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An approximation-based approach versus an AI one for the study of CT images of abdominal aorta aneurysms

Lucrezia Rinelli, Arianna Travaglini, Nicolò Vescera, Gianluca Vinti

TL;DR

The study tackles the problem of estimating the patent lumen in CT images of abdominal aortic aneurysms without contrast agents. It pits a deterministic, SK-operator-based reconstruction against a U-Net-based AI approach, applying both to basal images and evaluating with standard segmentation indices. Results show the AI method achieving higher average accuracy and lower variability, while the deterministic method remains competitive and more interpretable, especially after removing calcium plaques. The work highlights complementary strengths: AI offers operator-free processing after ROI selection, whereas the deterministic approach provides transparent, controllable steps with solid performance improvements through plaque removal.

Abstract

This study evaluates two approaches applied to computed tomography (CT) images of patients with abdominal aortic aneurysm: one deterministic, based on tools of Approximation Theory, and one based on Artificial Intelligence. Both aim to segment the basal CT images to extract the patent area of the aortic vessel, in order to propose an alternative to nephrotoxic contrast agents for diagnosing this pathology. While the deterministic approach employs sampling Kantorovich operators and the theory behind, leveraging the reconstruction and enhancement capabilities of these operators applied to images, the artificial intelligence-based approach lays on a U-net neural network. The results obtained from testing the two methods have been compared numerically and visually to assess their performances, demonstrating that both models yield accurate results.

An approximation-based approach versus an AI one for the study of CT images of abdominal aorta aneurysms

TL;DR

The study tackles the problem of estimating the patent lumen in CT images of abdominal aortic aneurysms without contrast agents. It pits a deterministic, SK-operator-based reconstruction against a U-Net-based AI approach, applying both to basal images and evaluating with standard segmentation indices. Results show the AI method achieving higher average accuracy and lower variability, while the deterministic method remains competitive and more interpretable, especially after removing calcium plaques. The work highlights complementary strengths: AI offers operator-free processing after ROI selection, whereas the deterministic approach provides transparent, controllable steps with solid performance improvements through plaque removal.

Abstract

This study evaluates two approaches applied to computed tomography (CT) images of patients with abdominal aortic aneurysm: one deterministic, based on tools of Approximation Theory, and one based on Artificial Intelligence. Both aim to segment the basal CT images to extract the patent area of the aortic vessel, in order to propose an alternative to nephrotoxic contrast agents for diagnosing this pathology. While the deterministic approach employs sampling Kantorovich operators and the theory behind, leveraging the reconstruction and enhancement capabilities of these operators applied to images, the artificial intelligence-based approach lays on a U-net neural network. The results obtained from testing the two methods have been compared numerically and visually to assess their performances, demonstrating that both models yield accurate results.
Paper Structure (12 sections, 2 theorems, 23 equations, 13 figures, 6 tables)

This paper contains 12 sections, 2 theorems, 23 equations, 13 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Preliminaries and approximation results
  3. Deterministic approach (DA)
  4. Description of the mathematical model
  5. Description of the dataset
  6. Results of the DA
  7. Artificial Intelligence approach (AI)
  8. Description of the U-Net model
  9. Description of the dataset
  10. Results of the AI approach
  11. Comparison
  12. Conclusions

Key Result

Theorem 2.1

Let $f\in C^0(\mathbb{R}^n)$. Then, for every $\underline{x}\in\mathbb{R}^n$, In particular, if $f\in C(\mathbb{R}^n)$, then where $C(\mathbb{R}^{n})$ (resp. $C^{0}(\mathbb{R}^n)$) denotes the space of uniformly continuous and bounded (resp. continuous and bounded) functions on $\mathbb{R}^{n}$.

Figures (13)

  • Figure 1: Reconstruction by SK operators, with the bidimensional Jackson type kernel $J^{2}_{12}$, $w=20$ and scaling factor $R=2$. On the left we can see the original image, on the right the reconstructed one.
  • Figure 2: Scheme of the segmentation algorithm.
  • Figure 3: Pre-processing steps of the dataset.
  • Figure 4: Interface and output of the portal ImageLab. We highlighted in black the calcium plaques.
  • Figure 5: Test dataset with examples, identification number of the patients and number of slices related to the aneurysmatic tracts.
  • ...and 8 more figures

Theorems & Definitions (3)

  • Definition 2.1
  • Theorem 2.1
  • Theorem 2.2