A P.D.E Based Approach for Medial Axis Detection

In the present work we deal with the assistance to the diagnostic of coronaries stenosis from X-rays angiographies. Our goal is a 3D-reconstruction of the coronarian tree, therefore the extraction of some 2D characteristics is necessary. Here, we treat the problem of the 2D vessels medial axis extraction. The vessels geometry looks like valleys embedded in the image surface. Using differential geometry we can locally characterize medial axis as bottom lines of valleys. However, we have to calculate the image local derivatives, which is an ill-posed and noise sensitive problem. To overcome this drawback, we use a PDE based approach. We first consider the PDE?s numerical scheme as an iterative method known as fixed point search. So, we obtain a new method which assure the stability of the resolution process. The combinaison of this method and of an original PDE generates a scale-space where we can detect arteries of various diameters. We use then the eigenvalues and eigenvectors of the Weingarten endomorphism to define a new valley-ness measure. We have tested this technique on several angiographies, where the medial axis have well been extracted, even in presence of strong stenosis. Furthermore, the extracted axis are one pixel large and quite continuous.