The present work describes a framework for morphological characterization of galaxies based on the Spectral Graph Wavelet Transform. A galaxy image is sampled with a number of points randomly chosen, whose Delaunay triangulation results in an arbitrary graph. The average intensity value in a 5×5 vicinity of a pixel related to a graph vertex is assigned to the corresponding graph vertex. A weight inversely proportional to the photometric distance between each pair of vertices is assigned to the respective graph edge. The Spectral Graph Wavelet Transform is computed from this weighted graph with real-valued vertices yielding a high-dimensional feature vector, which is reduced to a two dimensional vector through Principal Component Analysis. The proposed framework has been assessed through two case studies, namely, the case study of analyzing (i) 2D binary images from shapes and preliminary results of (ii) 2D gray tone images from galaxies. The obtained results imply the suitability of this framework for the characterization of galaxies images. Copyright © 2013 by The Institute of Electrical and Electronics Engineers, Inc.