3D shape-dependent thinning method for trabecular bone characterization

Curve and surface thinning are widely-used skeletonization techniques for modeling objects in three dimensions. In the case of trabecular bone analysis, however, neither curve nor surface thinning is really efficient since the internal geometry of the object is usually composed of both rod and plate shapes. The purpose of this paper is to propose an original method called hybrid skeleton which better matches the geometry of the data compared to curve and surface skeletons. In the hybrid skeleton algorithm, 1D curves represent rod-shaped zones whereas 2D surfaces represent plate-shaped elements.

The proposed hybrid skeleton algorithm is based on a combination of three methods. (1) A new variant of the method proposed by Bonnassie et al. for the classification of voxels as belonging to plate-like or rod-like structures, where the medial axis (MA) algorithm is replaced by a fast and connected skeletonization algorithm. In addition, the reversibility of the MA algorithm is replaced by an isotropic region-growth method to spread the rod and plate labels back to the original object. (2) A well chosen surface thinning method applied on the plate voxels set. (3) A well chosen curve skeleton thinning method applied on the rod voxels set. The efficiency and the robustness of the proposed algorithm were evaluated using synthesis test vectors. A clinical study was led on micro-CT (computed tomography) images of two different populations of osteoarthritic and osteoporotic trabecular bone samples. The morphological and topological characteristics of the two populations were evaluated using the proposed hybrid skeleton as well as the classification algorithm.

When evaluated on test vectors and compared to Bonnassie's algorithm, the proposed classification algorithm gives a slightly better rate of classification. The hybrid skeleton preserves the shape information of the processed objects. Interesting morphological and topological features as well as volumetric ones were extracted from the skeleton and from the classified volumes, respectively. The extracted features enable the two populations of osteoarthritic and osteoporotic trabecular bone samples to be distinguished.

Compared to curve-based or surface-based skeletons, the hybrid skeleton better matches the geometry of the data. Each rod is represented by a one-voxel-thick arc and each plate is represented by a one-voxel-thick surface. The hybrid skeleton as well as the proposed classification algorithm introduce relevant parameters linked to the presence of plates in the trabecular bone data, showing that rods and plates contain independent information about trabeculae. The hybrid skeleton offers a new opportunity for precise studies of porous media such as trabecular bone.