This paper is dedicated to the analysis of 3D data of carbon fiber reinforced silicon carbide ceramics. In the production process of C/SiC, a porous carbon preform reinforced with bundles of carbon fibers is infiltrated with liquid silicon at approximately 1 500 °C. The reaction between liquid silicon and carbon creates a layer of silicon carbide while the silicon vanishes almost completely. This material is able to withstand extremely high temperatures and it is extremely tough with respect to fracture. To increase the efficiency of the costly and time consuming production process, methods for monitoring the quality of the material are helpful. For instance, the thickness of the silicon carbide layer is a valuable measure. Moreover, due to different coefficients of thermal expansion of the components, typically cracks appear during the production process. For effective analysis 3D high resolution image data are necessary that can be acquired by synchrotron computed tomography. In a first image processing step, we segment the 3D image data with a convex optimization approach incorporating spatial regularity. Further, we work on the detection of cracks using an eigenvalue analysis of the 3D Hessian matrix determined in each pixel.