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 a novel approach to automated delineation of linear structures that form complex and potentially loopy networks. This is in contrast to earlier approaches that usually assume a tree topology for the networks. At the heart of our method is an Integer Programming formulation that allows us to find the global optimum of an objective function designed to allow cycles but penalize spurious junctions and early terminations. We demonstrate that it outperforms state-of-the-art techniques on a wide range of datasets.

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.

Although tracing linear structures in 2D images and 3D image stacks has received much attention over the years, full automation remains elusive. In this paper, we formulate the delineation problem as one of solving a Quadratic Mixed Integer Program (Q-MIP) in a graph of potential paths, which can be done optimally up to a very small tolerance. We further propose a novel approach to weighting these paths, which results in a Q-MIP solution that accurately matches the ground truth. We demonstrate that our approach outperforms a state-of-the-art technique based on the k-Minimum Spanning Tree formulation on a 2D dataset of aerial images and a 3D dataset of confocal microscopy stacks.

In this paper, we present a new approach for segmentation of tubular structures in 2D images providing minimal interaction. The main objective is to extract centerlines and boundaries of the vessels at the same time. The first step is to represent the trajectory of the vessel not as a 2D curve but to go up a dimension and represent the entire vessel as a 3D curve, where each point represents a 2D disc (two coordinates for the center point and one for the radius). The 2D vessel structure is then obtained as the envelope of the family of discs traversed along this 3D curve. Since this 2D shape is defined simply from a 3D curve, we are able to fully exploit minimal path techniques to obtain globally minimizing trajectories between two or more user supplied points using front propagation. The main contribution of our approach consists on building a multi-resolution metric that guides the propagation in this 3D space. We have chosen to exploit the tubular structure of the vessels one wants to extract to built an anisotropic metric giving higher speed on the center of the vessels and also when the minimal path tangent is coherent with the vessel's direction. This measure is required to be robust against the disturbance introduced by noise or adjacent structures with intensity similar to the target vessel. Indeed, if we examine the flux of the projected image gradient along a given direction on a circle of a given radius (or scale), one can prove that this flux is maximal at the center of the vessel, in its direction and with its exact radius. This approach is called optimally oriented flux. Combining anisotropic minimal paths techniques and optimally oriented flux we obtain promising results on noisy synthetic and real data.

In this paper, we present a new method for segmenting closed contours and surfaces. Our work builds on a variant of the Fast Marching algorithm. First, an initial point on the desired contour is chosen by the user. Next, new keypoints are detected automatically using a front propagation approach. We assume that the desired object has a closed boundary. This a-priori knowledge on the topology is used to devise a relevant criterion for stopping the keypoint detection and front propagation. The final domain visited by the front will yield a band surrounding the object of interest. Linking pairs of neighboring keypoints with minimal paths allows us to extract a closed contour from a 2D image. Detection of a variety of objects on real images is demonstrated. Using a similar same idea, we can extract networks of minimal paths from a 3D image called Geodesic Meshing. The proposed method is applied to 3D data with promising results.