Reconstructing Evolving Tree Structures in Time Lapse Sequences by Enforcing Time-Consistency.

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.

Network Flow Integer Programming to Track Elliptical Cells in Time-Lapse Sequences.

We propose a novel approach to automatically tracking elliptical cell populations in time-lapse image sequences. Given an initial segmentation, we account for partial occlusions and overlaps by generating an over-complete set of competing detection hypotheses. To this end, we fit ellipses to portions of the initial regions and build a hierarchy of ellipses, which are then treated as cell candidates. We then select temporally consistent ones by solving to optimality an integer program with only one type of flow variables. This eliminates the need for heuristics to handle missed detections due to partial occlusions and complex morphology. We demonstrate the effectiveness of our approach on a range of challenging sequences consisting of clumped cells and show that it outperforms state-of-the-art techniques.

Multiscale Centerline Detection.

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.

Simultaneous segmentation and anatomical labeling of the cerebral vasculature.

We present a novel algorithm for the simultaneous segmentation and anatomical labeling of the cerebral vasculature. Unlike existing approaches that first attempt to obtain a good segmentation and then perform labeling, we optimize for both by simultaneously taking into account the image evidence and the prior knowledge about the geometry and connectivity of the vasculature. This is achieved by first constructing an overcomplete graph capturing the vasculature, and then selecting and labeling the subset of edges that most likely represents the true vasculature. We formulate the latter problem as an Integer Program (IP), which can be solved efficiently to provable optimality. We evaluate our approach on a publicly available dataset of 50 cerebral MRA images, and demonstrate that it compares favorably against state-of-the-art methods.

Reconstructing Curvilinear Networks Using Path Classifiers and Integer Programming.

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.

Tracking Interacting Objects Using Intertwined Flows.

In this paper, we show that tracking different kinds of interacting objects can be formulated as a network-flow mixed integer program. This is made possible by tracking all objects simultaneously using intertwined flow variables and expressing the fact that one object can appear or disappear at locations where another is in terms of linear flow constraints. Our proposed method is able to track invisible objects whose only evidence is the presence of other objects that contain them. Furthermore, our tracklet-based implementation yields real-time tracking performance. We demonstrate the power of our approach on scenes involving cars and pedestrians, bags being carried and dropped by people, and balls being passed from one player to the next in team sports. In particular, we show that by estimating jointly and globally the trajectories of different types of objects, the presence of the ones which were not initially detected based solely on image evidence can be inferred from the detections of the others.

Simultaneous segmentation and anatomical labeling of the cerebral vasculature.

We present a novel algorithm for the simultaneous segmentation and anatomical labeling of the cerebral vasculature. The method first constructs an overcomplete graph capturing the vasculature. It then selects and labels the subset of edges that most likely represents the true vasculature. Unlike existing approaches that first attempt to obtain a good segmentation and then perform labeling, we jointly optimize for both by simultaneously taking into account the image evidence and the prior knowledge about the geometry and connectivity of the vasculature. This results in an Integer Program (IP), which we solve optimally using a branch-and-cut algorithm. We evaluate our approach on a public dataset of 50 cerebral MRA images, and demonstrate that it compares favorably against state-of-the-art methods.

Automated reconstruction of dendritic and axonal trees by global optimization with geometric priors.

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.

Multiple Object Tracking Using K-Shortest Paths Optimization.

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.

Reconstructing geometrically consistent tree structures from noisy images.

We present a novel approach to fully automated reconstruction of tree structures in noisy 2D images. Unlike in earlier approaches, we explicitly handle crossovers and bifurcation points, and impose geometric constraints while optimizing a global cost function. We use manually annotated retinal scans to evaluate our method and demonstrate that it brings about a very substantial improvement.