Hyperbolic Equations In Image Processing

The methods based on PDE (Partial Differential Equation) for image analysis and processing have been more and more popular in the research of morphological image processing, PDE is a relatively fine method for image analysis and processing, and can be used in image de-noising,enhancement and segmentation. Dilation and erosion are the fundamental operations in morphological image processing. However , the widely-used schemes from the literature suffer from significant blurring at discontinuities. We address this problem by developing a novel algorithm for morphological dilation/erosion. It uses the viscosity form of an upwind scheme in order to quantify the undesired diffusive effects. Our experiments show that the method gives a very sharp resolution of moving fronts, and it approximates rotation invariance verywell.