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ISPRS Int. J. Geo-Inf. 2017, 6(4), 100; doi:10.3390/ijgi6040100

Affine-Invariant Triangulation of Spatio-Temporal Data with an Application to Image Retrieval

1
Luciad, Gaston Geenslaan 11, 3001 Leuven, Belgium
2
UHasselt – Hasselt University and transnational University Limburg, Databases and Theoretical Computer Science Research Group, Agoralaan, Gebouw D, 3590 Diepenbeek, Belgium
3
Department of Computer Science & Engineering, University of Nebraska-Lincoln, 256 Avery Hall, 1144 T Street, Lincoln, NE 68588-0115, USA
*
Author to whom correspondence should be addressed.
Received: 10 February 2017 / Revised: 22 March 2017 / Accepted: 25 March 2017 / Published: 28 March 2017
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Abstract

In the geometric data model for spatio-temporal data, introduced by Chomicki and Revesz [1], spatio-temporal data are modelled as a finite collection of triangles that are transformed by time-dependent affinities of the plane. To facilitate querying and animation of spatio-temporal data, we present a normal form for data in the geometric data model. We propose an algorithm for constructing this normal form via a spatio-temporal triangulation of geometric data objects. This triangulation algorithm generates new geometric data objects that partition the given objects both in space and in time. A particular property of the proposed partition is that it is invariant under time-dependent affine transformations, and hence independent of the particular choice of coordinate system used to describe the spatio-temporal data in. We can show that our algorithm works correctly and has a polynomial time complexity (of reasonably low degree in the number of input triangles and the maximal degree of the polynomial functions that describe the transformation functions). We also discuss several possible applications of this spatio-temporal triangulation. The application of our affine-invariant spatial triangulation method to image indexing and retrieval is discussed and an experimental evaluation is given in the context of bird images. View Full-Text
Keywords: spatio-temporal data models; affine transformations; triangulations spatio-temporal data models; affine transformations; triangulations
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Haesevoets, S.; Kuijpers, B.; Revesz, P.Z. Affine-Invariant Triangulation of Spatio-Temporal Data with an Application to Image Retrieval. ISPRS Int. J. Geo-Inf. 2017, 6, 100.

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