### Segmentation of biomedical images using geodesic methods

Laurent D. Cohen

CEREMADE , Université Paris Dauphine

September 1, 2015 at 11:00 AM

McConnell Engineering Room 437

Tubular and tree structures appear very commonly in biomedical images like vessels, microtubules
or neuron cells. Minimal paths have been used for long as an interactive tool to segment these
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. On a different level, the user interaction can be minimized by adding iteratively
what we called the keypoints, for example to obtain a closed curve from a single initial point. The
result is then a set of minimal paths between pairs of keypoints. This can also be applied to
branching structures in both 2D and 3D images.
Geodesic Voting consists in computing geodesics between a given source point and a set of points
scattered in the image. The geodesic density is defined at each pixel of the image as the number of
geodesics that pass over this pixel. The target structure corresponds to image points with a high
geodesic density. We will illustrate different possible applications of this approach.
In this talk we will present recent methods based on geodesics for biomedical applications, like
automatic segmentation of vascular tree in retinal images.