Some Extensions of the K-means Algorithm for Image Segmentation and Pattern Classiication

In this paper we present some extensions to the k-means algorithm for vector quantization that permit its eecient use in image segmentation and pattern classiication tasks. It is shown that by introducing state variables that correspond to certain statistics of the dynamic behavior of the algorithm, it is possible to nd the representative centers of the lower dimensional manifolds that deene the boundaries between classes, for clouds of multi-dimensional, multi-class data; this permits one, for example, to nd class boundaries directly from sparse data (e.g., in image segmentation tasks) or to eeciently place centers for pattern classiication (e.g., with local Gaussian classiiers). The same state variables can be used to deene algorithms for determining adaptively the optimal number of centers for clouds of data with space-varying density. Some examples of the application of these extensions are also given.