The algorithms of Material Point Method and Image Morphing seem similar. Both of them compute a group of parameters/coefficients based on the initialized particles/landmarks, then, update every element in the output through the parameters/coefficients:

Material Point Method

1. Initialize the parameters of material points / particles: position. velocity, mass, volume, and stress. There could be other combinations of parameters, it depends on the material being simulated.

2. Compute the parameters of each grid for the simulation of the material, such as deformation, fluid animation, by projecting data from the material points to the grid.

3. In each time phase, the parameters of material points (or the grids)  are updated based on those of the grids.

Image Morphing

1. Initialize landmarks on the input images.

2. Compute the coefficients of the transformation based on the landmarks’ positions.

3. In each time phase, the corresponding positions in the input images are compute based on the coefficients of the transformation.