Shape transformation of multidimensional density functions using distribution interpolation of the Radon transforms

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 Implicit Functions (IF). First, we perform distribution interpolation on the precalculated Radon transforms of two different density functions, and then an intermediate density function is obtained by an inverse Radon transform. This approach guarantees a smooth transition along all the directions the Radon transform is calculated for. Unlike the IF 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.