Christophe Lohou

Christophe Lohou, Bruno Miguel

Aortic dissection is a serious pathology and requires an emergency management. It is characterized by one or more tears of the intimal wall of the normal blood duct of the aorta (true lumen); the blood under pressure then creates a second blood lumen (false lumen) in the media tissue. The two lumens are separated by an intimal wall, called flap. From the segmentation of connected lumens (more precisely, blood inside lumens) of an aortic dissection 3D Computed Tomography Angiography (CTA) image, our previous studies allow us to retrieve the intimal flap by using Mathematical Morphology operators, and characterize intimal tears by 3d thin surfaces that fill them, these surfaces are obtained by operating the Aktouf et al. closing algorithm proposed in the framework of Digital Topology. Indeed, intimal tears are 3D holes in the intimal flap; although it is impossible to directly segment such non-concrete data, it is nevertheless possible to "materialize" them with these 3D filling surfaces that may be quantified or make easier the visualization of these holes. In this paper, we use these surfaces that fill tears to cut connections between lumens in order to separate them. This is the first time that surfaces filling tears are used as an image processing operator (to disconnect several parts of a 3D object). This lumen separation allows us to provide one of the first cartographies of an aortic dissection, that may better visually assist physicians during their diagnosis. Our method is able to disconnect lumens, that may also lead to enhance several current investigations (registration, segmentation, hemodynamics).

Christophe Lohou

In this paper, we propose a topological classification of points for 2D discrete binary images. This classification is based on the values of the calculus of topological numbers. Six classes of points are proposed: isolated point, interior point, simple point, curve point, point of intersection of 3 curves, point of intersection of 4 curves. The number of configurations of each class is also given.

Christophe Lohou

In this paper, we adapt the two topological numbers, which have been proposed to efficiently characterize simple points in specific neighborhoods for 3D binary images, to the case of 2D binary images. Unlike the 3D case, we only use a single neighborhood to define these two topological numbers for the 2D case. Then, we characterize simple points either by using the two topological numbers or by a single topological number linked to another one condition. We compare the characterization of simple points by topological numbers with two other ones based on Hilditch crossing number and Yokoi number. We also highlight the number of possible configurations corresponding to a simple point, which also represents the maximum limit of local configurations that a thinning algorithm operating by parallel deletion of simple (individual) points may delete while preserving topology (limit usually not reachable, depending on the deletion strategy).