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Multi-Vector Feature Space Based on Pseudo-Euclidean Space
and Oblique Basis for Similarity Searches of Images
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Yasuo Yamane, Futjisu Laboratories Ltd. *

Tadashi Hoshiai, Futjisu Laboratories Ltd.

Hiroshi Tsuda, Futjisu Laboratories Ltd.

Kaoru Katayama, Tokyo Metropolitan University

Manabu Ohta, Tokyo Metropolitan University

Hiroshi Ishikawa, Tokyo Metropolitan University

Investigators have tried to increase the precision of similarity
searches of images by using distance functions that reflect the
similarity of features. When the quadratic-form distance is used,
however, dissimilar images can be judged to be similar. We therefore
propose that the similarity of images be evaluated using a measure
of distance in a multi-vector feature space based on pseudo-Euclidean
space and an oblique basis (MVPO). In this space an image is
represented by a set of vectors each of which represents each
feature. And we propose a distance (called D-distance) between
two sets of vectors. Roughly speaking, it is the distance between solids.
Another representative distance used in similarity searches is
the Earth Mover's Distance (EMD). It can be formalized using MVPO,
and that explains well why EMD outperforms quad-ratic-form distance.
The main difference between EMD and D-distance is that EMD is based
on partial matching and D-distance is based on total matching.
We also discuss performance issues of MPVO and D-distance
to address practical use of them.