Image Processing with numpy, scipy and matplotlibs in sage

In this post, I would like to show how to use  a few different features of numpy, scipy and matplotlibs to accomplish a few basic image processing tasks: some trivial image manipulation, segmentation, obtaining of structural information, etc.  An excellent way to show a good set of these techniques is by working through a complex project.  In this case, I have chosen the following:

Given a HAADF-STEM micrograph of a bronze-type Niobium Tungsten oxide (left), find a script that constructs a good approximation to its structural model (right).

Courtesy of ETH Zurich

For pedagogical purposes, I took the following approach to solving this problem:

1. Segmentation of the atoms by thresholding and morphological operations.
2. Connected component labeling to extract each single atom for posterior examination.
3. Computation of the centers of mass of each label identified as an atom. This presents us with a lattice of points in the plane that shows a first insight in the structural model of the oxide.
4. Computation of Delaunay triangulation and Voronoi diagram of the previous lattice of points. The combination of information from these two graphs will lead us to a decent (approximation to the actual) structural model of our sample.

Let us proceed in this direction: