Distance Quantization Method for Fast Nearest Neighbor Search Computations with applications to Motion Estimation

The problem of given a query vector finding its nearest neighbor within a large set of vectors in high dimensional space arises in many applications. It often poses serious computational challenges due to the size of data point set (database), dimensionality of the search space, and the metric complexity. There exists a wealth of results in the literature that reduce complexity primarily based on altering the data set while still computing the chosen distance metric to full precision. However further significant simplification is attainable with our proposed approach which reduces the search metric computation resolution by applying non-uniform quantization within the metric computation process, in such a way that the minimum distance ranking is most likely to be preserved. This paper provides analytical and experimental studies of our proposed approach. We present an analytical formulation of the search performance measure that gives insight into understanding this approach. Based on this formulation we present a quantizer optimized to minimize the impact of quantization on identifying the nearest neighbor. The main advantages of this approach are that: i) it can reduce the number and complexity of required arithmetic operations significantly, ii) complexity does not increase with the order of l_p norm or input bit size, and increases only slowly with dimensionality, and most importantly iii) the penalty to be paid in performance for the complexity reduction is very small if designed optimally. Motion estimation and compensation for video coding is chosen as an example application. Without requiring any filtering, transform, or sorting process, using a simple hardware oriented mapping, our experimental results show on average 0.05 dB loss using only 1 bit per pixel distance (0.01 dB when 2 bits are used) instead of typical 8 or 16 bits metrics.