Multi-scale line segmentation with automatic estimation of width, contrast and tangential direction in 2D and 3D medical images

Efficient Detection of Second-Degree Variations in 2D and 3D Images

“…After computing and sorting the eigenvalues according to magnitude, a curvilinear structure called line (in this paper: string) is detected when the two largest ones have (approximately) the same magnitude and sign (negative for bright lines, positive for dark lines) whereas the third one is close to zero. The geometrical mean Lorenz et al [41], [42] are using the Hessian of 3D second derivatives in a similar manner to what has been presented in this paper. After deriving the eigen values, their relative signs and magnitudes are exploited to distinguish between strings (called lines) and planes, although the given measure for "line-ness" seems to discriminate poorly against "plane-ness".…”

“…line q , which yields a highly discriminative lineness measure line f . So far we have solved the derotation equation (4) ) ( ) ( (41) From (41) …”

3-D axon structure extraction and analysis in confocal fluorescence microscopy images

“…In the first step, every point in the image volume is assigned a similarity measurement to 3D line structures using the 3D line filtering method. Previous research in modeling multidimensional line structure is exemplified by the work of Steger et al and Sato et al (Haralick, Watson, & Laffey, 1983;Koller, Gerig, Szekely, & Dettwiler, 1995;Lorenz, Carlsen, Buzug, Fassnacht, & Weese, 1997;Sato, Araki, Hanayama, Naito, & Tamura, 1998;Sato, Nakajima et al, 1998;Steger, 1996Steger, , 1998. In this project, the 3D line filtering is achieved by using the Hessian matrix, a descriptor that is widely used to describe the second-order structures of local intensity variations around each point in the 3D space.…”

A Multi-scale Geometric Flow for Segmenting Vasculature in MRI

“…Several multi-scale approaches to modeling tubular structures in intensity images have been based on properties of the Eigen values of the Hessian matrix H [11,16,4]. These methods exploit the fact that at locations centered within tubular structures the smallest Eigen value of H is close to zero (reflecting the low curvature along the direction of the vessel) and the two other Eigen values are high and are close to being equal, reflecting the fact that the cross-section of the vessel is approximately circular.…”