Unsupervised Spectral-Spatial Classification of Hyperspectral Imagery using Real and Complex Features and Generalized Histograms Julio M. Duarte-Carvajalino, a Guillermo Sapiro, b Miguel Velez-Reyes a a University of Puerto Rico at Mayagüez, Mayagüez, PR, USA 00681-9048; b University of Minnesota, Minneapolis, MN USA 55455-0436 ABSTRACT In this work, we study unsupervised classification algorithms for hyperspectral images based on band-by-band scalar histograms and vector-valued generalized histograms, obtained by vector quantization. The corresponding histograms are compared by dissimilarity metrics such as the chi-square, Kolmogorov-Smirnorv, and earth mover’s distances. The histograms are constructed from homogeneous regions in the images identified by a pre-segmentation algorithm and distance metrics between pixels. We compare the traditional spectral-only segmentation algorithms C-means and ISODATA, versus spectral-spatial segmentation algorithms such as unsupervised ECHO and a novel segmentation algorithm based on scale-space concepts. We also evaluate the use of complex features consisting of the real spectrum and its derivative as the imaginary part. The comparison between the different segmentation algorithms and distance metrics is based on their unsupervised classification accuracy using three real hyperspectral images with known ground truth. Keywords: Unsupervised classification, generalized histograms, earth mover’s distance, hyperspectral imaging, scale- space, complex features, geometric PDEs. 1. INTRODUCTION The use of histograms for unsupervised classification of hyperspectral imagery has been recently proposed, 1 where simple segmentation algorithms such as C-means are used to identify spectrally homogeneous regions in the images. The main idea of the approach consists of obtaining an over-segmented image and then performs statistical merging of the segments, based on dissimilarity metrics between distributions, approximated by histograms. Histograms can be computed for each segment using the intensity on each band, a subset of bands, or the principal components of the image. 1 Alternatively, vector-valued or generalized histograms can be computed from a segmented hyperspectral image using vector quantization methods. 2,3 The scalar histograms are compared using different dissimilarity metrics between distributions such 4-6 as the Chi-Square and Kolmogorov-Smirnov distances for the scalar case and the earth mover’s distance for vector-valued histograms. This histogram approach is truly unsupervised, since it does not assume any prior knowledge on the distribution of the data. In this work, we study the effects on the unsupervised classification accuracy of band by band scalar histograms using Chi-square and Kolmogorov distances, versus generalized histograms using the earth mover’s distance, combined with different segmentation algorithms such as C-means 7 and ISODATA, 8 that consider only the spectral dimension, versus the unsupervised Extraction and Classification of Homogeneous Objects (un-ECHO) segmentation algorithms proposed by Landgrebe et al, 9 Jimenez et al, 10 and our previous segmentation algorithm based on the scale-space concept, 11,12 which consider spatial relationships as well. The earth mover’s distance provides greater flexibility than scalar distances between histograms, since it exploits the whole spectra and allows the use of vectorial distances such as the Euclidean and spectral angle distances, traditionally used in hyperspectral imagery. In addition, we also evaluate the use of complex hyperspectral features, consisting of the real spectrums of the image and their derivatives as the imaginary part. Hence, complex features add two new distances in hyperspectral imaging, the Euclidean and spectral angles between complex vectors, with expected improved class separability. 13 We use four hyperspectral images of known ground truth to evaluate the effects of each metric, segmentation, and type of histogram on the classification a {jmartin, mvelez}@ece.uprm.edu (phone +1.787.832.2825) b guile@umn.edu (phone +1.612.625.1343) Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XIV, edited by Sylvia S. Shen, Paul E. Lewis, Proc. of SPIE Vol. 6966, 69660F, (2008) · 0277-786X/08/$18 · doi: 10.1117/12.779142 Proc. of SPIE Vol. 6966 69660F-1 2008 SPIE Digital Library -- Subscriber Archive Copy