Local interpolation schemes for landmark-based image registration: a comparison

In this paper we focus, from a mathematical point of view, on properties and performances of some local interpolation schemes for landmark-based image registration. Precisely, we consider modified Shepard's interpolants, Wendland's functions, and Lobachevsky splines. They are quite unlike each other, but all of them are compactly supported and enjoy interesting theoretical and computational properties. In particular, we point out some unusual forms of the considered functions. Finally, detailed numerical comparisons are given, considering also Gaussians and thin plate splines, which are really globally supported but widely used in applications

Parametrising arbitrary galaxy morphologies: potentials and pitfalls

We demonstrate that morphological observables (e.g. steepness of the radial light profile, ellipticity, asymmetry) are intertwined and cannot be measured independently of each other. We present strong arguments in favour of model-based parametrisation schemes, namely reliability assessment, disentanglement of morphological observables, and PSF modelling. Furthermore, we demonstrate that estimates of the concentration and Sersic index obtained from the Zurich Structure & Morphology catalogue are in excellent agreement with theoretical predictions. We also demonstrate that the incautious use of the concentration index for classification purposes can cause a severe loss of the discriminative information contained in a given data sample. Moreover, we show that, for poorly resolved galaxies, concentration index and M_20 suffer from strong discontinuities, i.e. similar morphologies are not necessarily mapped to neighbouring points in the parameter space. This limits the reliability of these parameters for classification purposes. Two-dimensional Sersic profiles accounting for centroid and ellipticity are identified as the currently most reliable parametrisation scheme in the regime of intermediate signal-to-noise ratios and resolutions, where asymmetries and substructures do not play an important role. We argue that basis functions provide good parametrisation schemes in the regimes of high signal-to-noise ratios and resolutions. Concerning Sersic profiles, we show that scale radii cannot be compared directly for profiles of different Sersic indices. Furthermore, we show that parameter spaces are typically highly nonlinear. This implies that significant caution is required when distance-based classificaton methods are used.Comment: 18 pages, 13 figure

Weak-lensing shear estimates with general adaptive moments, and studies of bias by pixellation, PSF distortions, and noise

In weak gravitational lensing, weighted quadrupole moments of the brightness profile in galaxy images are a common way to estimate gravitational shear. We employ general adaptive moments (GLAM) to study causes of shear bias on a fundamental level and for a practical definition of an image ellipticity. The GLAM ellipticity has useful properties for any chosen weight profile: the weighted ellipticity is identical to that of isophotes of elliptical images, and in absence of noise and pixellation it is always an unbiased estimator of reduced shear. We show that moment-based techniques, adaptive or unweighted, are similar to a model-based approach in the sense that they can be seen as imperfect fit of an elliptical profile to the image. Due to residuals in the fit, moment-based estimates of ellipticities are prone to underfitting bias when inferred from observed images. The estimation is fundamentally limited mainly by pixellation which destroys information on the original, pre-seeing image. We give an optimized estimator for the pre-seeing GLAM ellipticity and quantify its bias for noise-free images. To deal with pixel noise, we consider a Bayesian approach where the posterior of the GLAM ellipticity can be inconsistent with the true ellipticity if we do not properly account for our ignorance about fit residuals. This underfitting bias is S/N-independent but changes with the pre-seeing brightness profile and the correlation or heterogeneity of pixel noise over the post-seeing image. Furthermore, when inferring a constant ellipticity or, more relevantly, constant shear from a source sample with a distribution of intrinsic properties (sizes, centroid positions, intrinsic shapes), an additional, now noise-dependent bias arises towards low S/N if incorrect priors for the intrinsic properties are used. We discuss the origin of this prior bias.Comment: 18 pages; 5 figures; accepted by A&A after major revision, especially of Sect. 3.3 that corrects the previous discussion on the bias by marginalizatio

Rotational 3D Printing of Sensor Devices using Reactive Ink Chemistries

This paper charts progress in three key areas of a project supported by both UK government and UK industry to manufacture novel sensor devices using rotary 3D printing technology and innovative ink chemistries; (1) the development of an STL file slicing algorithm that returns constant Z height 2D contour data at a resolution that matches the given print head setup, allowing digital images to be generated of the correct size without the need for scaling; (2) the development of image transformation algorithms which allow images to be printed at higher resolutions using tilted print heads and; (3) the formulation of multi part reaction inks which combine and react on the substrate to form solid material layers with a finite thickness. A Direct Light Projection (DLP) technique demonstrated the robustness of the slice data by constructing fine detailed three dimensional test pieces which were comparable to identical parts built in an identical way from slice data obtained using commercial software. Material systems currently under investigation include plaster, stiff polyamides and epoxy polymers and conductive metallic’s. Early experimental results show conductivities of silver approaching 1.42x105 Siemens/m.Mechanical Engineerin

From 3D Point Clouds to Pose-Normalised Depth Maps

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)

3-D facial expression representation using B-spline statistical shape model

Effective representation and recognition of human faces are essential in a number of applications including human-computer interaction (HCI), bio-metrics or video conferencing. This paper presents initial results obtained for a novel method of 3-D facial expressions representation based on the shape space vector of the statistical shape model. The statistical shape model is constructed based on the control points of the B-spline surfaces of the train-ing data set. The model fitting for the data is achieved by a modified iterative closest point (ICP) method with the surface deformations restricted to the es-timated shape space. The proposed method is fully automated and tested on the synthetic 3-D facial data with various facial expressions. Experimental results show that the proposed 3-D facial expression representation can be potentially used for practical applications

Circumstellar discs in Galactic centre clusters: Disc-bearing B-type stars in the Quintuplet and Arches clusters

We investigate the circumstellar disc fraction as determined from L-band excess observations of the young, massive Arches and Quintuplet clusters residing in the central molecular zone of the Milky Way. The Quintuplet cluster was searched for L-band excess sources for the first time. We find a total of 26 excess sources in the Quintuplet cluster and 21 in the Arches cluster, of which 13 are new detections. With the aid of proper motion membership samples, the disc fraction of the Quintuplet cluster was derived for the first time to be 4.0 +/- 0.7%. There is no evidence for a radially varying disc fraction in this cluster. In the case of the Arches cluster, a disc fraction of 9.2 +/- 1.2% approximately out to the cluster's predicted tidal radius, r < 1.5 pc, is observed. This excess fraction is consistent with our previously found disc fraction in the cluster in the radial range 0.3 < r < 0.8 pc. In both clusters, the host star mass range covers late A- to early B-type stars, 2 < M < 15 Msun, as derived from J-band photospheric magnitudes. We discuss the unexpected finding of dusty circumstellar discs in these UV intense environments in the context of primordial disc survival and formation scenarios of secondary discs. We consider the possibility that the L-band excess sources in the Arches and Quintuplet clusters could be the high-mass counterparts to T Tauri pre-transitional discs. As such a scenario requires a long pre-transitional disc lifetime in a UV intense environment, we suggest that mass transfer discs in binary systems are a likely formation mechanism for the B-star discs observed in these starburst clusters.Comment: 47 pages, 22 figures, accepted by A&

Theoretical Engineering and Satellite Comlink of a PTVD-SHAM System

This paper focuses on super helical memory system's design, 'Engineering, Architectural and Satellite Communications' as a theoretical approach of an invention-model to 'store time-data'. The current release entails three concepts: 1- an in-depth theoretical physics engineering of the chip including its, 2- architectural concept based on VLSI methods, and 3- the time-data versus data-time algorithm. The 'Parallel Time Varying & Data Super-helical Access Memory' (PTVD-SHAM), possesses a waterfall effect in its architecture dealing with the process of voltage output-switch into diverse logic and quantum states described as 'Boolean logic & image-logic', respectively. Quantum dot computational methods are explained by utilizing coiled carbon nanotubes (CCNTs) and CNT field effect transistors (CNFETs) in the chip's architecture. Quantum confinement, categorized quantum well substrate, and B-field flux involvements are discussed in theory. Multi-access of coherent sequences of 'qubit addressing' in any magnitude, gained as pre-defined, here e.g., the 'big O notation' asymptotically confined into singularity while possessing a magnitude of 'infinity' for the orientation of array displacement. Gaussian curvature of k(k<0) is debated in aim of specifying the 2D electron gas characteristics, data storage system for defining short and long time cycles for different CCNT diameters where space-time continuum is folded by chance for the particle. Precise pre/post data timing for, e.g., seismic waves before earthquake mantle-reach event occurrence, including time varying self-clocking devices in diverse geographic locations for radar systems is illustrated in the Subsections of the paper. The theoretical fabrication process, electromigration between chip's components is discussed as well.Comment: 50 pages, 10 figures (3 multi-figures), 2 tables. v.1: 1 postulate entailing hypothetical ideas, design and model on future technological advances of PTVD-SHAM. The results of the previous paper [arXiv:0707.1151v6], are extended in order to prove some introductory conjectures in theoretical engineering advanced to architectural analysi

Difference image photometry with bright variable backgrounds

Over the last two decades the Andromeda Galaxy (M31) has been something of a test-bed for methods aimed at obtaining accurate time-domain relative photometry within highly crowded fields. Difference imaging methods, originally pioneered towards M31, have evolved into sophisticated methods, such as the Optimal Image Subtraction (OIS) method of Alard & Lupton (1998), that today are most widely used to survey variable stars, transients and microlensing events in our own Galaxy. We show that modern difference image (DIA) algorithms such as OIS, whilst spectacularly successful towards the Milky Way bulge, may perform badly towards high surface brightness targets such as the M31 bulge. Poor results can occur in the presence of common systematics which add spurious flux contributions to images, such as internal reflections, scattered light or fringing. Using data from the Angstrom Project microlensing survey of the M31 bulge, we show that very good results are usually obtainable by first performing careful photometric alignment prior to using OIS to perform point-spread function (PSF) matching. This separation of background matching and PSF matching, a common feature of earlier M31 photometry techniques, allows us to take full advantage of the powerful PSF matching flexibility offered by OIS towards high surface brightness targets. We find that difference images produced this way have noise distributions close to Gaussian, showing significant improvement upon results achieved using OIS alone. We show that with this correction light-curves of variable stars and transients can be recovered to within ~10 arcseconds of the M31 nucleus. Our method is simple to implement and is quick enough to be incorporated within real-time DIA pipelines. (Abridged)Comment: 12 pages. Accepted for publication in MNRAS. Includes an expanded discussion of DIA testing and results, including additional lightcurve example