Image Segmentation Using Active Contours Driven by the Bhattacharyya Gradient Flow

©2007 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or distribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.DOI: 10.1109/TIP.2007.908073This paper addresses the problem of image segmentation by means of active contours, whose evolution is driven by the gradient flow derived froman energy functional that is based on the Bhattacharyya distance. In particular, given the values of a photometric variable (or of a set thereof), which is to be used for classifying the image pixels, the active contours are designed to converge to the shape that results in maximal discrepancy between the empirical distributions of the photometric variable inside and outside of the contours. The above discrepancy is measured by means of the Bhattacharyya distance that proves to be an extremely useful tool for solving the problem at hand. The proposed methodology can be viewed as a generalization of the segmentation methods, in which active contours maximize the difference between a finite number of empirical moments of the "inside" and "outside" distributions. Furthermore, it is shown that the proposed methodology is very versatile and flexible in the sense that it allows one to easily accommodate a diversity of the image features based on which the segmentation should be performed. As an additional contribution, a method for automatically adjusting the smoothness properties of the empirical distributions is proposed. Such a procedure is crucial in situations when the number of data samples (supporting a certain segmentation class) varies considerably in the course of the evolution of the active contour. In this case, the smoothness properties of the empirical distributions have to be properly adjusted to avoid either over- or underestimation artifacts. Finally, a number of relevant segmentation results are demonstrated and some further research directions are discussed

The Storm-Track Response to Idealized SST Perturbations in an Aquaplanet GCM

The tropospheric response to midlatitude SST anomalies has been investigated through a series of aquaplanet simulations using a high-resolution version of the Hadley Centre atmosphere model (HadAM3) under perpetual equinox conditions. Model integrations show that increases in the midlatitude SST gradient generally lead to stronger storm tracks that are shifted slightly poleward, consistent with changes in the lower-tropospheric baroclinicity. The large-scale atmospheric response is, however, highly sensitive to the position of the SST gradient anomaly relative to that of the subtropical jet in the unperturbed atmosphere. In particular, when SST gradients are increased very close to the subtropical jet, then the Hadley cell and subtropical jet is strengthened while the storm track and eddy-driven jet are shifted equatorward. Conversely, if the subtropical SST gradients are reduced and the midlatitude gradients increased, then the storm track shows a strong poleward shift and a well-separated eddy-driven jet is produced. The sign of the SST anomaly is shown to play a secondary role in determining the overall tropospheric response. These findings are used to provide a new and consistent interpretation of some previous GCM studies concerning the atmospheric response to midlatitude SST anomalies

Estimation of vector fields in unconstrained and inequality constrained variational problems for segmentation and registration

Vector fields arise in many problems of computer vision, particularly in non-rigid registration. In this paper, we develop coupled partial differential equations (PDEs) to estimate vector fields that define the deformation between objects, and the contour or surface that defines the segmentation of the objects as well.We also explore the utility of inequality constraints applied to variational problems in vision such as estimation of deformation fields in non-rigid registration and tracking. To solve inequality constrained vector field estimation problems, we apply tools from the Kuhn-Tucker theorem in optimization theory. Our technique differs from recently popular joint segmentation and registration algorithms, particularly in its coupled set of PDEs derived from the same set of energy terms for registration and segmentation. We present both the theory and results that demonstrate our approach

What is the relationship between photospheric flow fields and solar flares?

We estimated photospheric velocities by separately applying the Fourier Local Correlation Tracking (FLCT) and Differential Affine Velocity Estimator (DAVE) methods to 2708 co-registered pairs of SOHO/MDI magnetograms, with nominal 96-minute cadence and ~2" pixels, from 46 active regions (ARs) from 1996-1998 over the time interval t45 when each AR was within 45^o of disk center. For each magnetogram pair, we computed the average estimated radial magnetic field, B; and each tracking method produced an independently estimated flow field, u. We then quantitatively characterized these magnetic and flow fields by computing several extensive and intensive properties of each; extensive properties scale with AR size, while intensive properties do not depend directly on AR size. Intensive flow properties included moments of speeds, horizontal divergences, and radial curls; extensive flow properties included sums of these properties over each AR, and a crude proxy for the ideal Poynting flux, the total |u| B^2. Several magnetic quantities were also computed, including: total unsigned flux; a measure of the amount of unsigned flux near strong-field polarity inversion lines, R; and the total B^2. Next, using correlation and discriminant analysis, we investigated the associations between these properties and flares from the GOES flare catalog, when averaged over both t45 and shorter time windows, of 6 and 24 hours. We found R and total |u| B^2 to be most strongly associated with flares; no intensive flow properties were strongly associated with flares.Comment: 57 pages, 13 figures; revised content; added URL to manuscript with higher-quality image

Implicit High-Order Flux Reconstruction Solver for High-Speed Compressible Flows

The present paper addresses the development and implementation of the first high-order Flux Reconstruction (FR) solver for high-speed flows within the open-source COOLFluiD (Computational Object-Oriented Libraries for Fluid Dynamics) platform. The resulting solver is fully implicit and able to simulate compressible flow problems governed by either the Euler or the Navier-Stokes equations in two and three dimensions. Furthermore, it can run in parallel on multiple CPU-cores and is designed to handle unstructured grids consisting of both straight and curved edged quadrilateral or hexahedral elements. While most of the implementation relies on state-of-the-art FR algorithms, an improved and more case-independent shock capturing scheme has been developed in order to tackle the first viscous hypersonic simulations using the FR method. Extensive verification of the FR solver has been performed through the use of reproducible benchmark test cases with flow speeds ranging from subsonic to hypersonic, up to Mach 17.6. The obtained results have been favorably compared to those available in literature. Furthermore, so-called super-accuracy is retrieved for certain cases when solving the Euler equations. The strengths of the FR solver in terms of computational accuracy per degree of freedom are also illustrated. Finally, the influence of the characterizing parameters of the FR method as well as the the influence of the novel shock capturing scheme on the accuracy of the developed solver is discussed

Astrophysical turbulence modeling

The role of turbulence in various astrophysical settings is reviewed. Among the differences to laboratory and atmospheric turbulence we highlight the ubiquitous presence of magnetic fields that are generally produced and maintained by dynamo action. The extreme temperature and density contrasts and stratifications are emphasized in connection with turbulence in the interstellar medium and in stars with outer convection zones, respectively. In many cases turbulence plays an essential role in facilitating enhanced transport of mass, momentum, energy, and magnetic fields in terms of the corresponding coarse-grained mean fields. Those transport properties are usually strongly modified by anisotropies and often completely new effects emerge in such a description that have no correspondence in terms of the original (non coarse-grained) fields.Comment: 88 pages, 26 figures, published in Reports on Progress in Physic

The dynamical balance, transport and circulation of the Antarctic Circumpolar Current

The physical ingredients of the ACC circulation are reviewed. A picture of thecirculation is sketched by means of recent observations of the WOCE decade. Wepresent and discuss the role of forcing functions (wind stress, surfacebuoyancy flux) in the balance of the (quasi)-zonal flow, the meridionalcirculation and their relation to the ACC transport. Emphasis will be on theinterrelation of the zonal momentum balance and the meridional circulation, theimportance of diapycnal mixing and eddy processes. Finally, new model conceptsare described: a model of the ACC transport dependence on wind stress andbuoyancy flux, based on linear wave theory; and a model of the meridionaloverturning of the Southern Ocean, based on zonally averaged dynamics with eddyparameterization

Directional Geodesic Active Contours

We present a non-conformal metric that generalizes the geodesic active contours approach for image segmentation. The new metric is obtained by adding to the Euclidean metric an additional term that penalizes the misalignment of the curve with the image gradient and multiplying the resulting metric by a conformal factor that depends on the edge intensity. In this way, a closer fitting to the edge direction results. The provided experimental results address the computation of the geodesics of the new metric by applying a gradient descent to externally provided curves. The good performance of the proposed techniques is demonstrated in comparison with other active contours methods