We present a parallel implementation of a statistical shape model registration to 3D ultrasound images of the lumbar vertebrae (L2-L4). Covariance Matrix Adaptation Evolution Strategy optimization technique, along with Linear Correlation of Linear Combination similarity metric have been used, to improve the robustness and capture range of the registration approach. Instantiation and ultrasound ...

Let X be a metric space and let μ be a probability measure on it. Consider a Lipschitz map T : X → Rn, with Lipschitz constant ≤ 1. Then one can ask whether the image TX can have large projections on many directions. For a large class of spaces X, we show that there are directions φ ∈ Sn−1 on which the projection of the image TX is small on the average (in L2(μ)), with bounds depending on the d...

We prove a removal of singularities result for Bach-flat metrics in dimension 4 under the assumption of bounded L2-norm of curvature, bounded Sobolev constant and a volume growth bound. This result extends the removal of singularities result for special classes of Bach-flat metrics obtained by Tian and Viaclovsby. For the proof we emulate Cheeger and Tian and analyze the decay rates of solution...

Riesz potentials of fractal measures μ in metric spaces and their inverses are introduced . They define self–adjoint operators in the Hilbert space L2(μ) and the former are shown to be compact. In the Euclidean case the corresponding spectral asymptotics are derived with Besov space methods. The inverses of the Riesz potentials are fractal pseudodifferential operators. For the order two operato...

The field of computational photography, and in particular the design and implementation of coded apertures, has yielded impressive results in the last years. In this paper we introduce perceptually-optimized coded apertures for defocused deblurring. We obtain near-optimal apertures by means of optimization, with a novel evaluation function that includes two existing image quality perceptual met...

This is a sequel to our paper (Lett. Math. Phys. (2000)), triggered from a question posed by Marcel, Ovsienko, and Roger in their paper (1997). In this paper, we show that the multicomponent (or vector) Ito equation, modified dispersive water wave equation, and modified dispersionless long wave equation are the geodesic flows with respect to an L2 metric on the semidirect product space ̂ Diffs(S...

This paper shows that when the Riemannian metric on a contact manifold is blown up along the direction orthogonal to the contact distribution, the corresponding harmonic forms rescaled and normalized in the L2-norms will converge to Rumin’s harmonic forms. This proves a conjecture in Gromov [11]. This result can also be reformulated in terms of spectral sequences, after Forman, Mazzeo-Melrose. ...

We study the Schrödinger operator −∆ − αδ(x − Γ) in L2(R3) with a δ interaction supported by an infinite non-planar surface Γ which is smooth, admits a global normal parameterization with a uniformly elliptic metric. We show that if Γ is asymptotically planar in a suitable sense and α > 0 is sufficiently large this operator has a non-empty discrete spectrum and derive an asymptotic expansion of...

Object correlation and maneuver detection are persistent problems in space surveillance and space object catalog maintenance. This paper demonstrates the utility of using quadratic trajectory control cost, an analog to the trajectory L2-norm in control, as a distance metric with which to both correlate object tracks and detect maneuvers using Uncorrelated Tracks (UCTs), real-time sensor measure...

Building on work of Dubickas and Smyth regarding the metric Mahler measure and the authors regarding extremal norms associated to the Mahler measure, the authors introduce a new set of norms associated to the Mahler measure of algebraic numbers which allow for an equivalent reformulation of problems like the Lehmer problem and the Schinzel-Zassenhaus conjecture on a single spectrum. We present ...