We show a framework for growth analysis of plant roots in object coordinates which is one requirement for the botanical evaluation of growth mechanisms in roots. The method presented here is appliable on long image sequences up to several days, it has no limit for the sequence length. First we estimate the displacement vector field with the structure tensor method. Thereafter we determine the physiological coordinates of the root by active contours. The contours are first fitted on the root boundary and yield the data for the calculation of the middle line as the object coordinate axis of the root. In the third step the displacement field is sampled at the position of the middle line and projected onto it. The result is an array of tangential displacement vectors along the root which is used to compute the spatially resolved expansion rate of the root in physiological coordinates. Finally, the potential of the presented framework is demonstrated on synthetic and real data.