Vebjorn Ljosa, Arnab Bhattacharya, and Ambuj K. Singh:
“Indexing Spatially Sensitive Distance Measures Using Multi-Resolution Lower Bounds,”
in Proceedings of the 10th International Conference on Extending Database Technology (EDBT), p. 865-883, March, 2006, doi:10.1007/11687238_51.
Comparison of images requires a distance metric that is sensitive to the spatial location of objects and features. Such sensitive distance measures can, however, be computationally infeasible due to the high dimensionality of feature spaces coupled with the need to model the spatial structure of the images.
We present a novel multi-resolution approach to indexing spatially sensitive distance measures. We derive practical lower bounds for the earth mover's distance (EMD). Multiple levels of lower bounds, one for each resolution of the index structure, are incorporated into algorithms for answering range queries and k-NN queries, both by sequential scan and using an M-tree index structure. Experiments show that using the lower bounds reduces the running time of similarity queries by a factor of up to 36 compared to a sequential scan without lower bounds. Computing separately for each dimension of the feature vector yields a speedup of ~14. By combining the two techniques, similarity queries can be answered more than 500 times faster.