  We present a novel discrete optimization-based approach to generate
downsampled versions of binary images that are guaranteed to have the same
topology as the original, measured by the zeroth and first Betti numbers of the
black regions, while having good similarity to the original image as measured
by IoU and Dice scores. To our best knowledge, all existing binary image
downsampling methods do not have such topology-preserving guarantees. We also
implemented a baseline morphological operation (dilation)-based approach that
always generates topologically correct results. However, we found the
similarity scores to be much worse. We demonstrate several applications of our
approach. First, generating smaller versions of medical image segmentation
masks for easier human inspection. Second, improving the efficiency of binary
image operations, including persistent homology computation and shortest path
computation, by substituting the original images with smaller ones. In
particular, the latter is a novel application that is made feasible only by the
full topology-preservation guarantee of our method.
