1. A method, comprising: receiving an input indicative of respective apparent locations of a plurality of points disposed along a length of a probe inside a body of a subject; applying a model of known mechanical properties of the probe to the respective apparent locations so as to minimize a first cost function with respect to shapes that can be assumed by the probe in the body; choosing a shape responsively to the minimized first cost function and determining preliminary coordinates of the apparent locations responsively to the shape; minimizing a second cost function with respect to differences between the apparent locations and the preliminary coordinates; and generating corrected coordinates of the points along the length of the probe based on the minimized second cost function.