This thesis presents an intuitive, fast and accurate interactive segmentation method for visualizing and analyzing 3D medical images. This method combines a general deformable subdivision surface model with a novel sketch-line user initialization process. The model is simply and precisely initialized with a few quick sketch lines drawn across the width of the target object on several key slices of the volume image. The smooth surface constructed using these lines is extremely close to the shape of the object boundary, making the model's task of snapping to this boundary much simpler and hence more likely to succeed in noisy images with minimal user editing.This subdivision-surface based deformable model provides a foundation for precise user steering/editing capabilities and all of the simple, intuitive user interactions are seamlessly integrated with advanced visualization capabilities. Furthermore, to demonstrate its efficiency and accuracy, this new model has been used to segment objects from several 3D data sets.