Systems and methods are provided for generating a distance metric. An image manipulation application receives first and second input images. The image manipulation application generates first and second sets of points corresponding to respective edges of a first object in the first input image and a second object in the second input image. The image manipulation application determines costs of arcs connecting each point from the first set to each point of the second set based on point descriptors for each point of each arc. The image manipulation application determines a minimum set of costs between the first set and the second set that includes a cost of each arc connecting each point of the second set to a point in the first set. The image manipulation application obtains, based at least in part on the minimum set of costs, a distance metric for first and second input images.