  Selective segmentation is an important application of image processing. In
contrast to global segmentation in which all objects are segmented, selective
segmentation is used to isolate specific objects in an image and is of
particular interest in medical imaging -- permitting segmentation and review of
a single organ. An important consideration is to minimise the amount of user
input to obtain the segmentation; this differs from interactive segmentation in
which more user input is allowed than selective segmentation. To achieve
selection, we propose a selective segmentation model which uses the
edge-weighted geodesic distance from a marker set as a penalty term. It is
demonstrated that this edge-weighted geodesic penalty term improves on previous
selective penalty terms. A convex formulation of the model is also presented,
allowing arbitrary initialisation. It is shown that the proposed model is less
parameter dependent and requires less user input than previous models. Further
modifications are made to the edge-weighted geodesic distance term to ensure
segmentation robustness to noise and blur. We can show that the overall
Euler-Lagrange equation admits a unique viscosity solution. Numerical results
show that the result is robust to user input and permits selective
segmentations that are not possible with other models.
