3-D curvilinear structure detection filter via structure-ball analysis

Curvilinear structure detection filters are crucial building blocks in many medical image processing applications, where they are used to detect important structures, such as blood vessels, airways, and other similar fibrous tissues. Unfortunately, most of these filters are plagued by an implicit single structure direction assumption, which results in a loss of signal around bifurcations. This peculiarity limits the performance of all subsequent processes, such as understanding angiography acquisitions, computing an accurate segmentation or tractography, or automatically classifying image voxels. This paper presents a new 3-D curvilinear structure detection filter based on the analysis of the structure ball, a geometric construction representing second order differences sampled in many directions. The structure ball is defined formally, and its computation on a discreet image is discussed. A contrast invariant diffusion index easing voxel analysis and visualization is also introduced, and different structure ball shape descriptors are proposed. A new curvilinear structure detection filter is defined based on the shape descriptors that best characterize curvilinear structures. The new filter produces a vesselness measure that is robust to the presence of X- and Y-junctions along the structure by going beyond the single direction assumption. At the same time, it stays conceptually simple and deterministic, and allows for an intuitive representation of the structure's principal directions. Sample results are provided for synthetic images and for two medical imaging modalities.