A method and apparatus for approximating a path of movement of a target. The method includes referencing a temporal sequence of images, identifying a plurality of data points associated with a selected volume element of the volume of interest, and calculating an estimated location of the selected volume element based on a cost function having a constraint which favors continuous spatial motion of the selected volume element over time. Each of the images of the temporal sequence of images depicts a volume of interest. Each of the plurality of data points corresponds to one of the images.