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Scale-spaces induced by diffusion processes play an important role in many computer vision tasks. Automatically selecting the most appropriate scale for a particular problem is a central issue for the practical applicability of such scale-space techniques. This paper concentrates on automatic scale selection when nonlinear diffusion scale-spaces are utilized for image denoising. The problem is studied in a statistical model selection framework and cross-validation techniques are utilized to address it in a principled way. The proposed novel algorithms do not require knowledge of the noise variance and have acceptable computational cost. Extensive experiments on natural images show that the proposed methodology leads to robust algorithms, which outperform existing techniques for a wide range of noise types and noise levels.