2,412 research outputs found

    From 3D Point Clouds to Pose-Normalised Depth Maps

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    We consider the problem of generating either pairwise-aligned or pose-normalised depth maps from noisy 3D point clouds in a relatively unrestricted poses. Our system is deployed in a 3D face alignment application and consists of the following four stages: (i) data filtering, (ii) nose tip identification and sub-vertex localisation, (iii) computation of the (relative) face orientation, (iv) generation of either a pose aligned or a pose normalised depth map. We generate an implicit radial basis function (RBF) model of the facial surface and this is employed within all four stages of the process. For example, in stage (ii), construction of novel invariant features is based on sampling this RBF over a set of concentric spheres to give a spherically-sampled RBF (SSR) shape histogram. In stage (iii), a second novel descriptor, called an isoradius contour curvature signal, is defined, which allows rotational alignment to be determined using a simple process of 1D correlation. We test our system on both the University of York (UoY) 3D face dataset and the Face Recognition Grand Challenge (FRGC) 3D data. For the more challenging UoY data, our SSR descriptors significantly outperform three variants of spin images, successfully identifying nose vertices at a rate of 99.6%. Nose localisation performance on the higher quality FRGC data, which has only small pose variations, is 99.9%. Our best system successfully normalises the pose of 3D faces at rates of 99.1% (UoY data) and 99.6% (FRGC data)

    On the density of polyharmonic splines

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    This article treats the question of fundamentality of the translates of a polyharmonic spline kernel (also known as a surface spline) in the space of continuous functions on a compact set \Omega\subset \RR^d when the translates are restricted to Ω\Omega. Fundamentality is not hard to demonstrate when a low degree polynomial may be added or when translates are permitted to lie outside of Ω\Omega; the challenge of this problem stems from the presence of the boundary, for which all successful approximation schemes require an added polynomial. When Ω\Omega is the unit ball, we demonstrate that translates of polyharmonic splines are fundamental by considering two related problems: the fundamentality in the space of functions vanishing at the boundary and fundamentality of the restricted kernel in the space of continuous function on the sphere. This gives rise to a new approximation scheme composed of two parts: one which approximates purely on ∂Ω\partial \Omega, and a second part involving a shift invariant approximant of a function vanishing outside of a neighborhood Ω\Omega.Comment: 17 page

    Highly Localized RBF Lagrange Functions for Finite Difference Methods on Spheres

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    The aim of this paper is to show how rapidly decaying RBF Lagrange functions on the spheres can be used to create effective, stable finite difference methods based on radial basis functions (RBF-FD). For certain classes of PDEs this approach leads to precise convergence estimates for stencils which grow moderately with increasing discretization fineness

    Measurement of Amplitude and Phase Pupil Variation for EUV Lithography Systems

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    Aberration control and characterization in a state of the art photolithographic lens have the tightest tolerances of any optical system. This is especially true in next generation extreme ultraviolet lithography systems with estimates for the wavefront tolerance below 500 pm RMS. These systems use radiation at a wavelength of 13.5 nm. No materials sufficiently refract this radiation, so reflective lens designs must be used. The mirrors are constructed as Bragg reflectors and much of the intense power of the source is ultimately distributed through the system as heat with each reflection. Moreover, the angle dependent reflection of these mirrors can also lead to amplitude asymmetries across the pupil. While interferometric techniques are the de-facto standard of wavefront analysis, they require the use of additional optics and are therefore difficult to implement during system use. Moreover, interferometric techniques cannot measure amplitude pupil variation. In this work both the pupil amplitude and phase variation of several EUV lithography systems will be measured using images of binary targets formed by each system. Using the systems’ own images to monitor its wavefront has the benefit of providing an aberration monitor during system use. Models will be constructed between wavefront variation and a space-domain basis in which the effects of aberrations are separable. This allows both the amplitude and pupil variation to be rapidly extracted from these systems. Finally, the theory of anamorphic primary aberrations will be developed and the image-based method will be extended to these types of systems
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