Abstract: Local singularity analysis of catalyst surface SEM image for multifractal growth process is discussed. The local singularity strength obtained with the continuous wavelet transform can provide more accurate absolute Holder exponent and the spatial location of singularities than the single fractal dimension describing global property and the singularity spectrum. The singularity strength distribution image provides the characterization of fractal measures supported by two dimension digital images, and can determine the active region distribution on catalyst surface.