Robust non-rigid registration of 2D and 3D graphs

We present a new approach to matching graphs embedded in ℝ
²
or ℝ
³
. Unlike earlier methods, our approach does not rely on the similarity of local appearance features, does not require an initial alignment, can handle partial matches, and can cope with non-linear deformations and topological differences. To handle arbitrary non-linear deformations, we represent them as Gaussian Processes. In the absence of appearance information, we iteratively establish correspondences between graph nodes, update the structure accordingly, and use the current mapping estimate to find the most likely correspondences that will be used in the next iteration. This makes the computation tractable. We demonstrate the effectiveness of our approach first on synthetic cases and then on angiography data, retinal fundus images, and microscopy image stacks acquired at very different resolutions.