Analysis and detection of 3-D curvilinear structures

In this paper we present a new method for estimating confidence and curvature of 3-D curvilinear structures. The gradient structure tensor (GST) models shift-invariance. The eigenstructure of the tensor allows estimation of local dimensionality, orientation, and the corresponding confidence value. Local rotational invariance, which occurs often in images, causes a lower confidence estimate. This underestimation can be corrected for by a parabolic deformation of the data, in such a way that it becomes translational invariant. We show that the optimal deformation can be found analytically and yields a local curvature estimate as a valuable by-product. We tested our new method on synthetic images and applied it to the detection of channels in 3-D seismic data.