Fast estimation of intrinsic volumes in 3D gray value images

The intrinsic volumes or their densities are versatile structural characteristics that can be estimated efficiently from digital image data, given a segmentation yielding the structural component of interest as foreground. In this contribution, Ohser's algorithm is generalized to operate on integer gray value images. The new algorithm derives the intrinsic volumes for each possible global gray value threshold in the image. It is highly efficient since it collects all neccesary structural information in a single pass through the image. The novel algorithm is well suited for computing the Minkowski functions of the parallel body if combined with the Euclidean distance transformation. This application scenario is demonstrated by means of computed tomography image data of polar ice samples. Moreover, the algorithm is applied to the problem of threshold selection in computed tomography images of material microstructures.