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Motion Field Regularization for Sliding Objects Using Global Linear Optimization

In image registration it is often necessary to employ regularization in one form or another to be able to find 
 
a plausible displacement field. In medical applications, it is useful to define different constraints for different 
 
areas of the data. For instance to measure if organs have moved as expected after a finished treatment. One 
 
common problem is how to find plausible motion vectors far away from known motion. This paper introduces 
 
a new method to build and solve a Global Linear Optimizations (GLO) problem with a novel set of terms 
 
which enable specification of border areas to allow a sliding motion. The GLO approach is important especially 
 
because it allows simultaneous incorporation of several different constraints using information from 
 
medical atlases such as localization and properties of organs. The power and validity of the method is demonstrated 
 
using two simple, but relevant 2D test images. Conceptual comparisons with previous methods are 
 
also made to highlight the contributions made in this paper. The discussion explains important future work 
 
and experiments as well as exciting future improvements to the GLO framework.