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Geodesic Methods for Interactive Image Segmentation using Finsler metrics

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VMVW01 - Variational methods, new optimisation techniques and new fast numerical algorithms

Minimal paths have been used for long as an interactive tool to find edges or tubular structures as cost minimizing curves. The user usually provides start and end points on the image and gets the minimal path as output. These minimal paths correspond to minimal geodesics according to some adapted metric. They are a way to find a (set of) curve(s) globally minimizing the geodesic active contours energy. Finding a geodesic distance can be solved by the Eikonal equation using the fast and efficient Fast Marching method.
Different metrics can be adapted to various problems. In the past years we have introduced different extensions of these minimal paths that improve either the interactive aspects or the results. For example, the metric can take into account both scale and orientation of the path. This leads to solving an anisotropic minimal path in a 2D or 3D+radius space.
We recently introduced the use of Finsler metrics allowing to take into account the local curvature in order to smooth the path. It can also be adapted to take into account a region term inside the closed curve formed by a set of minimal geodesics.  

Co-authors: Da Chen and J.-M. Mirebeau

This talk is part of the Isaac Newton Institute Seminar Series series.

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