Efficient and reliable schemes for nonlinear diffusion filtering

Abstract

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Efficient numerical schemes for gradient vector flow

“…We will denoted this scheme by the AFI scheme. Given the above form of A l , all the above approximation schemes can be solved efficiently by the Thomas algorithm [12]. Notice that the above iterative solutions (14)- (17) solves the TGGVF and without any extra computational cost as the matrices A l are calculated only once.…”

“…The matrices A l corresponds to the derivatives along the l th coordinate axis, i.e the matrix-vector multiplication A l u is the discrete approximation of ∂x l g(x)∂x l u − 1 m h(x)u which is simply given by [12,13] j∈N (i)…”

Liver Segmentation Approach Using Graph Cuts and Iteratively Estimated Shape and Intensity Constrains

“…After mapping the whole CT volume to a gray scale volume, a nonlinear diffusion filter [15] is applied to each 2D slice in the volume to reduce the noise and increase the liver homogeneity.…”

On Semi-implicit Splitting Schemes for the Beltrami Color Flow

“…Historically, additive operator splitting (AOS) schemes were first developed for (nonlinear elliptic/parabolic) monotone equations and Navier-Stokes equations [12,13]. In image processing applications, the AOS scheme was found to be an efficient way for approximating the Perona-Malik filter [29], especially if symmetry in scale-space is required. The AOS scheme is first order in time, semi-implicit, and unconditionally stable with respect to its time-step [13,29].…”