A segmentation procedure of the pervious area of the aorta artery from CT images without contrast medium

Abstract

In this paper, we develop an algorithm for the segmentation of the pervious lumen of the aorta artery in computed tomography (CT) images without contrast medium, a challenging task due to the closeness gray levels of the different zones to segment. The novel approach of the proposed procedure mainly resides in enhancing the resolution of the image by the application of the algorithm deduced from the mathematical theory of sampling Kantorovich operators.After the application of suitable digital image processing techniques, the pervious zone of the artery can be distinguished from the occluded one. Numerical tests have been performed using 233 CT images, and suitable numerical errors have been computed and introduced ex novo to evaluate the performance of the proposed method. The above procedure is completely automatic in all its parts after the initial region of interest (ROI) selection. The main advantages of this approach relies in the potential possibility of performing diagnosis concerning vascular pathologies even for patients with severe kidney diseases or allergic problems, for which CT images with contrast medium cannot be achieved.

The Riemann-Lebesgue Integral of Interval-Valued Multifunctions

“…More precisely, if A is the region of interest (ROI) of a given image and B is the corresponding approximation of the ROI A detected by a suitable edge detection algorithm, the Hausdorff distance measure the displacement between A and B, in fact evaluating the accuracy (i.e., the approximation error) of the method. For instance, in [55] the Hausdorff distance has been used in order to evaluate the degree of accuracy of an algorithm for the detection of the pervious area of the aorta artery from CT images without contrast medium. This procedure is useful, for example, in the diagnosis of aneurysms of the abdominal aorta artery, especially for patients with severe kidneys pathology for which CT images with contrast medium can not be performed.…”

Hahn-Banach and Sandwich Theorems for Equivariant Vector Lattice-Valued Operators and Applications

“…Among the consequences of this theorem we recall, for instance, the Fencheltype duality theorem which has several applications in minimax theorems, in particular in Economics and stochastic programming (see, e.g., [3, 13, 37-39, 43, 44]) and image and/or document reconstruction (see, e.g., [2,4,9,15,16,19,20]).…”

“…∈ B}, getting the assertion. Now, as a consequence of Theorem 3.3, we give the next Fenchel-type duality theorem, extending to equivariance [6, Theorem 2] and [47, Theorem 2].Ì ÓÖ Ñ 4.2º Let U : D(U ) → R, V : D(V ) → R be convex and G-equivariant functions, where D(U ) and D(V ) satisfy(19). Letr = {U (x) + V (x) : x ∈ D(U ) ∩ D(V )} exist in R,where r is as in Problem 2.7) , and let U c , V c be as in Problem 2.8).…”

On a Durrmeyer-type modification of the Exponential sampling series

“…This represents a wide field of investigations, due to its practical applications in various sectors of applied sciences (see e.g. [1,2,[20][21][22][23][24][25] and references therein).…”