Edge Detection with Geometric Transforms and Isotropic Nonlinear Equation

In image processing wavelet transform methods are known to provide efficient schemes for detecting edges and reducing noise. However, they are unable to differentiate between noise and small details and therefore remove the small details resulting in the formation of oscillations around edges. Methods based on isotropic nonlinear equations have been used to enhance edges in images and to reduce oscillations around the edges but are not capable of removing noise effectively around them. In this paper, we solve the isotropic nonlinear equation in a geometric transform space and thereby reducing both noise and oscillations around the edges. The proposed synergic method combines the advantages of both techniques. The numerical experiments involve the investigation of two-dimensional geometric transforms in the detection of edges in noisy images.