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(a) Electron backscatter diffraction image taken from a particle of wulfenite.
The detection of straight lines is key for the identiffication of the particle's crystalline
phase. (c) Gray image of infection with H1N1 in MDCK-SIAT1 cells. The detection
of circles is important for automated counting process in clonogenic assays. Our
approach was used, without any changes, to automatically detect the straight lines
and circles shown in (a) and (c) from the edge information shown in (b) and (d),
respectively.
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A General Framework for Subspace Detection in Unordered Multidimensional Data
Pattern Recognition.
Volume 45, Number 9, September 2012, pp. 3566-3579. [DOI]
Contents
The analysis of large volumes of unordered multidimensional data is a problem
confronted by scientists and data analysts every day. Often, it involves searching
for data alignments that emerge as well-defined structures or geometric patterns
in datasets. For example, straight lines, circles, and ellipses represent meaningful
structures in data collected from electron backscatter diffraction, particle accelerators,
and clonogenic assays. Also, customers with similar behavior describe linear
correlations in e-commerce databases. We describe a general approach for detecting
data alignments in large unordered noisy multidimensional datasets. In contrast to
classical techniques such as the Hough transforms, which are designed for detecting
a specific type of alignment on a given type of input, our approach is independent of
the geometric properties of the alignments to be detected, as well as independent of
the type of input data. Thus, it allows concurrent detection of multiple kinds of data
alignments, in datasets containing multiple types of data. Given its general nature,
optimizations developed for our technique immediately benefit all its applications,
regardless the type of input data.
Paper
Full Paper (pre-print)
The final publication is available at ScienceDirect - Elsevier
Supplementary Materials
Some Models of Geometry and the Geometric Interpretation of Subspaces
Standard Hough Transforms for Straight Line Detection as a Particular Case of the Proposed Subspace Detection Framework
Voronoi Diagram as Byproduct of the Proposed Subspace Detection Framework
Notation
Citation
Fernandes, Leandro A. F. and Manuel M. Oliveira.
"A General Framework for Subspace Detection in Unordered Multidimensional Data".
Pattern Recognition. Volume 45, Number 9, September 2012, pp. 3566-3579.
BibTeX
@article {FernadesOliveira2012GFSD,
author = {Leandro A. F. Fernandes and Manuel M. Oliveira},
title = {A General Framework for Subspace Detection in Unordered Multidimensional Data},
journal = {Pattern Recognition},
year = {2012},
volume = {45}
number = {9},
pages = {3566-3579},
doi = {http://dx.doi.org/10.1016/j.patcog.2012.02.033},
issn = {0031-3203}
}
Keywords
Hough transform, Geometric algebra, Parameter space, Subspace detection, Shape detection, Blade, Grassmannian, Coordinate chart, Line, Circle,
Plane, Sphere, Conic section, Flat, Round, Quadric.
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CNPq-Brazil fellowships and grants #142627/2007-0 and 308936/2010-8, FAPERGS PQG 10/1322-0 |