Multi-scale 3D representation via volumetric quasi-random scale space

A novel nonlinear volumetric scale-space framework is proposed for multi-scale volumetric data representation. The problem is formulated as a Bayesian least-squares estimator, and a quasi-random density estimation approach is introduced for estimating the posterior distribution between consecutive volumetric scale space realizations. Experimental results using both synthetic and real MR volumetric data demonstrate the effectiveness of the proposed scale-space framework for three-dimensional representation with significantly better structural separation and localization across all scales when compared to existing volumetric scale-space frameworks such as volumetric anisotropic diffusion and volumetric linear Gaussian scale-space, especially under scenarios with high noise levels.