A linear time implementation of k-means for multilevel thresholding of grayscale images

Abstract

In this paper we present a method based on the k-means algorithm for multilevel thresholding of grayscale images. The clustering is computed over the histogram rather than on the full list of intensity levels. Our implementation runs in linear time per iteration proportional to the number of bins of the histogram, not depending on the size of the image nor on the number of clusters/levels as in a traditional implementation. Therefore, it is possible to get a large speedup when the number of bins of the histogram is significantly shorter than the number of pixels. In order to achieve that running time, two restrictions were exploited in our implementation: (I) we target only grayscale images and (II) thresholding does not use spatial information.