Abstract-We present a new approach for matching sets of branching curvilinear structures that form graphs embedded in R 2 or R 3 and may be subject to deformations. Unlike earlier methods, ours does not rely on local appearance similarity nor does require a good initial alignment. Furthermore, it can cope with non-linear deformations, topological differences, and partial graphs. To handle arbitrary non-linear deformations, we use Gaussian Processes to represent the geometrical mapping relating the two graphs. In the absence of appearance information, we iteratively establish correspondences between points, update the mapping accordingly, and use it to estimate where to find the most likely correspondences that will be used in the next step. To make the computation tractable for large graphs, the set of new potential matches considered at each iteration is not selected at random as in many RANSAC-based algorithms. Instead, we introduce a so-called Active Testing Search strategy that performs a priority search to favor the most likely matches and speed-up the process. 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.

The homography between pairs of images are typically computed from the correspondence of keypoints, which are established by using image descriptors. When these descriptors are not reliable, either because of repetitive patterns or large amounts of clutter, additional priors need to be considered. The Blind PnP algorithm makes use of geometric priors to guide the search for matches while computing camera pose. Inspired by this, we propose a novel approach for homography estimation that combines geometric priors with appearance priors of ambiguous descriptors. More specifically, for each point we retain its best candidates according to appearance. We then prune the set of potential matches by iteratively shrinking the regions of the image that are consistent with the geometric prior. We can then successfully compute homographies between pairs of images containing highly repetitive patterns and even under oblique viewing conditions.

We present a new approach to matching graphs embedded

We present a novel approach to simultaneously reconstruct the 3D structure of a non-rigid coronary tree and estimate point correspondences between an input X-ray image and a reference 3D shape. At the core of our approach lies an optimization scheme that iteratively fits a generative 3D model of increasing complexity and guides the matching process. As a result, and in contrast to existing approaches that assume rigidity or quasi-rigidity of the structure, our method is able to retrieve large non-linear deformations even when the input data is corrupted by the presence of noise and partial occlusions. We extensively evaluate our approach under synthetic and real data and demonstrate a remarkable improvement compared to state-of-the-art.

We present an algorithm for geometric matching of graphs embedded in 2D or 3D space. It is applicable for registering any graph-like structures appearing in biomedical images, such as blood vessels, pulmonary bronchi, nerve fibers, or dendritic arbors. Our approach does not rely on the similarity of local appearance features, so it is suitable for multimodal registration with a large difference in appearance. Unlike earlier methods, the algorithm uses edge shape, does not require an initial pose estimate, can handle partial matches, and can cope with nonlinear deformations and topological differences.The matching consists of two steps. First, we find an affine transform that roughly aligns the graphs by exploring the set of all consistent correspondences between the nodes. This can be done at an acceptably low computational expense by using parameter uncertainties for pruning, backtracking as needed. Parameter uncertainties are updated in a Kalman-like scheme with each match.In the second step we allow for a nonlinear part of the deformation, modeled as a Gaussian Process. Short sequences of edges are grouped into superedges, which are then matched between graphs. This allows for topological differences. A maximum consistent set of superedge matches is found using a dedicated branch-and-bound solver, which is over 100 times faster than a standard linear programming approach. Geometrical and topological consistency of candidate matches is determined in a fast hierarchical manner.We demonstrate the effectiveness of our technique at registering angiography and retinal fundus images, as well as neural image stacks.