Thermal plasma spraying is an important manufacturing technique that creates a thermal barrier coating to protect the surface underneath from wear, erosion, oxidation and corrosion. In this paper, we develop a new microstructure classification and quantification (MCQ) module that could fully automatically classify and quantify two types of microstructures, globular and interlamellar, in the top coat layer of thermal barrier coating images captured from light microscope. The MCQ module utilizes the masks obtained from the Thermal Barrier Coating Porosity Measurement (TBCPM) framework and applies the morphological filtering of erosion to the images to differentiate globular and interlamellar that are physically distinct and are eroded away at a different rate. The microstructures exhibit complicated spatial relations, for example, a segment might contain microstructures of both types. To deal with this difficulty, we build a forest of hierarchical trees of segments when eroding the images and then traverse this forest of the trees in post order following a carefully designed rule to determine if two neighboring segments should be merged. Our experimental results on the synthesized images with non-overlapping and overlapping segments show an average accuracy of 98.77% and 93.12% respectively.