Multiscale Shannon’s Entropy Modeling of Orientation and Distance in Steel Fiber Micro-Tomography Data

This paper is concerned with the modeling and analysis of the orientation and distance between steel fibers in X-ray micro-tomography data. The advantage of combining both orientation and separation in a model is that it helps provide a detailed understanding of how the steel fibers are arranged, which is easy to compare. The developed models are designed to summarize the randomness of the orientation distribution of the steel fibers both locally and across an entire volume based on multiscale entropy. Theoretical modeling, simulation, and application to real imaging data are shown here. The theoretical modeling of multiscale entropy for orientation includes a proof showing the final form of the multiscale taken over a linear range of scales. A series of image processing operations are also included to overcome interslice connectivity issues to help derive the statistical descriptions of the orientation distributions of the steel fibers. The results demonstrate that multiscale entropy provides unique insights into both simulated and real imaging data of steel fiber reinforced concrete.