Index spaces for 3D retrieval: toward a better understanding of their geometry and distribution

E. Paquet; H. L. Viktor

doi:10.1117/12.837238

4 February 2010 Index spaces for 3D retrieval: toward a better understanding of their geometry and distribution

E. Paquet, H. L. Viktor

Proceedings Volume 7526, Three-Dimensional Image Processing (3DIP) and Applications; 75260J (2010) https://doi.org/10.1117/12.837238
Event: IS&T/SPIE Electronic Imaging, 2010, San Jose, California, United States

Abstract

Distance is a fundamental concept when considering the information retrieval and cluster analysis of 3D information. That is, a large number of information retrieval descriptor comparison and cluster analysis algorithms are built around the very concept of the distance, such as the Mahalanobis or Manhattan distances, between points. Although not always explicitly stated, a significant proportion of these distances are, by nature, Euclidian. This implies that it is assumed that the data distribution, from a geometrical point of view, may be associated with a Euclidian flat space. In this paper, we draw attention to the fact that this association is, in many situations, not appropriate. Rather, the data should often be characterised by a Riemannian curved space. It is shown how to construct such a curved space and how to analyse its geometry from a topological point of view. The paper also illustrates how, in curved space, the distance between two points may be calculated. In addition, the consequences for information retrieval and cluster analysis algorithms are discussed.

Citation Download Citation

E. Paquet and H. L. Viktor "Index spaces for 3D retrieval: toward a better understanding of their geometry and distribution", Proc. SPIE 7526, Three-Dimensional Image Processing (3DIP) and Applications, 75260J (4 February 2010); https://doi.org/10.1117/12.837238

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