Quasi-random nonlinear scale space

A novel nonlinear scale space framework is proposed for the purpose of multi-scale image representation. The scale space decomposition problem is formulated as a general Bayesian least-squares estimation problem. A quasi-random density estimation approach is introduced for estimating the posterior distribution between consecutive scale space realizations. In addition, the application of the proposed nonlinear scale space framework for edge detection is proposed. Experimental results demonstrate the effectiveness of the proposed scale space framework for constructing scale space representations with significantly better structural localization across all scales when compared to state-of-the-art scale space frameworks such as anisotropic diffusion, regularized nonlinear diffusion, complex nonlinear diffusion, and iterative bilateral scale space methods, especially under scenarios with high noise levels.