A number of techniques for halftoning gray scale images has been proposed. Unfortunately a reliable methodology of comparing results still has to be developed. Our work is focused on analysis of edge information in halftoned images. In particular we are interested in the preservation of the original image edges and the appearance of edge artifacts created by the halftoning process. Our approach is a multiscale analysis based on a wavelet transform. The wavelet smoothing function is approximately a derivative of a Gaussian function. Image edges are found by identifying extrema points of the wavelet transform. The edge points of the same scale are connected into contours. Edge contours are linked into a pyramid structure across multiple scales. Evolution of wavelet maxima in this pyramid allows us to classify discontinuities in the image and to measure their significance. We studied performance of popular halftoning methods on images with various types of edges. Multiscale edge structures are identified in original gray scale and halftoned images. Corresponding values of the wavelet transform are compared. Our experiments show that proposed methdology can be used to measure fidelity of edge reproduction by the halftoning process. Also, various contouring artifacts can be reliably identified.