Computation of scale space images requires numerical integration of partial differential equations, which demands large computational costs especially in nonlinear cases. In this paper, we present a computational scheme for nonlinear scale spaces based on iterated filtering of original images. This scheme is found to be a special case of numerical integration with a particularly adapted integration steplength. We show the stability of the iteration with local windows and that with global ones and analyze the deformation of edge waveforms in the filtering. Computational costs are evaluated experimentally for both local and global windows and finally we apply the nonlinear multi-scale smoothing to contrast enhancement of images.