Local Scale Controlled Anisotropic Di usion 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 di usion stops at the place and time determined by the minimum reliable local scale and a spatial variant, anisotropic local noise estimate. It shows nisotropic, nonlinear di usion equation using di usion coe cients/tensors that continuously depend on the gradient is not necessary to achieve sharp, undistorted, stable edge detection across many scales. The new di usion is anisotropic and asymmetric only at places it needs to be, i.e., at signi cant edges. It not only does not di use across signi cant edges, but also enhances edges. It advances geometry-driven di usion because it is a piecewise linear model rather than a full nonlinear model, thus it is simple to implement and analyze, and avoids the di culties and problems associated with nonlinear di usion. It advances local scale control by introducing spatial variant, anisotropic local noise estimation, and local stopping of di usion. The original local scale control was based on the unrealistic assumption of uniformly distributed noise independent of the image signal. The local noise estimate signi cantly improves local scale control.