Microtubules (MTs) promote important cellular functions including migration, intracellular trafficking, and chromosome segregation. The centrosome, comprised of two centrioles surrounded by the pericentriolar material (PCM), is the cell's central MT-organizing center. Centrosomes in cancer cells are commonly numerically amplified. However, the question of how the amplification of centrosomes alters MT organization capacity is not well studied. We developed a quantitative image-processing and machine learning-aided approach for the semi-automated analysis of MT organization. We designed a convolutional neural network-based approach for detecting centrosomes, and an automated pipeline for analyzing MT organization around centrosomes, encapsulated in a semi-automatic graphical tool. Using this tool, we find that breast cancer cells with supernumerary centrosomes not only have more PCM protein per centrosome, which gradually increases with increasing centriole numbers, but also exhibit expansion in PCM size. Furthermore, cells with amplified centrosomes have more growing MT ends, higher MT density and altered spatial distribution of MTs around amplified centrosomes. Thus, the semi-automated approach developed here enables rapid and quantitative analyses revealing important facets of centrosomal aberrations.