A radial structure tensor and its use for shape-encoding medical visualization of tubular and nodular structures

The concept of curvature and shape-based rendering is beneficial for medical visualization of CT and MRI image volumes. Color-coding of local shape properties derived from the analysis of the local Hessian can implicitly highlight tubular structures such as vessels and airways, and guide the attention to potentially malignant nodular structures such as tumors, enlarged lymph nodes, or aneurysms. For some clinical applications, however, the evaluation of the Hessian matrix does not yield satisfactory renderings, in particular for hollow structures such as airways, and densely embedded low contrast structures such as lymph nodes. Therefore, as a complement to Hessian-based shape-encoding rendering, this paper introduces a combination of an efficient sparse radial gradient sampling scheme in conjunction with a novel representation, the radial structure tensor (RST). As an extension of the well-known general structure tensor, which has only positive definite eigenvalues, the radial structure tensor correlates position and direction of the gradient vectors in a local neighborhood, and thus yields positive and negative eigenvalues which can be used to discriminate between different shapes. As Hessian-based rendering, also RST-based rendering is ideally suited for GPU implementation. Feedback from clinicians indicates that shape-encoding rendering can be an effective image navigation tool to aid diagnostic workflow and quality assurance.