Local scale measure from the topographic map and application to remote sensing images

In this paper, we propose a spatially accurate definition of scale for images. The proposed definition of local scale relies on the hierarchical structure of the topographic map, the set of all level lines of an image. Namely, a connected component of a level line is associated with each point of the image and the scale at this point is then computed from the corresponding shape. Level lines are selected under the assumption that the blur is uniform over the image, a realistic assumption for satellite images. First, we discuss the links between the proposed approach and recent scale definitions making use of the total variation flow or the Rudin-Osher-Fatemi model. This comparison sheds some light on the relationships between morphological and variational approaches to scale definitions. Then we perform several experiments on synthetic and satellite images and numerically compare our local scale definition with results using the linear scale space, variational, or morphological approaches. These experiments suggest that the proposed method enables a robust and spatially accurate computation of local scales, without the need for complex parameter tuning.