Three optical flow image registration (IR) methods referred to as Combined Compressible Local Global (CCLG) optical flow, Large Displacements Optical Flow (LDOF), and Large Displacement Compressible Optical Flow (LDCOF) are introduced. The three novel methods are designed to account for difficulties raised by 4D throacic Computed Tomography (CT) image registration problems, which currently cannot be effectively addressed by existing methods. The 4D CT image registration problem is more challenging than typical IR problems for three key reasons. First, voxel intensities for CT images are proportional to the density of the material imaged. Given that the density of lung tissue changes with respiration, the constant voxel intensity assumption employed by most IR methods is invalid for thoracic CT images. Second, due to the image acquisition procedure, 4D CT image sets are known to suffer from image noise, blurring, and artifacts. Finally, the large size of the image sets requires a computationally efficient and parallelizable algorithm. The CCLG method models compressible image flow with the mass conservation equation coupled with a local-global strategy that alleviates the effects of image noise, and incorporates local image information into the voxel motion model. After a finite element discretization, the resulting large scale linear system is solved using a parallelizable, multi-grid preconditioned conjugate gradient algorithm. The LDOF and LDCOF methods are designed for image sets containing large voxel displacements or erroneous image artifacts. Both methods incorporate unknown image information into the IR problem formulation, which results in a nonlinear least squares problem for both the pixel displacement components and the unknown image values. An alternating linear least squares algorithm is introduced for solving the LDOF and LDCOF nonlinear least squares problems efficiently. After Chapter 1 introduces the basics of IR, the main body of the thesis is divided into two parts. Part 1 is a review of existing IR methodologies. Part 2 derives the three aforementioned new approaches and presents testing results for the three methods, respectively. The computational experiments are carried out on both synthetic and genuine image data. Finally, the thesis concludes in Chapter 8 with a discussion of possible areas of future research.