• Distance transformation;
  • mean thickness;
  • micro-CT;
  • stereology;
  • structural parameters;
  • thickness distribution;
  • three-dimensional morphometry;
  • trabecular bone structure

Three-dimensional (3-D) structural parameters derived from lower-dimensional measurements using indirect morphometric methods may be strongly biased if the measured objects deviate from the assumed structure model. With the introduction of 3-D microscopic measuring techniques it is possible to obtain a complete depiction of complex spatial structures. As a consequence, new 3-D methods have recently been developed for the estimation of morphometric parameters such as volume, surface area and connectivity by direct processing of the 3-D images. Structure thickness is an important morphometric parameter which is usually defined for specific structure models only. In this paper we propose a general thickness definition for arbitrary structures allowing us to calculate the mean structure thickness and the thickness distribution of 3-D objects in a direct way and independently of an assumed structure model. Additionally, an efficient implementation for the practical usage of the method is described using distance transformation. The new method is applied to trabecular bone structures measured with a 3-D micro-computed tomography system.