Estimation of the 3D self-similarity parameter of trabecular bone from its 2D projection.

It has been shown that the analysis of two dimensional (2D) bone X-ray images based on the fractional Brownian motion (fBm) model is a good indicator for quantifying alterations in the three dimensional (3D) bone micro-architecture. However, this 2D measurement is not a direct assessment of the 3D bone properties. In this paper, we first show that S(3D), the self-similarity parameter of 3D fBm, is linked to S(2D), that of its 2D projection, by S(3D)=S(2D)-0.