We address two specific issues related to the problem of OF computation from tagged MR images. First, the validity of the brightness constancy assumption of HSOF is studied in Section 3.1, and a modification to HSOF is proposed and tested when the BCE condition of HSOF is not satisfied. Second, the issue of regularization in OF algorithms is addressed in Section 3.2. Significant research on these goals has been completed and published ([14], [15], [16], [17]).