Abstract: An anisotropic diffusion equation based on the morphological operator is proposed to make up for the defeat of the generalized PM diffusion not to preserve edge details. Its diffusion coefficient is dependent not only on the gradient of the image, but also on the second derivatives estimated on the image after being applied to the morphological close-open operator. The new operator is capable of removing noise efficiently and preserving the edge locality and thin edges. Experiments show that the processed images have high fidelity and constrast and that the new operator has an advantage of removing noise in images with heavy Gaussian noise.

Key words: scale space, anisotropic, diffusion equation, morphology