From Active Contours to Minimal Geodesic Paths: New Solutions to Active Contours Problems by Eikonal Equations
This work provides a unified framework for image analysis tasks, but it appears incremental as it builds on existing minimal path and active contour methods.
The authors tackled active contour problems by using minimal geodesic paths derived from Eikonal equations, enabling solutions for tasks like boundary detection and image segmentation with efficient numerical implementations.
In this chapter, we give an overview of part of our previous work based on the minimal path framework and the Eikonal partial differential equation (PDE). We show that by designing adequate Riemannian and Randers geodesic metrics the minimal paths can be utilized to search for solutions to almost all of the active contour problems and to the Euler-Mumford elastica problem, which allows to blend the advantages from minimal geodesic paths and those original approaches, i.e. the active contours and elastica curves. The proposed minimal path-based models can be applied to deal with a broad variety of image analysis tasks such as boundary detection, image segmentation and tubular structure extraction. The numerical implementations for the computation of minimal paths are known to be quite efficient thanks to the Eikonal solvers such as the Finsler variant of the fast marching method.