This paper introduces a complete pipeline of image processing methods in order to analyze and track the internal structures of a composite material. As a first step, input Xray images are denoised, enhanced, separated into different morphological components, and geometrically filtered in order to isolate the interesting fiber inside the composite material. This requires the design of specific algorithms preserving very thin image details while being able to remove undesired image regions that may be sometimes large. For this purpose, we use state-of the-art techniques based on recent achievements in diffusion PDE's and modern harmonic analysis tools. Then, the shapes of the remaining fibered composite are individually analyzed by the use of a tensor-based tracking algorithm. We illustrate how this set of techniques allows the dynamic analysis of the composite structure when submitted to external mechanical loads.