6,209 research outputs found
On Range Searching with Semialgebraic Sets II
Let be a set of points in . We present a linear-size data
structure for answering range queries on with constant-complexity
semialgebraic sets as ranges, in time close to . It essentially
matches the performance of similar structures for simplex range searching, and,
for , significantly improves earlier solutions by the first two authors
obtained in~1994. This almost settles a long-standing open problem in range
searching.
The data structure is based on the polynomial-partitioning technique of Guth
and Katz [arXiv:1011.4105], which shows that for a parameter , , there exists a -variate polynomial of degree such that
each connected component of contains at most points
of , where is the zero set of . We present an efficient randomized
algorithm for computing such a polynomial partition, which is of independent
interest and is likely to have additional applications
WARP: Wavelets with adaptive recursive partitioning for multi-dimensional data
Effective identification of asymmetric and local features in images and other
data observed on multi-dimensional grids plays a critical role in a wide range
of applications including biomedical and natural image processing. Moreover,
the ever increasing amount of image data, in terms of both the resolution per
image and the number of images processed per application, requires algorithms
and methods for such applications to be computationally efficient. We develop a
new probabilistic framework for multi-dimensional data to overcome these
challenges through incorporating data adaptivity into discrete wavelet
transforms, thereby allowing them to adapt to the geometric structure of the
data while maintaining the linear computational scalability. By exploiting a
connection between the local directionality of wavelet transforms and recursive
dyadic partitioning on the grid points of the observation, we obtain the
desired adaptivity through adding to the traditional Bayesian wavelet
regression framework an additional layer of Bayesian modeling on the space of
recursive partitions over the grid points. We derive the corresponding
inference recipe in the form of a recursive representation of the exact
posterior, and develop a class of efficient recursive message passing
algorithms for achieving exact Bayesian inference with a computational
complexity linear in the resolution and sample size of the images. While our
framework is applicable to a range of problems including multi-dimensional
signal processing, compression, and structural learning, we illustrate its work
and evaluate its performance in the context of 2D and 3D image reconstruction
using real images from the ImageNet database. We also apply the framework to
analyze a data set from retinal optical coherence tomography
Fast connected component labeling algorithm: a non voxel-based approach
This paper presents a new approach to achieve connected component labeling on both binary images and volumes by using the Extreme Vertices Model (EVM), a representation model for orthogonal
polyhedra, applied to digital images and volume datasets recently. In contrast with previous techniques, this method does not use a voxel-based approach but deals with the inner sections of the object.Postprint (published version
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