Learning the dynamics and time-recursive boundary detection of deformable objects

We propose a principled framework for recursively segmenting deformable objects across a sequence of frames. We demonstrate the usefulness of this method on left ventricular segmentation across a cardiac cycle. The approach involves a technique for learning the system dynamics together with methods of particle-based smoothing as well as non-parametric belief propagation on a loopy graphical model capturing the temporal periodicity of the heart. The dynamic system state is a low-dimensional representation of the boundary, and the boundary estimation involves incorporating curve evolution into recursive state estimation. By formulating the problem as one of state estimation, the segmentation at each particular time is based not only on the data observed at that instant, but also on predictions based on past and future boundary estimates. Although the paper focuses on left ventricle segmentation, the method generalizes to temporally segmenting any deformable object

A variational model for data fitting on manifolds by minimizing the acceleration of a B\'ezier curve

We derive a variational model to fit a composite B\'ezier curve to a set of data points on a Riemannian manifold. The resulting curve is obtained in such a way that its mean squared acceleration is minimal in addition to remaining close the data points. We approximate the acceleration by discretizing the squared second order derivative along the curve. We derive a closed-form, numerically stable and efficient algorithm to compute the gradient of a B\'ezier curve on manifolds with respect to its control points, expressed as a concatenation of so-called adjoint Jacobi fields. Several examples illustrate the capabilites and validity of this approach both for interpolation and approximation. The examples also illustrate that the approach outperforms previous works tackling this problem

Fusion of Urban TanDEM-X raw DEMs using variational models

Recently, a new global Digital Elevation Model (DEM) with pixel spacing of 0.4 arcseconds and relative height accuracy finer than 2m for flat areas (slopes 20%) was created through the TanDEM-X mission. One important step of the chain of global DEM generation is to mosaic and fuse multiple raw DEM tiles to reach the target height accuracy. Currently, Weighted Averaging (WA) is applied as a fast and simple method for TanDEM-X raw DEM fusion in which the weights are computed from height error maps delivered from the Interferometric TanDEM-X Processor (ITP). However, evaluations show that WA is not the perfect DEM fusion method for urban areas especially in confrontation with edges such as building outlines. The main focus of this paper is to investigate more advanced variational approaches such as TV-L1 and Huber models. Furthermore, we also assess the performance of variational models for fusing raw DEMs produced from data takes with different baseline configurations and height of ambiguities. The results illustrate the high efficiency of variational models for TanDEM-X raw DEM fusion in comparison to WA. Using variational models could improve the DEM quality by up to 2m particularly in inner-city subsets.Comment: This is the pre-acceptance version, to read the final version, please go to IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing on IEEE Xplor

An Exactly Solvable Phase-Field Theory of Dislocation Dynamics, Strain Hardening and Hysteresis in Ductile Single Crystals

An exactly solvable phase-field theory of dislocation dynamics, strain hardening and hysteresis in ductile single crystals is developed. The theory accounts for: an arbitrary number and arrangement of dislocation lines over a slip plane; the long-range elastic interactions between dislocation lines; the core structure of the dislocations resulting from a piecewise quadratic Peierls potential; the interaction between the dislocations and an applied resolved shear stress field; and the irreversible interactions with short-range obstacles and lattice friction, resulting in hardening, path dependency and hysteresis. A chief advantage of the present theory is that it is analytically tractable, in the sense that the complexity of the calculations may be reduced, with the aid of closed form analytical solutions, to the determination of the value of the phase field at point-obstacle sites. In particular, no numerical grid is required in calculations. The phase-field representation enables complex geometrical and topological transitions in the dislocation ensemble, including dislocation loop nucleation, bow-out, pinching, and the formation of Orowan loops. The theory also permits the consideration of obstacles of varying strengths and dislocation line-energy anisotropy. The theory predicts a range of behaviors which are in qualitative agreement with observation, including: hardening and dislocation multiplication in single slip under monotonic loading; the Bauschinger effect under reverse loading; the fading memory effect, whereby reverse yielding gradually eliminates the influence of previous loading; the evolution of the dislocation density under cycling loading, leading to characteristic `butterfly' curves; and others