In virtual reality/augmented reality (VR/AR) applications, especially
medical image visualization, it is highly desirable to magnify region of
interests. In this work, we propose a novel method for virtual magnifying
glass for visualizing volumetric data based on Optimal Mass
Transportation. An optimal mass transportation map deforms a volume to
itself, transforms the source measure (volumetric element) to the target
measure with the minimal transportation cost. Solving the optimal mass
transportation problem is equivalent to a convex optimization, and can be
converted to computing power Voronoi diagrams in classical
computational geometry. The proposed method allows the user to
accurately control the target measure, and select multiple regions of
interests with irregular shapes. We demonstrate the effectiveness and
efficiency of our method with several volume data sets from medical
applications.