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.

Many recent delineation techniques owe much of their increased effectiveness to path classification algorithms that make it possible to distinguish promising paths from others. The downside of this development is that they require annotated training data, which is tedious to produce. In this paper, we propose an Active Learning approach that considerably speeds up the annotation process. Unlike standard ones, it takes advantage of the specificities of the delineation problem. It operates on a graph and can reduce the training set size by up to 80% without compromising the reconstruction quality. We will show that our approach outperforms conventional ones on various biomedical and natural image datasets, thus showing that it is broadly applicable.

We propose a novel approach to automated delineation of curvilinear structures that form complex and potentially loopy networks. By representing the image data as a graph of potential paths, we first show how to weight these paths using discriminatively-trained classifiers that are both robust and generic enough to be applied to very different imaging modalities. We then present an Integer Programming approach to finding the optimal subset of paths, subject to structural and topological constraints that eliminate implausible solutions. Unlike earlier approaches that assume a tree topology for the networks, ours explicitly models the fact that the networks may contain loops, and can reconstruct both cyclic and acyclic ones. We demonstrate the effectiveness of our approach on a variety of challenging datasets including aerial images of road networks and micrographs of neural arbors, and show that it outperforms state-of-the-art techniques.

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.

We propose a new approach to detecting irregular curvilinear structures in noisy image stacks. In contrast to earlier approaches that rely on circular models of the cross-sections, ours allows for the arbitrarily-shaped ones that are prevalent in biological imagery. This is achieved by maximizing the image gradient flux along multiple directions and radii, instead of only two with a unique radius as is usually done. This yields a more complex optimization problem for which we propose a computationally efficient solution. We demonstrate the effectiveness of our approach on a wide range of challenging gray scale and color datasets and show that it outperforms existing techniques, especially on very irregular structures.

We present a new approach to matching graphs embedded in ℝ2or ℝ3. 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.