Local scale controlled anisotropic diffusion with local noise estimate for image smoothing and edge detection

A novel local scale controlled piecewise linear diffusion for selective smoothing and edge detection is presented. The diffusion stops at the place and time determined by the minimum reliable local scale and a spatial variant, anisotropic local noise estimate. It shows anisotropic, nonlinear diffusion equation using diffusion coefficients/tensors that continuously depend on the gradient is not necessary to achieve sharp, distorted, stable edge detection across many scales. The new diffusion is anisotropic and asymmetric only at places it needs to be, i.e., at significant edges. It not only does not diffuse across significant edges, but also enhances edges. It advances geometry-driven diffusion because it is a piecewise linear model rather than a full nonlinear model, thus it is simple to implement and analyze, and avoids the difficulties and problems associated with nonlinear diffusion. It advances local scale control by introducing spatial variant, anisotropic local noise estimation, and local stopping of diffusion. The original local scale control was based on the unrealistic assumption of uniformly distributed noise independent of the image signal. The local noise estimate significantly improves local scale control.