WaveStat-cluster analysis of image data and wavelet coefficients

The WaveStat project deals with the exploratory Cluster Analysis of picture data and wavelet-built coefficients. Cluster Analysis means to collect elements (i.e. pixels) of the same property (in this context this means: gray value) to a cluster. These clusters can be visualized by colorizing them or by reconstructing them to a grayscale picture. In this article we will show that a cluster analysis can be done directly on picture data (pixels) or on wavelet coefficients resulting from a wavelet analysis of the image. The clustered coefficients then are transformed back using the inverse wavelet tranformation. The quality of this reconstruction depends on the used wavelet-transform, the used cluster algorithm and the number of iterations when performing the inverse wavelet-transform. This work uses the redundancy of wavelet coefficients to apply cluster analysis on these to achieve an image compression.