Fibrous materials such as fiber-reinforced composites are finding increasing application in the automotive, aerospace, and other industries. Fiber arrangements and defects at microscopic scales have direct impact on their stability. Two-dimensional images obtained by either non-destructive or destructive imaging cannot reveal the full fiber orientation information. Therefore, three-dimensional images obtained by micro computed tomography (?CT) are used. Since segmentation of these image datasets is often difficult due to low contrast, we propose a linear filtering scheme to extract local fiber orientations. Efficient implementations of these filters have been proposed, resulting in practical algorithms with acceptable runtimes in the scale of minutes to at most a few hours for common tomographic image sizes. We show how to condense the local orientation information into visual representations. In contrast to existing 3D orientation estimation methods, our method results in densely sampled orientation maps. The proposed method is applied to images of two different fiber materials and compared to orientation estimates based on measures obtained from integral geometry. We show conformance of the proposed orientation estimation methods with these known methods.