analysis and symbolic calculus, to diffeological spaces, we make a first proposal setting for optimization problems in this category. We show how…
Topological simplification is the process of reducing complexity of a function while maintaining its essential features. Its goal is to find a new filter function, which reorders cells of the input complex in a way which eliminates some…
We give necessary and sufficient criteria for elementary operations in a two-dimensional terrain to preserve the persistent homology induced by the height function. These operations are edge flips and removals of interior vertices,…
A trivializing map is a field transformation whose Jacobian determinant exactly cancels the interaction terms in the action, providing a representation of the theory in terms of a deterministic transformation of a distribution from which…
Can one reduce the size of a graph without significantly altering its basic properties? The graph reduction problem is hereby approached from the perspective of restricted spectral approximation, a modification of the spectral similarity…
As modeling and visualization applications proliferate, there arises a need to simplify large polygonal models at interactive rates. Unfortunately existing polygon mesh simplification algorithms are not well suited for this task because…
Spectral sparsification is a general technique developed by Spielman et al. to reduce the number of edges in a graph while retaining its structural properties. We investigate the use of spectral sparsification to produce good visual…
A line field on a manifold is a smooth map which assigns a tangent line to all but a finite number of points of the manifold. As such, it can be seen as a generalization of vector fields. They model a number of geometric and physical…
Shortest paths are not always simple. In planar networks, they can be very different from those with the smallest number of turns - the simplest paths. The statistical comparison of the lengths of the shortest and simplest paths provides a…
General-purpose Markov Chain Monte Carlo sampling algorithms suffer from a dramatic reduction in efficiency as the system being studied is driven towards a critical point. Recently, a series of seminal studies suggested that normalizing…
This text is aimed at undergraduates, or anyone else who enjoys thinking about shapes and numbers. The goal is to encourage the student to think deeply about seemingly simple things. The main objects of study are lines, squares, and the…
While advances in computing resources have made processing enormous amounts of data possible, human ability to identify patterns in such data has not scaled accordingly. Efficient computational methods for condensing and simplifying data…
Numerical computations involving rational matrices often benefit from preserving underlying matrix structures such as symmetry, Hermitian properties, or sparsity that reflect physical, geometric, or algebraic characteristics of the system.…