In this paper, we take advantage of the reconstruction properties of the sampling Kantorovich (SK) algorithm to estimate the volume of the human brain for the quantification of Alzheimer's biomarkers. At first, the goodness of the reconstructions is evaluated, comparing it to different interpolation methods by means of the Peak Signal to Noise Ratio (PSNR) index; then the stereological Cavalieri/Point‐counting technique is used to infer volumetric data starting from the knowledge of the planar sections. The comparison of the achieved results with synthetic references confirms the good performances of the new methodology.

In this paper, we carry out a study developed on 13,677 images from 15 patients affected by moderate/severe atheromatous disease of the abdominal aortic tract. A procedure to extract the pervious lumen of the aorta artery from basal CT images is exploited and tested on a large scale. In particular, the above method takes advantage of the reconstruction and enhancing properties of the sampling Kantorovich algorithm which allows the information content of images to be increased. The processed image is compared, slice by slice, by superposition, with the corresponding contrast medium reference image. Numerical indices of errors were computed and analyzed in order to test the validity of the proposed method. The results achieved confirm, both from the numerical and clinical point of view, the good performance and accuracy of the proposed method, opening the possibility to perform an assisted diagnosis avoiding the injection of the contrast medium.

This paper presents a study that leverages the important and innovative approximation properties of sampling Kantorovich operators, implemented in the processing of computed tomography (CT) images of patients with abdominal aortic aneurysm (AAA). By exploiting the remarkable reconstruction capabilities of these operators, we investigate a deterministic model grounded in a segmentation algorithm where sampling Kantorovich operators play a crucial role. This mathematically-based approach is compared with an artificial intelligence-based method employing a U-Net neural network. Both methods aim to segment the patent area of the aortic vessel, offering innovative and alternative techniques to the nephrotoxic contrast agents, typically used in diagnosing AAA. The results obtained from testing both methods were evaluated numerically and visually, demonstrating that both approaches yield accurate outcomes.