Curvilinear Structure Analysis by Ranking the Orientation Responses of Path Operators

Abstract

The analysis of thin curvilinear objects in 3D images is a complex and challenging task. In this article, we introduce a new, non-linear operator, called RORPO (Ranking the Orientation Responses of Path Operators). Inspired by the multidirectional paradigm currently used in linear filtering for thin structure analysis, RORPO is built upon the notion of path operator from mathematical morphology. This operator, unlike most operators commonly used for 3D curvilinear structure analysis, is discrete, non-linear and non-local. From this new operator, two main curvilinear structure characteristics can be estimated: an intensity feature, that can be assimilated to a quantitative measure of curvilinearity; and a directional feature, providing a quantitative measure of the structure's orientation. We provide a full description of the structural and algorithmic details for computing these two features from RORPO, and we discuss computational issues. We experimentally assess RORPO by comparison with three of the most popular curvilinear structure analysis filters, namely Frangi Vesselness, Optimally Oriented Flux, and Hybrid Diffusion with Continuous Switch. In particular, we show that our method provides up to 8 percent more true positive and 50 percent less false positives than the next best method, on synthetic and real 3D images.

Flow MRI simulation in complex 3D geometries: Application to the cerebral venous network

“…After assessing the validity of the framework in the previous simple models, this was evaluated on a realistic application of blood flow simulation in a realistic vessel geometry. To this end, a 3D cerebral venous network was modeled with segmentation methods, performed on real MRA acquisitions . Velocity data were generated by solving the Navier‐Stokes equations on a 3D tetrahedral mesh with CFD methods (the mean edge length of the tetrahedra was about 0.75 mm).…”

“…To this end, a 3D cerebral venous network was modeled with segmentation methods, performed on real MRA acquisitions. 24 Velocity data were generated by solving the Navier-Stokes equations on a 3D tetrahedral mesh with CFD methods 25 (the mean edge length of the tetrahedra was about 0.75 mm). The trajectories were then computed with particle tracking in the resulting mesh.…”

Curvilinear Structure Enhancement by Multiscale Top-Hat Tensor in 2D/3D Images

“…2) Path Operators Transform: A mathematical morphology-based path opening and closing operation to detect the curvilinear structures in retinal images was introduced by [13]. Recently, a new path operator called Ranking the Orientation Responses of Path Operators (RORPO) has been proposed to distinguish curvilinear objects from blob-like and planar structures in images [14], [15]. The main disadvantage of the RORPO approach is its high computation cost when applied to large volume image datasets.…”

Brain-Inspired Robust Delineation Operator

“…Mathematical morphology techniques assume a-priori knowldege about the geometry of the patterns of interest [12], such as size, orientation and width [13], or concavity [14]. Recently, a method called RORPO, based on morphological path operators was proposed for the delineation of 2D and 3D curvilinear patterns [15].…”