Ingeniería Civil Matemática certificada por 3 años hasta Diciembre de 2026
Kathryn Shalom Barraza Araya
Bachelor’s Thesis
Progression of Lung Damage Measured by Hausdorff Distance Approaches and Voronoi Diagrams
Thesis Advisor
Gerardo Honorato
Co-Advisor
Soledad Torres
Jaime Retamal
Sumary
The Hausdorff distance is a metric that quantifies the similarity between two sets in a metric space by measuring the greatest distance between the closest points of each set. It is particularly useful for evaluating changes in the shape and size of geometric structures. On the other hand, Voronoi diagrams partition space into regions associated with a set of generating points; they are based on proximity to these sets, which allows for modeling spatial interactions and neighborhood relationships between regions.
These mathematical concepts are applied to the study of lung transformation under various pathological conditions. Lung deterioration can manifest in different parts of its structure, and the distribution of damage is heterogeneous. This work analyzes two types of changes in the alveoli, as they represent an area where morphological alterations can be observed. Using the Hausdorff distance and Voronoi diagrams, it is possible to quantify and model these structural changes, providing a mathematical framework for analyzing lung damage. In this way, mathematical tools are used to explain phenomena observed in the medical field.
