  We propose a novel, connectivity-oriented loss function for training deep
convolutional networks to reconstruct network-like structures, like roads and
irrigation canals, from aerial images. The main idea behind our loss is to
express the connectivity of roads, or canals, in terms of disconnections that
they create between background regions of the image. In simple terms, a gap in
the predicted road causes two background regions, that lie on the opposite
sides of a ground truth road, to touch in prediction. Our loss function is
designed to prevent such unwanted connections between background regions, and
therefore close the gaps in predicted roads. It also prevents predicting false
positive roads and canals by penalizing unwarranted disconnections of
background regions. In order to capture even short, dead-ending road segments,
we evaluate the loss in small image crops. We show, in experiments on two
standard road benchmarks and a new data set of irrigation canals, that convnets
trained with our loss function recover road connectivity so well, that it
suffices to skeletonize their output to produce state of the art maps. A
distinct advantage of our approach is that the loss can be plugged in to any
existing training setup without further modifications.
