A NEW NUMERICAL METHOD FOR LEVEL SET MOTION IN NORMAL DIRECTION USED IN OPTICAL FLOW ESTIMATION

摘要

We present a new numerical method for the solution of level setadvection equation describing a motion in normal direction for which the speedis given by the sign function of the difference of two given functions. Takingone function as the initial condition, the solution evolves towards the secondgiven function. One of possible applications is an optical ow estimation tofind a deformation between two images in a video sequence. The new numericalmethod is based on a bilinear interpolation of discrete values as used for therepresentation of images. Under natural assumptions, it ensures a monotonedecrease of the absolute difference between the numerical solution and thetarget function, and it handles properly the discontinuity in the speed due tothe dependence on the sign function. To find the deformation between twofunctions (or images), the backward tracking of characteristics is used. Twonumerical experiments are presented, one with an exact solution to show anexperimental order of convergence and one based on two images of lungs toillustrate a possible application of the method for the optical ow estimation.