We develop a novel suite of image processing and statistical tools to better understand the elasticity of biopolymers in vitro. The principles of thermodynamics predict a relationship between the distribution of a biopolymer's shape configurations at thermal equilibrium over time and its stiffness. This provides a method for observing fluorescence microscopy data of thermally fluctuating biopolymers and analytically deriving their elastic properties. However, for stiff biopolymers, such as microtubules, it is difficult to distinguish between physical heterogeneity and experimental noise. We improve on preexisting methods by developing a more robust image processing method to study the shape configurations, and an advanced statistical method of deriving their elastic properties. To validate our algorithms, we benchmark it against numerically generated datasets with generated noise features mimicking those found in experiment. This allows scientists to analyze experimental data with an understand how image noise affects calculations. Lastly, we develop methods that generalize standard theories to include detecting heterogeneities in elasticity and compare our methods with both numerical and experimental datasets.