Many studies have shown that epicardial fat is associated with a higher risk of heart diseases. Accurate epicardial adipose tissue quantification is still an open research issue. Considering that manual approaches are generally user-dependent and time-consuming, computer-assisted tools can considerably improve the result repeatability as well as reduce the time required for performing an accurate segmentation. Unfortunately, fully automatic strategies might not always identify the Region of Interest (ROI) correctly. Moreover, they could require user interaction for handling unexpected events. This paper proposes a semi-automatic method for Epicardial Fat Volume (EFV) segmentation and quantification. Unlike supervised Machine Learning approaches, the method does not require any initial training or modeling phase to set up the system. As a further key novelty, the method also yields a subdivision into quartiles of the adipose tissue density. Quartile-based analysis conveys information about fat densities distribution, enabling an in-depth study towards a possible correlation between fat amounts, fat distribution, and heart diseases. Experimental tests were performed on 50 Calcium Score (CaSc) series and 95 Coronary Computed Tomography Angiography (CorCTA) series. Area-based and distance-based metrics were used to evaluate the segmentation accuracy, by obtaining Dice Similarity Coefficient (DSC) = 93.74% and Mean Absolute Distance (MAD) = 2.18 for CaSc, as well as DSC = 92.48% and MAD = 2.87 for CorCTA. Moreover, the Pearson and Spearman coefficients were computed for quantifying the correlation between the ground-truth EFV and the corresponding automated measurement, by obtaining 0.9591 and 0.9490 for CaSc, and 0.9513 and 0.9319 for CorCTA, respectively. In conclusion, the proposed EFV quantification and analysis method represents a clinically useable tool assisting the cardiologist to gain insights into a specific clinical scenario and leading towards personalized diagnosis and therapy.