Multi-vector feature space based on pseudo-Euclidean space and oblique basis for similarity searches of images

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.