Fast Asymmetric Fronts Propagation for Image Segmentation

Abstract

In this paper, we introduce a generalized asymmetric fronts propagation model based on the geodesic distance maps and the Eikonal partial differential equations. One of the key ingredients for the computation of the geodesic distance map is the geodesic metric, which can govern the action of the geodesic distance level set propagation. We consider a Finsler metric with the Randers form, through which the asymmetry and anisotropy enhancements can be taken into account to prevent the fronts leaking problem during the fronts propagation. These enhancements can be derived from the image edge-dependent vector field such as the gradient vector flow. The numerical implementations are carried out by the Finsler variant of the fast marching method, leading to very efficient interactive segmentation schemes. We apply the proposed Finsler fronts propagation model to image segmentation applications. Specifically, the foreground and background segmentation is implemented by the Voronoi index map. In addition, for the application of tubularity segmentation, we exploit the level set lines of the geodesic distance map associated to the proposed Finsler metric providing that a thresholding value is given.

A Generalized Asymmetric Dual-Front Model for Active Contours and Image Segmentation

“…The computation of Voronoi regions is carried out by assigning to each grid point x a label equivalent to the index of its closest source point set. This procedure can be done during the fast marching fronts propagation [57], [58].…”

Geodesic Paths for Image Segmentation with Implicit Region-based Homogeneity Enhancement

“…Note that for a gray level image I, the matrix (9) gets to be a vector, i.e. J (p) = (∂ x (G σ * I), ∂ y (G σ * I)) T , and the matrix W(p) can be also computed using (11).…”

“…As a type of implicit user intervention, shape priors are often taken into account in the graph-based applications to generate particular segmentations [5]- [8]. The Voronoi diagram-based segmentation approaches [9]- [11] depict a target through a voronoi region, where the user-provided scribbles serve as the source points for the computation of minimal weighted distance and for the propagation of labels. In [12], the scribbles were treated as a narrow region, from which a statistical model describing the image intensity distribution in the target regions is created.…”

From active contours to minimal geodesic paths: New solutions to active contours problems by Eikonal equations

“…For each point x ∈ Ω, the Finsler metric F F (x, u) can be defined through an asymmetric norm, which is a convex and 1-homogeneous function on its second argument. Basically, the asymmetry property of a Finsler metric allows to take advantages of path directions during the computation of the geodesic distance and of the geodesic paths, as explored in (Melonakos et al, 2008;Chen and Cohen, 2018).…”