Accurate staging of liver fibrosis is essential for early diagnosis and effective treatment, motivating the development of non-invasive, computation-based diagnostic methods. This study proposes a machine learning (ML) framework for liver fibrosis staging using magnetic resonance imaging (MRI), with an emphasis on feature extraction informed by geometric and topological characteristics of liver tissue. The framework is evaluated using controlled animal experiments and validated with clinical data from human subjects. In the animal study, mice were classified into four fibrosis stages: healthy (A0), mild (A1), moderate (A2), and severe (A3). Support Vector Machine (SVM) classifiers were developed using two handcrafted features—Euler characteristic numbers and estimated porosity—derived from MRI images to capture structural and connectivity changes associated with fibrosis progression. Three SVM configurations were investigated: models using estimated porosity alone, Euler characteristic numbers alone, and a combination of both features. In parallel, Convolutional Neural Network (CNN) models were trained as baseline approaches using binary and grayscale MRI images. After parameter optimization, CNN models achieved classification accuracies of 63.2\% and 64.5\% for binary and grayscale images, respectively. In contrast, SVM models demonstrated substantially higher performance, with accuracies of 93.3\% using estimated porosity alone, 74.6\% using Euler characteristic numbers alone, and 90.9\% using combined features. The porosity-based SVM achieved the best overall performance across all fibrosis stages and showed particular robustness in distinguishing early-stage (A1) fibrosis, indicating strong potential for early detection.