This work is devoted to registration and estimation of vector field of two following images. We use mathematical models created by Vemuri et. al., which allows to gain information about the movement of points from image, by help of information about change of intensity between those images. In case of registration we transform intensity function of one image to intensity function of other, by solving simple nonlinear partial differential equation. Principle of this equation is built on letting level-sets of first image to evolve to level-sets of the second, in direction of normal. For its computation we use Rouy-Tourin scheme. We also modified this equation into advection equation, which we solve utilizing finite volume method. By solving this equation we find morphing between images and also transformation between pixels. For purpose of finding this transformation Vemuri et. al. derives another nonlinear partial differential equation, which solution we present as well. We implemented all three methods in C language and tested them with simulated data.