We propose a novel approach to reconstructing curvilinear tree structures evolving over time, such as road networks in 2D aerial images or neural structures in 3D microscopy stacks acquired in vivo. To enforce temporal consistency, we simultaneously process all images in a sequence, as opposed to reconstructing structures of interest in each image independently. We formulate the problem as a Quadratic Mixed Integer Program and demonstrate the additional robustness that comes from using all available visual clues at once, instead of working frame by frame. Furthermore, when the linear structures undergo local changes over time, our approach automatically detects them.

We present an efficient matching method for generalized geometric graphs. Such graphs consist of vertices in space connected by curves and can represent many real world structures such as road networks in remote sensing, or vessel networks in medical imaging. Graph matching can be used for very fast and possibly multimodal registration of images of these structures. We formulate the matching problem as a single player game solved using Monte Carlo Tree Search, which automatically balances exploring new possible matches and extending existing matches. Our method can handle partial matches, topological differences, geometrical distortion, does not use appearance information and does not require an initial alignment. Moreover, our method is very efficient-it can match graphs with thousands of nodes, which is an order of magnitude better than the best competing method, and the matching only takes a few seconds.

Many medical images contain graph-like geometrical structures such as blood vessels and neuronal networks. We present an algorithm for matching geometrical graphs, in order to quickly and robustly align such images. We use a sampling-based curve descriptor to prune dissimilar edges. The matching is modeled as a single-player game, growing the matching from a random initial correspondence. The coarse global solution is found using a Monte Carlo Tree Search and then refined locally. We show experimentally that our approach finds the correct matching in all tested datasets and is the fastest of all global methods.

We present a new approach for matching sets of branching curvilinear structures that form graphs embedded in R2 or R3 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 process regressions 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 with 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.

We propose an approach to reconstructing tree structures that evolve over time in 2D images and 3D image stacks such as neuronal axons or plant branches. Instead of reconstructing structures in each image independently, we do so for all images simultaneously to take advantage of temporal-consistency constraints. We show that this problem can be formulated as a Quadratic Mixed Integer Program and solved efficiently. The outcome of our approach is a framework that provides substantial improvements in reconstructions over traditional single time-instance formulations. Furthermore, an added benefit of our approach is the ability to automatically detect places where significant changes have occurred over time, which is challenging when considering large amounts of data.