The lungs are highly elastic organs, composed of a variety of structures: vasculature, airways and parenchyma. The unique mechanical properties of each of these structures form the composite material of the lung. Numerous pulmonary diseases affect these material properties. Clinically, these structural changes cannot be directly quantified. However, medical imaging modalities such as computed tomography and magnetic resonance imaging can be used to observe lung morphology. It would be helpful to be able to correlate regional morphological changes with changes in pulmonary function. We present an approach toward the quantification of pulmonary deformation via non-rigid registration of serial MR images of the lung using the variational framework implemented in the Insight toolkit. Conventional registration methods, as exemplified by a finite element implementation of the classic elastic matching technique, are shown to perform well over a set of vascular landmarks in the measurement of lung motion. This performance is maintained in an augmented system, which combines inhomogeneous material properties with the use of domain discretizations tailored to reflect the apparent geometry within the image and to reduce background effects. These adaptations lay the groundwork for biomechanical modeling of the lung using the finite element method.