Extraction of the zero-crossings of the curvature derivatives in volumic 3D medical images: a multi-scale approach

Recently, we have shown that the differential properties of the surfaces represented by 3D volumic images can be recovered using their partial derivatives. For instance, the crest lines can be characterized by the first, second and third partial derivatives of the grey level function I(x, y, z). In this paper, we show that: the computation of the partial derivatives of an image can be improved using recursive filters which approximate the Gaussian filter; a multi-scale approach solves many of the instability problems arising from the computation of the partial derivatives; and we illustrate the previous point for the crest line extraction (a crest point is a zero-crossing of the derivative of the maximum curvature along the maximum curvature direction). We present experimental results of crest point extraction on real 3-D medical data