High-Dimensional Feature Matching: Employing the Concept of Meaningful Nearest Neighbors

Matching of high-dimensional features using nearest neighbors search is an important part of image matching methods which are based on local invariant features. In this work we highlight effects pertinent to high-dimensional spaces that are significant for matching, yet have not been explicitly accounted for in previous work. In our approach, we require every nearest neighbor to be meaningful, that is, sufficiently close to a query feature such that it is an out-lier to a background feature distribution. We estimate the background feature distribution from the extended neighborhood of a query feature given by its k nearest neighbors. Based on the concept of meaningful nearest neighbors, we develop a novel high-dimensional feature matching method and evaluate its performance by conducting image matching on two challenging image data sets. A superior performance in terms of accuracy is shown in comparison to several state-of-the-art approaches. Additionally, to make search for k nearest neighbors more efficient, we develop a novel approximate nearest neighbors search method based on sparse coding with an overcomplete basis set that provides a ten-fold speed-up over an exhaustive search even for high dimensional spaces and retains excellent approximation to an exact nearest neighbors search.