Non-linear diffusion of image noise with minimal iterativity

Non-linear diffusion (ND) is an iterative difference equation used in several image processing applications such as denoising, segmentation, or compression. The number of iterations required to achieve optimal processing can be very high, making ND not suitable for real-time requirements. In this paper, we study how to reduce complexity of ND so as to achieve minimal number of iterations for real-time image denoising. To do this, we first study the relations between parameters of the iterative equation: the number of iterations, the time step, and the edge strength. We then proceed by estimating the minimally required number of iterations to achieve effective denoising. Then, we relate the edge strength to the number of iterations, to noise, and to the image structure. The resulted minimal iterativity ND is very fast, while still achieves similar or better noise reduction compared to related ND work. This paper also shows how the proposed spatial filter is suitable for structure-sensitive object segmentation and temporal noise reduction.