Image denoising in nonlinear scale-spaces: automatic scale selection via cross-validation

Multiscale, i.e. scale-space image analysis is a powerful framework for many image processing tasks. A fundamental issue with such scale-space techniques is the automatic selection of the most salient scale for a particular application. This paper considers optimal scale selection when nonlinear diffusion and morphological scale-spaces are utilized for image denoising. The problem is studied from a statistical model selection viewpoint 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, have acceptable computational cost and are readily integrated with a wide class of scale-space inducing processes which require setting of a scale parameter. Our experiments show that this methodology leads to robust algorithms, which outperform existing scale-selection techniques for a wide range of noise types and noise levels.