A hierarchical algorithm for approximate nearest neighbor searching in a dataset of pyramid-based image representations

Abstract

An algorithm for hierarchical searching an approximate nearest image in a given dataset relative to a submitted image is suggested. The algorithm is supposed to high dimension data and the decision is made in a space of the multiresolution pyramid-based image representations. A computational complexity of the algorithm increases as a logarithm of the image dimension (number of pixels) and as linear function of the dataset cardinality. An efficiency of the algorithm is estimated in terms of a probability distribution for the search errors defined by the differences of distances between the submitted images and the approximate or the nearest decisions, respectively. The algorithm has been tested for two applications, namely, for searching the approximate nearest hand-written digits in MNIST dataset and for gridding noisy images in a digital map taken from Google Maps. For these applications, the empirical search error distributions are calculated using the different values of the algorithm parameter which allows us to change the computational complexity. Also, the linear order of growth of the computational complexity while increasing the dataset cardinality can be decreased.