Microtubules are stiff biopolymers that play crucial roles in intracellular transport and structural support within cells. There are various microtubule associated proteins (MAPs), such as tau, which bind to microtubules and regulate their dynamics. Mutations in these proteins have been implicated in several notable diseases, including neuropathies and dementias; it has been hypothesized that the resulting changes in the mechanical properties of microtubules are important in understanding their mechanism of action. To quantify these effects, fluorescently-labeled microtubules are imaged and a statistical analysis is performed on the shapes they adopt under thermal excitation. Here, we describe a newly-developed algorithm that fits a continuous smooth curve to the fluorescent image and represents the polymer shape using an orthogonal polynomial basis. In comparison to previous efforts, this new method is significantly more robust to noise and gaps in the fluorescence signal, allowing for larger ensembles of data to be analyzed. Using this method, we are able to determine the fluctuation spectra of different classes of microtubules in order to assess the effects of polymerization conditions, small molecule inhibitors, and various MAPs on the stiffness of microtubules.