The incidence of renal calculi is a serious global health concern, and accurate diagnostic procedures play a key role in treating this disease. The current study proposes a dual-stage framework to automate the classification and accurate segmentation of kidney stones utilizing a computed tomography scan image. In the first part, a CNN model using a transfer-learning ResNet-50 architecture was formulated to classify renal stone images into normal, fragmentable (F-type), and non-fragmentable (NF-type) types. The proposed CNN architecture was trained to yield a high diagnostic accuracy, with the final network achieving 99.39% accuracy. In the second stage, the image segmentation is performed using the following three methods: maximally stable extremal regions (MSER), Region Growing, and a proposed new Hybrid image segmentation technique. The hybrid proposed image segmentation technique leverages a key strategy that combines region growing and MSER segmentation to extract the periphery of the kidney stone and yield accurate morphological descriptors. The results indicate that the three methods used in this research are anatomically consistent. Also, the segmentation of pre-filtered images minimizes errors and demonstrates efficacy and feasibility to optimize ESWL procedures to increase efficiency through accurate kidney stone analysis.