1,033 research outputs found
Avoiding the Global Sort: A Faster Contour Tree Algorithm
We revisit the classical problem of computing the \emph{contour tree} of a
scalar field , where is a
triangulated simplicial mesh in . The contour tree is a
fundamental topological structure that tracks the evolution of level sets of
and has numerous applications in data analysis and visualization.
All existing algorithms begin with a global sort of at least all critical
values of , which can require (roughly) time. Existing
lower bounds show that there are pathological instances where this sort is
required. We present the first algorithm whose time complexity depends on the
contour tree structure, and avoids the global sort for non-pathological inputs.
If denotes the set of critical points in , the running time is
roughly , where is the depth of in
the contour tree. This matches all existing upper bounds, but is a significant
improvement when the contour tree is short and fat. Specifically, our approach
ensures that any comparison made is between nodes in the same descending path
in the contour tree, allowing us to argue strong optimality properties of our
algorithm.
Our algorithm requires several novel ideas: partitioning in
well-behaved portions, a local growing procedure to iteratively build contour
trees, and the use of heavy path decompositions for the time complexity
analysis
Surface networks
© Copyright CASA, UCL. The desire to understand and exploit the structure of continuous surfaces is common to researchers in a range of disciplines. Few examples of the varied surfaces forming an integral part of modern subjects include terrain, population density, surface atmospheric pressure, physico-chemical surfaces, computer graphics, and metrological surfaces. The focus of the work here is a group of data structures called Surface Networks, which abstract 2-dimensional surfaces by storing only the most important (also called fundamental, critical or surface-specific) points and lines in the surfaces. Surface networks are intelligent and “natural ” data structures because they store a surface as a framework of “surface ” elements unlike the DEM or TIN data structures. This report presents an overview of the previous works and the ideas being developed by the authors of this report. The research on surface networks has fou
Simple I/O-efficient flow accumulation on grid terrains
The flow accumulation problem for grid terrains takes as input a matrix of
flow directions, that specifies for each cell of the grid to which of its eight
neighbours any incoming water would flow. The problem is to compute, for each
cell c, from how many cells of the terrain water would reach c. We show that
this problem can be solved in O(scan(N)) I/Os for a terrain of N cells. Taking
constant factors in the I/O-efficiency into account, our algorithm may be an
order of magnitude faster than the previously known algorithm that is based on
time-forward processing and needs O(sort(N)) I/Os.Comment: This paper is an exact copy of the paper that appeared in the
abstract collection of the Workshop on Massive Data Algorithms, Aarhus, 200
Use of plan curvature variations for the identification of ridges and channels on DEM
This paper proposes novel improvements in the traditional algorithms for the identification of ridge and channel (also called ravines) topographic features on raster digital elevation models (DEMs). The overall methodology consists of two main steps: (1) smoothing the DEM by applying a mean filter, and (2) detection of ridge and channel features as cells with positive and negative plan curvature respectively, along with a decline and incline in plan curvature away from the cell in direction orthogonal to the feature axis respectively. The paper demonstrates a simple approach to visualize the multi-scale structure of terrains and utilize it for semi-automated topographic feature identification. Despite its simplicity, the revised algorithm produced markedly superior outputs than a comparatively sophisticated feature extraction algorithm based on conic-section analysis of terrain
- …