A strain energy filter for 3D vessel enhancement with application to pulmonary CT images

The traditional Hessian-related vessel filters often suffer from detecting complex structures like bifurcations due to an over-simplified cylindrical model. To solve this problem, we present a shape-tuned strain energy density function to measure vessel likelihood in 3D medical images. This method is initially inspired by established stress–strain principles in mechanics. By considering the Hessian matrix as a stress tensor, the three invariants from orthogonal tensor decomposition are used independently or combined to formulate distinctive functions for vascular shape discrimination, brightness contrast and structure strength measuring. Moreover, a mathematical description of Hessian eigenvalues for general vessel shapes is obtained, based on an intensity continuity assumption, and a relative Hessian strength term is presented to ensure the dominance of second-order derivatives as well as suppress undesired step-edges. Finally, we adopt the multi-scale scheme to find an optimal solution through scale space. The proposed method is validated in experiments with a digital phantom and non-contrast-enhanced pulmonary CT data. It is shown that our model performed more effectively in enhancing vessel bifurcations and preserving details, compared to three existing filters.

Figure optionsDownload high-quality image (110 K)Download as PowerPoint slideResearch highlights
► The stress–strain principle and tensor invariants are introduced to detect image derivative structures.
► A mathematical description of Hessian eigenvalues for general vessel shapes is obtained from an intensity continuity assumption.
► Define a new vessel likelihood function to enhance complex vascular structures including bifurcations and feature details.
► The filtering performance was verified by quantitative evaluation and cross-validation in synthetic and clinical dataset experiments.