Locally Linear Embedding Clustering Algorithm for Natural Imagery

AbstractThe ability to characterize the color content of natural imagery is animportant application of image processing. The pixel by pixel coloring ofimages may be viewed naturally as points in color space, and the inherentstructure and distribution of these points a ords a quantization, throughclustering, of the color information in the image. In this paper, we presenta novel topologically driven clustering algorithm that permits segmentationof the color features in a digital image. The algorithm blends Locally LinearEmbedding (LLE) and vector quantization by mapping color information toa lower dimensional space, identifying distinct color regions, and classify-ing pixels together based on both a proximity measure and color content.It is observed that these techniques permit a signi cant reduction in colorresolution while maintaining the visually important features of images.Keywords:Color Image Quantization, Geometric Data Analysis, Locally LinearEmbedding, Manifold Learning, Clustering, Subspace Segmentation1. IntroductionManifold learning in data analysis assumes that a set of observations,taken as a whole, is locally well approximated by a topological (or even ge-ometric) manifold. This assumption implies that the data is locally wellapproximated by a linear space, i.e., it is locally at. A fundamental goalof manifold learning is to uncover the underlying structure of this approxi-mating manifold and to nd low dimensional representations that preservethe structure and topology of the original data set optimally [1], [2], [3]. Afrequent simplifying assumption is that the local dimension is constant over