We have a binary raster image in which we consider the white blobs (connected components). We define a distance between two blobs to be the length of the shortest path between any two respective pixels (topological distance), or alternatively the shortest Euclidean distance between two pixels. In general the two definitions give similar results and any can be chosen for convenience.
Is there a known efficient algorithm to build the Minimum Spanning Tree of the blobs, where the edge weights are the distances ? By efficient we mean one that does not require the computation of all pairwise distances, nor a variable number of passes across the whole image.
(In the case of isolated points, the Euclidean Minimum Spanning Tree is known to be constructible in time $O(n\log(n))$ via the Voronoi diagram.)