Image analysis of protein fibrils is a key step for a quantitative understanding of the mechanisms responsible for aggregation and deposition of amyloids. In this paper, we develop a fully automated method to detect and measure all characteristics of fibrils. After detecting the fibrils centerline, we propose a tracking-based method to estimate the local width, length and curvature of fibrils. We also discriminate between branches and overlapping of fibrils by comparing the orientations of the fibril segments at their intersection point. We test our method on Transmission Electron Microscopy (TEM) images of human, bank vole, and ovine PrP (prion protein) fibrils, and analyze the result to evidence structural differences between different types of fibrils. The proposed method has high estimation accuracy in detections and is further compared with a state-of-art method.