We have generalised a class of similarity measures that are designed to address the problems associated with indexing high-dimensional feature space. The features are stored and indexed component wise. For each dimension we retrieve only those objects close the query point and then apply a local distance function to this subset. Thus we can dramatically reduce the amount of data looked at. We have evaluated these distance measures within a content-based image retrieval (CBIR) framework to determine the trade-off between the percentage of the data retrieved and the precision. Our results show that up to 90% of the data can be ignored whilst maintaining, and in some cases improving, retrieval performance.