Temporal registration of 2D X-ray mammogram using Triangular B-splines Finite Element Method (TBFEM)

In this paper we develop a novel image processing technique to register two dimensional temporal mammograms for effective diagnosis and therapy. Our registration framework is founded upon triangular B-spline finite element method (TBFEM). In contrast to tensor-product B-splines, which is widely used in medical imaging, triangular B-splines are much more powerful, associated with many desirable advantages for image registration, such as flexible triangular domain, local control, space-varying smoothness, and sharp feature modeling. Empowered by the rigorous theory of triangular B-splines, our method can explicitly model the transformation between temporal mammogram pairs over irregular region of interest(ROI), using a collection of triangular B-splines. In addition, it is also capable of describing C⁰ continuous deformation at the interfaces between different elastic tissues, while the overall displacement field is smooth. Our registration process consists of two steps: 1) The template image is first nonlinearly deformed using TBFEM model, subject to pre-segmented feature constraints; 2) The deformed template image is further perturbed by applying pseudo image forces, aiming to reducing intensity-based discrepancies. The proposed registration framework has been tested extensively on practical clinical data, and the experimental results demonstrates that the registration accuracy is improved comparing to using conventional FEMs. Besides, the modeling of local C⁰ continuities of the displacement field helps to further increase the registration quality considerably.