Quantitative measurements of the coronary artery tree substructures from Cardiac Multislice-CT data sets is an important goal to improve the diagnosis and treatment of coronary artery disease. This paper presents an algorithm based on morphological grayscale reconstruction through 2D slice images devoted to the extraction of the 3D coronary artery tree. The proposed procedure is conceived as a first step prior to the segmentation and inspection of interesting substructures in the coronaries. The correct extraction of the left coronary arteries has been validated in 9 CT-datasets with satisfactory results, particularly concerning speed and robustness.