Estimation of Separating Planes between Touching 3D Objects Using Power Watershed

The problem of separating touching or overlapping objects is classical in imaging. Many solutions have been proposed in 2D. While similar, the problem in 3D has differentiating features: apparent overlap due to projection effects does not exist, but real or apparent interpenetration can occur only due to either physical particle fusion or partial volume effects. Often the ability to separate objects logically is sufficient, however sometimes finding the orientation of tangent separating plane is useful. In this article, we propose a method based on power watershed for separating 3D touching objects and estimate a precise separating plane. Power watershed is used in two steps, first to obtain individual object identification, and in a second step to allow sub-voxel accuracy in the plane fitting procedure. We show that our approach is much more precise than a simple segmentation. We illustrate this in an application involving the shearing of a sample of sand grains imaged in various configurations by micro-CT tomography. Our technique measures the orientation of the contacts between grains, a quantity that is explicitly used in soil mechanics modeling, but which has up until now been difficult to measure from experiments.