State of the Art of Level Set Methods in Segmentation and Registration of Medical Imaging Modalities - Biomedical Image Analysis - page 53

Figure 2.3: Illustration of extension for gradient-based speed terms. (a) Region
of interest from a chest MRI scan with a level set curve initialized inside the spine.
(b) Gradient map of the MRI image with prior smoothing with a Gaussian filter.
(c) Multiplying term for speed function, proportional to the inverse edge map
from (b). (d) Extension of the speed term in (c) from values under the zero level
contour.

2.2.4 Geodesic Active Contours

Geodesic active contours were introduced simultaneously by Kichenassamy
et al. [15] and Caselles et al. [16] as a segmentation framework, derived from
energy-based snakes active contours, performing contour extraction via the
computation of geodesics, i.e., minimal distance curves in a Riemannian space
derived from the image. Given an image I and for a given differentiable curve
C ( p ) , p ∈ [0 , 1] they define the following energy:

1

E ( C ) = g ( |∇ I ( C ( p )) | ) | C ( p ) | dp , (2.13)

0