Indexing volumetric shapes with matching and packing

摘要

We describe a novel algorithm for bulk-loading an index with high-dimensional data and apply it to the problem of volumetric shape matching. Our matching and packing algorithm is a general approach for packing data according to a similarity metric. First, an approximate \(k\)-nearest neighbor graph is constructed using vantage-point initialization, an improvement to previous work that decreases construction time while improving the quality of approximation. Then, graph matching is iteratively performed to pack related items closely together. The end result is a dense index with good performance. We define a new query specification for shape matching that uses minimum and maximum shape constraints to explicitly specify the spatial requirements of the desired shape. This specification provides a natural language for performing volumetric shape matching and is readily supported by the geometry-based similarity search (GSS) tree, an indexing structure that maintains explicit representations of volumetric shape. We describe our implementation of a GSS tree for volumetric shape matching and provide a comprehensive evaluation of parameter sensitivity, performance, and scalability. Compared to previous bulk-loading algorithms, we find that matching and packing can construct a GSS tree index in the same amount of time that is denser, flatter, and better performing, with an observed average performance improvement of 2X.