Abstract-Multi-object tracking can be achieved by detecting objects in individual frames and then linking detections across frames. Such an approach can be made very robust to the occasional detection failure: If an object is not detected in a frame but is in previous and following ones, a correct trajectory will nevertheless be produced. By contrast, a false-positive detection in a few frames will be ignored. However, when dealing with a multiple target problem, the linking step results in a difficult optimization problem in the space of all possible families of trajectories. This is usually dealt with by sampling or greedy search based on variants of Dynamic Programming, which can easily miss the global optimum. In this paper, we show that reformulating that step as a constrained flow optimization results in a convex problem. We take advantage of its particular structure to solve it using the k-shortest paths algorithm, which is very fast. This new approach is far simpler formally and algorithmically than existing techniques and lets us demonstrate excellent performance in two very different contexts.

We present a novel probabilistic approach to fully automated delineation of tree structures in noisy 2D images and 3D image stacks. Unlike earlier methods that rely mostly on local evidence, ours builds a set of candidate trees over many different subsets of points likely to belong to the optimal tree and then chooses the best one according to a global objective function that combines image evidence with geometric priors. Since the best tree does not necessarily span all the points, the algorithm is able to eliminate false detections while retaining the correct tree topology. Manually annotated brightfield micrographs, retinal scans and the DIADEM challenge datasets are used to evaluate the performance of our method. We used the DIADEM metric to quantitatively evaluate the topological accuracy of the reconstructions and showed that the use of the geometric regularization yields a substantial improvement.

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 stateof-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.

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.

Abstract-Finding the centerline and estimating the radius of linear structures is a critical first step in many applications, ranging from road delineation in 2D aerial images to modeling blood vessels, lung bronchi, and dendritic arbors in 3D biomedical image stacks. Existing techniques rely either on filters designed to respond to ideal cylindrical structures or on classification techniques. The former tend to become unreliable when the linear structures are very irregular while the latter often has difficulties distinguishing centerline locations from neighboring ones, thus losing accuracy. We solve this problem by reformulating centerline detection in terms of a regression problem. We first train regressors to return the distances to the closest centerline in scale-space, and we apply them to the input images or volumes. The centerlines and the corresponding scale then correspond to the regressors local maxima, which can be easily identified. We show that our method outperforms state-of-the-art techniques for various 2D and 3D datasets. Moreover, our approach is very generic and also performs well on contour detection. We show an improvement above recent contour detection algorithms on the BSDS500 dataset.