Fast nearest neighbor search in medical image databases

We examine the problem of finding similar tumor shapes. Starting from a natural similarity function (the so-called 'max morphological distance'), we show how to lower-bound it and how to search for nearest neighbors in large collections of tumor-like shapes. Specifically, we use state-of-the-art concepts from morphology, namely the 'pattern spectrum' of a shape, to map each shape to a point in n-dimensional space. Following [16, 30], we organize the n-d points in an R-tree. We show that the L(infinity) (=max) norm in the n-d space lower-bounds the actual distance. This guarantees no false dismissals for range queries. In addition, we present a nearest neighbor algorithm that also guarantees no false dismissals. Finally, we implemented the method and tested it against a testbed of realistic tumor shapes, using an established tumor-growth model of Murray Eden[13]. The experiments show that our method is up to 27 times faster than straightforward sequential scanning.