Distribution Interpolation of the Radon Transforms for Shape Transformation of Gray-Scale Images and Volumes

In this paper, we extend 1D distribution interpolation to 2D and 3D by using the Radon transform. Our algorithm is fundamentally different from previous shape transformation techniques, since it considers the objects to be interpolated as density distributions rather than level sets of density functions. First, we perform distribution interpolation on the precalculated Radon transforms of two different density functions, and then an intermediate density function is obtained by a consistent inverse Radon transform. This approach guarantees a smooth transition along all the directions the Radon transform is calculated for. Unlike the previous methods, our technique is able to interpolate between features that do not even overlap and it does not require a one dimension higher object representation. We will demonstrate that these advantageous properties can be well exploited for 3D modeling and metamorphosis.