Poisson's Equation Based Image Registration: An Application for Matching 2D Mammograms

Registration is a critical step in identifying the morphological disparity between the temporal and bilateral mammograms. Since the object involved is deformable in nature, deformable (non-rigid or physical) registration schemes are preferable to remove the internal geometrical distortions. The basic idea is to mimic the property of the tissue under examination before constructing the regularizer. Elastic, visco-elastic and fluid are the three important physical models found in literature. Elastic model mimics small deformation and hence cannot be applied for problems involving large deformation. Visco-elastic models and fluid models are considered as alternates. These models assume the breast to possess the properties of visco-elastic or fluid, which is contrary to the real property. After a careful and intensive literature analysis, we conclude that model mimicking breast has to be hyper elastic. Hence, we have proposed an idea called hyper-elastic image registration to match 2D mammograms. Experimentally, we tested with 89 pairs of bilateral and temporal 2D mammograms and compared with other models. We have introduced a star rating scheme for validating our results, which along with visual analysis utilizes a quantitative measure too.