Volume Tensor Estimation Using a Virtual Line Grid: Study of a Developing Pheasant Brain

The volume tensor provides a robust estimate of the shape and orientation of an object in space. In this paper, we introduce Fakir method for estimating the tensor of an object in 3D data set based on the intersections of objects boundary with virtual lines. We calculate the precision of shape estimates by predicting the variance of estimators of integrals based on systematic sampling. To demonstrate the ability of the Fakir method, we measure changes in shape and orientation of compartments in the pheasant brain during development.