Brain aneurysm segmentation in CTA and 3DRA using geodesic active regions based on second order prototype features and non parametric density estimation

Coupling the geodesic active contours model with statistical information based on regions introduces robustness in the segmentation of images with weak or inhomogeneous gradients. In the estimation of the probability density function for each region take part the definition of the features that describe the image inside the different regions and the method of density estimation itself. A Gaussian Mixture Model is frequently proposed for density estimation. This approach is based on the assumption that the intensity distribution of the image is the most discriminant feature in a region. However, the use of second order features provides a better discrimination of the different regions, as these features represent more accurately the local properties of the image manifold. Due to the high dimensionality of the problem, the use of non parametric density estimation methods becomes necessary. In this article, we present a novel method of introducing the second order information of an image for non parametric estimation of the probability density functions of the different tissues that are present in medical images. The novelty of the method stems on the use of the response of the image under an orthogonal harmonic operator set projected onto a prototype space for feature generation. The technique described here is applied to the segmentation of brain aneurysms in Computed Tomography Angiography (CTA) and 3D Rotational Angiography (3DRA) showing a qualitative improvement from the Gaussian Mixture Model approach.