Double Bachelor’s Thesis - Machine Learning and Fractal-Based Analysis for the Automated Diagnosis of Cardiovascular Diseases Using Magnetic Resonance

Aug 5, 2026

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Cardiac magnetic resonance (CMR) serves as a reference imaging modality for cardiovascular diagnosis, yet traditional manual or semi-automated assessment of volume and shape parameters is slow and susceptible to human error while failing to represent the complexity of cardiac tissue. This thesis presents an automated diagnosis approach using ischemic heart disease as a use case, combining supervised machine learning with fractal-based analysis. Haussdorff dimension, box-counting dimension, and lacunarity are introduced, linked, and computed through dedicated algorithms. Fractal features extracted from UK Biobank CMR textures quantify complexity and heterogeneity for left ventricle, right ventricle, and myocardium, and are used alongside vascular risk factors and conventional indexes. Models including SVM, XGBoost, and random forests are evaluated using balanced accuracy, F1 score, precision, and recall, showing improved accuracy and reliability when fractal features are included.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages87

Reading Time3 h 39 min

AccessFree to download

Abstract

Introduction

Motivation

Objectives

State of the art

Document organization

Fractal dimensions and lacunarity

Hausdorff measure and dimension

Haussdorff dimension

Geometric invariant

Computing Hausdorff dimension

Box-counting dimension

Geometric invariant

Computing box-counting dimension

Lacunarity

Computing lacunarity

Classification models

Support Vector Machines

Random forest

Extreme Gradient Boosting

Explainability: SHAP

Image feature extraction

Dataset

Interpolation

The anisotropy problem

Interpolating images

Normalisation

Computing box-counting dimension and lacunarity

Methodology

Definition of the study sample

Feature classification

Feature combinations

Exploratory analysis

Vascular Risk Factors and CMR measures

Fractal Features

Models

K-Fold Cross Validation

Model A: SVM

Model B: RF

Model C: XGB

Results

Evaluation metrics

Models performances

Model A

Model B

Model C

Explainability analysis

Conclusions

Project conclusions

Further work

Appendices

Fractal sets

Lagrange multipliers

Tables

Statistical tests

Double Bachelor’s degree in Mathematics and Computer Science Bachelor’s Thesis MACHINE LEARNING AND FRACTAL-BASED ANALYSIS FOR THE AUTOMATED DIAGNOSIS OF CARDIOVASCULAR DISEASES USING MAGNETIC RESONANCE Autor: Sergi Romero Gris Director: Dra. Polyxeni Gkontra Dr. Joan Carles Tatjer Montaña Realitzat a: Departament de Matemàtiques i Informàtica Barcelona, 13 de juny de 2023 Contents Abstract iv 1 Introduction 1 1.1 Motivation .................................. 1 1.2 Objectives .................................. 1 1.3 State of the art ................................ 2 1.4 Document organization .......................... 3 2 Fractal dimensions and lacunarity 5 2.1 Hausdorff measure and dimension .................... 5 2.1.1 Haussdorff dimension ....................... 6 2.1.2 Geometric invariant ........................ 7 2.1.3 Computing Hausdorff dimension ................ 9 2.2 Box-counting dimension .......................... 13 2.2.1 Box-counting dimension ...................... 13 2.2.2 Geometric invariant ........................ 17 2.2.3 Computing box-counting dimension ............... 18 2.3 Lacunarity .................................. 23 2.3.1 Lacunarity .............................. 24 2.3.2 Computing lacunarity ....................... 24 3 Classification models 27 3.1 Support Vector Machines ......................... 27 3.2 Random forest ................................ 30 3.3 Extreme Gradient Boosting ........................ 31 3.4 Explainability: SHAP ............................ 33 4 Image feature extraction 35 4.1 Dataset .................................... 35 4.2 Interpolation ................................. 36 4.2.1 The anisotropy problem ...................... 36 4.2.2 Interpolating images ........................ 36 4.3 Normalisation ................................ 40 4.4 Computing box-counting dimension and lacunarity .......... 40 5 Methodology 43 5.1 Definition of the study sample ...................... 43 5.2 Feature classification ............................ 44 5.2.1 Feature combinations ....................... 45 5.3 Exploratory analysis ............................ 45 5.3.1 Vascular Risk Factors and CMR measures ........... 45 5.3.2 Fractal Features ........................... 45 5.4 Models .................................... 48 5.4.1 K-Fold Cross Validation ...................... 48 5.4.2 Model A: SVM ........................... 49 5.4.3 Model B: RF ............................. 50 5.4.4 Model C: XGB ............................ 50 6 Results 53 6.1 Evaluation metrics ............................. 53 6.2 Models performances ............................ 54 6.2.1 Model A ............................... 54 6.2.2 Model B ............................... 55 6.2.3 Model C ............................... 56 6.3 Explainability analysis ........................... 57 7 Conclusions 61 7.1 Project conclusions ............................. 61 7.2 Further work ................................. 62 A Fractal sets 65 B Lagrange multipliers 67 C Tables 69 C.1 Population’s disease summary ...................... 69 C.2 Subjects’ characteristics ........................... 69 D Statistical tests 73 D.1 Rank sum test ................................ 73 Bibliography 75 Abstract Cardiac magnetic resonance (CMR) is the reference imaging modality for the diagnose of cardiovascular diseases. Traditionally, simple CMR parameters related to the volume and shape of the cardiac structures are calculated by the medical professionals by means of manual or semi-automated approaches. This process is time-consuming and prone to human errors. Moreover, despite the importance of these traditional CMR indexes, they often fail to fully capture the complexity of the cardiac tissue. In this work, we propose a novel approach for automated cardiovascular disease diagnosis, using ischemic heart dise

FAQs

What is the main goal of this thesis?

Develop an automated cardiovascular disease diagnosis method using ischemic heart disease as a use case, leveraging supervised machine learning together with fractal-based features extracted from cardiac magnetic resonance images.

How are fractal features computed and what concepts are used?

The study introduces and explores Haussdorff dimension, box-counting dimension, and lacunarity, including computational algorithms for calculating box-counting dimension and lacunarity from CMR textures.

Which machine learning models and evaluation metrics are used?

Models include SVM, random forests, and XGBoost, evaluated with balanced accuracy, F1 score, precision, and recall to determine whether fractal features improve diagnosis performance.

Aug 5, 2026

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