Image registration plays an important role in pulmonary image analysis. Accurate image registration is a challenging problem when the lungs have deformation with large distance. Registration results estimate the local tissue movement and are useful for studying lung mechanical quantities. In this thesis, we propose a new registration algorithm and a registration scheme to solve lung CT matching problems. Approaches to study lung functions are discussed and presented through a practical application. The overall objective of our project is to develop image registration techniques and analysis approaches to measure lung functions at high resolution. We design a nonrigid volumetric registration algorithm to catch lung motion from a pair of intrasubject CT images acquired at different inflation levels. This registration algorithm preserves both parenchymal tissue volume and vesselness measure, and is regularized by a linear elasticity cost. Validation methods for lung CT matching are introduced and used to evaluate the performance of different registration algorithms. Evaluation shows the feature-based vesselness constraint can efficiently improve the registration accuracy around lung boundaries and in the base lung region. Meanwhile, a new scheme to solve complex registration problem is introduced utilizing both surface and volumetric registration. The first step of this scheme is to register the boundaries of two images using surface registration. The resulting boundary displacements are extended to the entire ROI domains using the Element Free Galerkin Method (EFGM) based on weighted extended B-Splines (WEB-Splines). These displacement fields are used as initial conditions for the tissue volume– and vessel–preserving non-rigid registration over the object domain. Both B-Splines and WEB-Splines are used to parameterize the transformations. Our algorithms achieve high accuracy and provide reasonable lung function maps. The mean errors on landmarks, vessel locations, and fissure planes are on the order of 1 mm (sub-voxel level). Furthermore, we establish methods based on registration derived transformation to analyze mechanical quantities and measure regional lung function. The proposed registration method and lung function measurement are applied on a practical application to detect mechanical alternations in the lung following bronchoalveolar lavage, which achieves satisfactory results and demonstrates the applicability of our proposed approaches.