Linear snow accumulation models and applications

Noise reduction is an important pre-processing step in image processing. The undesirable side effect of many noise reduction methods is that they always blur the characteristic information of the images, the boundaries, which are supposed to be enhanced in image processing. Understanding the digital image as an uniform sample of a spatial curve and the de-noising process as the evolution of the spatial curve, we find that natural snow accumulation process is very similar as the evolution of the ground surface, which also can be viewed as a spatial curve. Based on this observation, one-dimensional and two-dimensional linear snow accumulation models are established in this paper. With two-dimensional linear snow accumulation model, we de-noised a 256-by-256 image with random noise. De-noising results are compared with that by the discrete 2-D wavelet transform, the reduced 2-D dual-tree wavelet transform, and the complex 2D dual-tree wavelet transform. These results show that our two-dimensional linear snow accumulation model works well in image noise reduction.