The distance transform (DT) is a general operator forming the basis of many methods in computer vision and geometry, with great potential for practical applications. However, all the optimal algorithms for the computation of the exact Euclidean DT (EDT) were proposed only since the 1990s. In this work, state-of-theart sequential 2D EDT algorithms are reviewed and compared, in an effort to reach more solid conclusions regarding their differences in speed and their exactness. Six of the best algorithms were fully implemented and compared in practice.The work of R. Fabbri was supported by CNPq (200875/2004-3) and FAPESP (03/09834-0); O. M. Bruno acknowledges support from FAPESP (03/09834-0) and CNPq (303746/04-1); L. Da F. Costa thanks FAPESP (99/12765-2 and 05/00587-5) and CNPq (308231/03-1).

Interest point-based multiview 3D reconstruction and calibration methods have been very successful in select applications but are not applicable when an abundance of feature points are not available. They also lead to an unorganized point cloud reconstruction where the geometry of the scene is not explicit. The multiview stereo methods on the other hand yield dense surface geometry but require a highly controlled or calibrated setting. We propose and develop a novel framework for 3D reconstruction and calibration based on image curve content, whose output is a 3D curve sketch, an unorganized set of 3D curve fragments. This approach, which is meant to augment the previous approaches, results in a reconstruction of geometric curve structure which can serve as a scaffold on which surface patches can be potentially reconstructed. It is intented for the setting where a number of images are available with coarsely calibrated cameras. The approach operates in two stages. A reliable partial 3D curve sketch is first reconstructed and this is used to refine the cameras to yield a more complete 3D curve sketch in a second stage. A key advantage of this approach is the ability to integrate information across a large number of views. The results have been evaluated on a few datasets.

We present a new minimal problem for relative pose estimation mixing point features with lines incident at points observed in three views and its efficient homotopy continuation solver. We demonstrate the generality of the approach by analyzing and solving an additional problem with mixed point and line correspondences in three views. The minimal problems include correspondences of (i) three points and one line and (ii) three points and two lines through two of the points which is reported and analyzed here for the first time. These are difficult to solve, as they have 216 and -as shown here -312 solutions, but cover important practical situations when line and point features appear together, e.g., in urban scenes or when observing curves. We demonstrate that even such difficult problems can be solved robustly using a suitable homotopy continuation technique and we provide an implementation optimized for minimal problems that can be integrated into engineering applications. Our simulated and real experiments demonstrate our solvers in the camera geometry computation task in structure from motion. We show that new solvers allow for reconstructing challenging scenes where the standard two-view initialization of structure from motion fails.

This paper reports on stable (or invariant) properties of human interaction networks, with benchmarks derived from public email lists. Activity, recognized through messages sent, along time and topology were observed in snapshots in a timeline, and at different scales. Our analysis shows that activity is practically the same for all networks across timescales ranging from seconds to months. The principal components of the participants in the topological metrics space remain practically unchanged as different sets of messages are considered. The activity of participants follows the expected scale-free trace, thus yielding the hub, intermediary and peripheral classes of vertices by comparison against the Erd\"os-R\'enyi model. The relative sizes of these three sectors are essentially the same for all email lists and the same along time. Typically, $<15\%$ of the vertices are hubs, 15-45\% are intermediary and $>45\%$ are peripheral vertices. Similar results for the distribution of participants in the three sectors and for the relative importance of the topological metrics were obtained for 12 additional networks from Facebook, Twitter and ParticipaBR. These properties are consistent with the literature and may be general for human interaction networks, which has important implications for establishing a typology of participants based on quantitative criteria.Comment: See ancillary Supporting Information PDF file for further tables and figures. More information on code and further files can be found at https://github.com/ttm/articleStabilityInteractionNetwork