Autopilot spatially-adaptive active contour parameterization for medical image segmentation

In this work, a novel framework for automated, spatially-adaptive adjustment of active contour regularization and data fidelity parameters is proposed and applied for medical image segmentation. The proposed framework is tailored upon the isomorphism observed between these parameters and the eigenvalues of diffusion tensors. Since such eigenvalues reflect the diffusivity of edge regions, we embed this information in regularization and data fidelity parameters by means of entropy-based, spatially-adaptive `heatmaps'. The latter are able to repel an active contour from randomly directed edge regions and guide it towards structured ones. Experiments are conducted on endoscopic as well as mammographic images. The segmentation results demonstrate that the proposed framework bypasses iterations dedicated to false local minima associated with noise, artifacts and inhomogeneities, speeding up contour convergence, whereas it maintains a high segmentation quality

Second order elastic metrics on the shape space of curves

Second order Sobolev metrics on the space of regular unparametrized planar curves have several desirable completeness properties not present in lower order metrics, but numerics are still largely missing. In this paper, we present algorithms to numerically solve the initial and boundary value problems for geodesics. The combination of these algorithms allows to compute Karcher means in a Riemannian gradient-based optimization scheme. Our framework has the advantage that the constants determining the weights of the zero, first, and second order terms of the metric can be chosen freely. Moreover, due to its generality, it could be applied to more general spaces of mapping. We demonstrate the effectiveness of our approach by analyzing a collection of shapes representing physical objects