Sub-pixel Segmentation with the Image Foresting Transform

The Image Foresting Transform (IFT) is a framework for image partitioning, commonly used for interactive segmentation. Given an image where a subset of the image elements (seed-points) have been assigned user-defined labels, the IFT completes the labeling by computing minimal cost paths from all image elements to the seed-points. Each image element is then given the same label as the closest seed-point. In its original form, the IFT produces crisp segmentations, i.e., each image element is assigned the label of exactly one seed-point. Here, we propose a modified version of the IFT that computes region boundaries with sub-pixel precision by allowing mixed labels at region boundaries. We demonstrate that the proposed sub-pixel IFT allows properties of the segmented object to be measured with higher precision.