3D echographic data segmentation and carotid artery turbulences mapping by Doppler velocimetry by a common approach based on calculus of variations

The DOLPHINS project is supported in part by the 4^th European RTD Framework Program, and deals with echographic applications dedicated to arterial walls and plaque segmentation, plaque motion and degree of stenoses analysis. For this purpose, we have adapted geodesic active contours methods for arterial walls segmentation, to characterize stenose severity with regularized high resolution Doppler spectrum analysis by turbulences mapping from a Doppler spectral width measurement. The original contribution of our approach consists in using the same calculus of variations framework for image segmentation and Doppler velocimetry. We prove that we can, by analogy, find the equivalent mean curvature flow equation, used for geodesic active contours, for Doppler analysis by considering the complex autoregressive polynomial as a closed plane curve immersed in the oriented Euclidean plane