1. An apparatus for determining three dimensional representations of a tortuous vessel, comprising: an external information processing unit for receiving a first set of images of a line object in the tortuous vessel, determining external energy information of said first set of images and outputting said external energy information; an internal information processing unit for receiving internal information related to the line object including a minimum bending radius, determining internal energy information of the line object and outputting said internal energy information; a 3D pullback path determination unit for receiving said external energy information and said internal energy information and determining a 3D pullback path that is physically feasible based on the line object; and means for receiving said 3D pullback path and for calculating three dimensional representations of the tortuous vessel based on said 3D pullback path, wherein the means for receiving and calculating receives 2D representations of the interior of the tortuous vessel at a plurality of points along the 3D pullback path, and wherein the means for receiving and calculating comprises a global interpolating means for interpolating using global behavior of the line object to approximate a local behavior between corresponding points of the plurality of 2D representations of the interior of the tortuous vessel, wherein the interpolating using the global behavior determines the three dimensional representations of the tortuous vessel.