We address the problem of detecting tree rings in microscopy images of shrub cross sections. This can be regarded as a special case of the instance segmentation task with several unique challenges such as the concentric circular ring shape of the objects and high precision requirements that result in inadequate performance of existing methods. We propose a new iterative method which we term Iterative Next Boundary Detection (INBD). It intuitively models the natural growth direction, starting from the center of the shrub cross section and detecting the next ring boundary in each iteration step. In our experiments, INBD shows superior performance to generic instance segmentation methods and is the only one with a built-in notion of chronological order. Our dataset and source code are available at http://github.com/alexander-g/INBD.