Extraction of Tubular Structures over an Orientation Domain

International audienceThis paper presents a new method to extract tubular structures from bi-dimensional images. The core of the proposed algorithm is the computation of geodesic curves over a four-dimensional space that includes local orientation and scale. These shortest paths follow closely the centerline of tubular structures, provide an estimation of the radius and can deal robustly with crossings over the image plane. Numerical experiments on a database of synthetic and natural images show the superiority of the proposed approach with respect to several method based on shortest paths extractions

Vessel tractography using an intensity based tensor model with branch detection

In this paper, we present a tubular structure seg- mentation method that utilizes a second order tensor constructed from directional intensity measurements, which is inspired from diffusion tensor image (DTI) modeling. The constructed anisotropic tensor which is fit inside a vessel drives the segmen- tation analogously to a tractography approach in DTI. Our model is initialized at a single seed point and is capable of capturing whole vessel trees by an automatic branch detection algorithm developed in the same framework. The centerline of the vessel as well as its thickness is extracted. Performance results within the Rotterdam Coronary Artery Algorithm Evaluation framework are provided for comparison with existing techniques. 96.4% average overlap with ground truth delineated by experts is obtained in addition to other measures reported in the paper. Moreover, we demonstrate further quantitative results over synthetic vascular datasets, and we provide quantitative experiments for branch detection on patient Computed Tomography Angiography (CTA) volumes, as well as qualitative evaluations on the same CTA datasets, from visual scores by a cardiologist expert

Sub-Riemannian Fast Marching in SE(2)

We propose a Fast Marching based implementation for computing sub-Riemanninan (SR) geodesics in the roto-translation group SE(2), with a metric depending on a cost induced by the image data. The key ingredient is a Riemannian approximation of the SR-metric. Then, a state of the art Fast Marching solver that is able to deal with extreme anisotropies is used to compute a SR-distance map as the solution of a corresponding eikonal equation. Subsequent backtracking on the distance map gives the geodesics. To validate the method, we consider the uniform cost case in which exact formulas for SR-geodesics are known and we show remarkable accuracy of the numerically computed SR-spheres. We also show a dramatic decrease in computational time with respect to a previous PDE-based iterative approach. Regarding image analysis applications, we show the potential of considering these data adaptive geodesics for a fully automated retinal vessel tree segmentation.Comment: CIARP 201

Coronary Artery Centerline Extraction in Cardiac CT Angiography Using a CNN-Based Orientation Classifier

Coronary artery centerline extraction in cardiac CT angiography (CCTA) images is a prerequisite for evaluation of stenoses and atherosclerotic plaque. We propose an algorithm that extracts coronary artery centerlines in CCTA using a convolutional neural network (CNN). A 3D dilated CNN is trained to predict the most likely direction and radius of an artery at any given point in a CCTA image based on a local image patch. Starting from a single seed point placed manually or automatically anywhere in a coronary artery, a tracker follows the vessel centerline in two directions using the predictions of the CNN. Tracking is terminated when no direction can be identified with high certainty. The CNN was trained using 32 manually annotated centerlines in a training set consisting of 8 CCTA images provided in the MICCAI 2008 Coronary Artery Tracking Challenge (CAT08). Evaluation using 24 test images of the CAT08 challenge showed that extracted centerlines had an average overlap of 93.7% with 96 manually annotated reference centerlines. Extracted centerline points were highly accurate, with an average distance of 0.21 mm to reference centerline points. In a second test set consisting of 50 CCTA scans, 5,448 markers in the coronary arteries were used as seed points to extract single centerlines. This showed strong correspondence between extracted centerlines and manually placed markers. In a third test set containing 36 CCTA scans, fully automatic seeding and centerline extraction led to extraction of on average 92% of clinically relevant coronary artery segments. The proposed method is able to accurately and efficiently determine the direction and radius of coronary arteries. The method can be trained with limited training data, and once trained allows fast automatic or interactive extraction of coronary artery trees from CCTA images.Comment: Accepted in Medical Image Analysi

On the non-local geometry of turbulence

A multi-scale methodology for the study of the non-local geometry of eddy structures in turbulence is developed. Starting from a given three-dimensional field, this consists of three main steps: extraction, characterization and classification of structures. The extraction step is done in two stages. First, a multi-scale decomposition based on the curvelet transform is applied to the full three-dimensional field, resulting in a finite set of component three-dimensional fields, one per scale. Second, by iso-contouring each component field at one or more iso-contour levels, a set of closed iso-surfaces is obtained that represents the structures at that scale. The characterization stage is based on the joint probability density function (p.d.f.), in terms of area coverage on each individual iso-surface, of two differential-geometry properties, the shape index and curvedness, plus the stretching parameter, a dimensionless global invariant of the surface. Taken together, this defines the geometrical signature of the iso-surface. The classification step is based on the construction of a finite set of parameters, obtained from algebraic functions of moments of the joint p.d.f. of each structure, that specify its location as a point in a multi-dimensional ‘feature space’. At each scale the set of points in feature space represents all structures at that scale, for the specified iso-contour value. This then allows the application, to the set, of clustering techniques that search for groups of structures with a common geometry. Results are presented of a first application of this technique to a passive scalar field obtained from 5123 direct numerical simulation of scalar mixing by forced, isotropic turbulence (Reλ = 265). These show transition, with decreasing scale, from blob-like structures in the larger scales to blob- and tube-like structures with small or moderate stretching in the inertial range of scales, and then toward tube and, predominantly, sheet-like structures with high level of stretching in the dissipation range of scales. Implications of these results for the dynamical behaviour of passive scalar stirring and mixing by turbulence are discussed