4. Geodetic operations and reconstruction

When the result of an operation must be constrained to remain within a certain region of space, or below (or above) a certain function, we speak of geodesic or conditional operations. These operations are based on the notion of geodesic distance: the geodesic distanced _X conditionally to a set X between two points of X is the length of the shortest path joining these two points while remaining in the set. If X is closed, there is a geodesic arc for any pair of points in X, and this is unique if X is simply connected. The geodesic distance is equal to the Euclidean distance if and only if X is convex. Let's now consider structuring elements that are balls of the geodesic distance: