Variational segmentation of elongated volumetric structures

Abstract

We present an interactive approach for segmenting thin volumetric structures. The proposed segmentation model is based on an anisotropic weighted Total Variation energy with a global volumetric constraint and is minimized using an efficient numerical approach and a convex relaxation. The algorithm is globally optimal w.r.t. the relaxed problem for any volumetric constraint. The binary solution of the relaxed problem equals the globally optimal solution of the original problem. Implemented on today's user-programmable graphics cards, it allows real-time user interaction. The method is applied to and evaluated on the task of articular cartilage segmentation of human knee joints and segmentation of tubular structures like liver vessels and airway trees.

Automatic atlas-based three-label cartilage segmentation from MR knee images

“…Figure 1 illustrates the problem with isotropic regularization which tends to shrink the segmentation boundary by cutting thin objects short and the benefit of anisotropic regularization. We choose G similar to [7] as…”

Surface Normal Integration for Convex Space-time Multi-view Reconstruction

“…Similar results have also been reported by [23]. We also tried estimating normals based on the data term f as done in [19] which also yields defective normals due to the fact that f is very noisy and misses a lot of data for most of our experiments. Kolev et al [12] estimated normal directions for the photoconsistency computation based on the visual hull.…”

“…The photoconsistency measure ρ : V×T → [0, 1] is detailed in the next section. D x x x performs a change of basis and aligns the local coordinate system along the favored surface normal n n n. As a result, ∇u is more likely to be aligned to n n n. On the one hand the anisotropic regularization better preserves small scale surface details [13], on the other hand it is important when reconstructing fine elongated structures [19] like human arms, or parts of clothes and hair.…”

“…D x x x (x x x,t) = ρ(x x x,t) 2 n n nn n n T + n n n 0 n n n T 0 + n n n 1 n n n T 1 is a symmetric positivedefinite matrix which accounts for an anisotropic spatial regularization and is defined similarly as in [19]. It lowers smoothing in the surface normal n n n ∈ R 3 direction and favors smoothness along the corresponding tangential directions n n n 0 and n n n 1 = n n n × n n n 0 .…”

Comparing algorithms for automated vessel segmentation in computed tomography scans of the lung: the VESSEL12 study

“…Vessel enhancement consisted of an analysis of the Hessian eigenvectors and computation of an offset vesselness function containing the gradient information sampled at circles of different radii perpendicular to the tube direction (eigenvector with smallest eigenvalue), a local symmetry measure, and an adaptive vesselness threshold. Centerline fragments from non-maxima suppression were then connected using a shortest path algorithm, and the vessel radius was estimated using a spherical ray-cast approach, which was finally refined by minimizing a geodesic active contour energy, as proposed by Reinbacher et al (2010). The final probability was obtained by weighting the segmentation based on the original vesselness response, which was rescaled to [0,255].…”