This dissertation reports a framework that improves the robustness and accuracy in computing dense optical-flow fields. We propose a global formulation with a regularization term. The regularization expressions are derived based on tensor theory and complex analysis. It is shown that while many regularizers have been proposed (image-driven, flow-driven, homogeneous, inhomogeneous, isotropic, anisotropic), most of them are based on the 2D translational motion model. These regularizers, strictly speaking, are valid for uniform 2D translational motion only, because what they do essentially is to penalize changes in a flow field. However, many flow patterns—such as rotation, zoom, and their combinations, induced by a 3D rigid-body motion—are not constant. The traditional regularizers then incorrectly penalize these legal flow patterns and result in biased estimates.

The purpose of this work is then to derive a new suite of regularization expressions that treat all valid flow patterns resulting from a 3D rigid-body motion equally, without unfairly penalizing any of them. Furthermore, we develop a framework of optical flow computation and flow model inference method. The proposed framework can fully utilize the power of the proposed 3D rigid body motion regularizers.