Registration algorithm: four basic blocks

Each registration algorithm contains the following four basic blocks of operations: (i) spatial transformation, (ii) similarity measure, (iii) interpolation, (iv) optimization. The registration usually runs in a cycle where each subsequent interaction makes us try to approach an optimal spatial transformation which will result in perfect alignment of the reference and floating images. Such improved registration requires some objective measurement that is determined by a suitable similarity measure.

The above description of the iterative algorithm shows clearly the implication of the blocks: similarity measure, spatial transformation. What about the other two? What do you think is the purpose of the interpolation block in the registration algorithm? And do you know any optimization methods, e.g. from numerical mathematics?

But enough for the theory. Let’s have a look at a few examples of the use of image registration.