Sources of contamination to weak lensing tomography: redshift-dependent shear measurement bias

The current methods available to estimate gravitational shear from astronomical images of galaxies introduce systematic errors which can affect the accuracy of weak lensing cosmological constraints. We study the impact of KSB shape measurement bias on the cosmological interpretation of tomographic two-point weak lensing shear statistics. We use a set of realistic image simulations produced by the STEP collaboration to derive shape measurement bias as a function of redshift. We define biased two-point weak lensing statistics and perform a likelihood analysis for two fiducial surveys. We present a derivation of the covariance matrix for tomography in real space and a fitting formula to calibrate it for non-Gaussianity. We find the biased aperture mass dispersion is reduced by ~20% at redshift ~1, and has a shallower scaling with redshift. This effect, if ignored in data analyses, biases sigma_8 and w_0 estimates by a few percent. The power of tomography is significantly reduced when marginalising over a range of realistic shape measurement biases. For a CFHTLS-Wide-like survey, [Omega_m, sigma_8] confidence regions are degraded by a factor of 2, whereas for a KIDS-like survey the factor is 3.5. Our results are strictly valid only for KSB methods but they demonstrate the need to marginalise over a redshift-dependent shape measurement bias in all future cosmological analyses.Comment: 13 pages, 8 figures. Submitted MNRA

Statistical Shape Modeling Using Morphological Representations

ISBN : 978-1-4244-7542-1International audienceThe aim of this paper is to propose tools for statistical analysis of shape families using morphological operators. Given a series of shape families (or shape categories), the approach consists in empirically computing shape statistics (i.e., mean shape and variance of shape) and then to use simple algorithms for random shape generation, for empirical shape confidence boundaries computation and for shape classification using Bayes rules. The main required ingredients for the present methods are well known in image processing, such as watershed on distance functions or log-polar transformation. Performance of classification is presented in a well-known shape database

L1TV computes the flat norm for boundaries

We show that the recently introduced L1TV functional can be used to explicitly compute the flat norm for co-dimension one boundaries. While this observation alone is very useful, other important implications for image analysis and shape statistics include a method for denoising sets which are not boundaries or which have higher co-dimension and the fact that using the flat norm to compute distances not only gives a distance, but also an informative decomposition of the distance. This decomposition is made to depend on scale using the "flat norm with scale" which we define in direct analogy to the L1TV functional. We illustrate the results and implications with examples and figures

High-resolution computed tomography reconstructions of invertebrate burrow systems

The architecture of biogenic structures can be highly influential in determining species contributions to major soil and sediment processes, but detailed 3-D characterisations are rare and descriptors of form and complexity are lacking. Here we provide replicate high-resolution micro-focus computed tomography (μ-CT) data for the complete burrow systems of three co-occurring, but functionally contrasting, sediment-dwelling inter-tidal invertebrates assembled alone, and in combination, in representative model aquaria. These data (≤2,000 raw image slices aquarium−1, isotropic voxel resolution, 81 μm) provide reference models that can be used for the development of novel structural analysis routines that will be of value within the fields of ecology, pedology, geomorphology, palaeobiology, ichnology and mechanical engineering. We also envisage opportunity for those investigating transport networks, vascular systems, plant rooting systems, neuron connectivity patterns, or those developing image analysis or statistics related to pattern or shape recognition. The dataset will allow investigators to develop or test novel methodology and ideas without the need to generate a complete three-dimensional computation of exemplar architecture

Optimal designs for three-dimensional shape analysis with spherical harmonic descriptors

We determine optimal designs for some regression models which are frequently used for describing three-dimensional shapes. These models are based on a Fourier expansion of a function defined on the unit sphere in terms of spherical harmonic basis functions. In particular, it is demonstrated that the uniform distribution on the sphere is optimal with respect to all $\Phi_p$ criteria proposed by Kiefer in 1974 and also optimal with respect to a criterion which maximizes a $p$ mean of the $r$ smallest eigenvalues of the variance--covariance matrix. This criterion is related to principal component analysis, which is the common tool for analyzing this type of image data. Moreover, discrete designs on the sphere are derived, which yield the same information matrix in the spherical harmonic regression model as the uniform distribution and are therefore directly implementable in practice. It is demonstrated that the new designs are substantially more efficient than the commonly used designs in three-dimensional shape analysis.Comment: Published at http://dx.doi.org/10.1214/009053605000000552 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Deformable Multisurface Segmentation of the Spine for Orthopedic Surgery Planning and Simulation

Purpose: We describe a shape-aware multisurface simplex deformable model for the segmentation of healthy as well as pathological lumbar spine in medical image data. Approach: This model provides an accurate and robust segmentation scheme for the identification of intervertebral disc pathologies to enable the minimally supervised planning and patient-specific simulation of spine surgery, in a manner that combines multisurface and shape statistics-based variants of the deformable simplex model. Statistical shape variation within the dataset has been captured by application of principal component analysis and incorporated during the segmentation process to refine results. In the case where shape statistics hinder detection of the pathological region, user assistance is allowed to disable the prior shape influence during deformation. Results: Results demonstrate validation against user-assisted expert segmentation, showing excellent boundary agreement and prevention of spatial overlap between neighboring surfaces. This section also plots the characteristics of the statistical shape model, such as compactness, generalizability and specificity, as a function of the number of modes used to represent the family of shapes. Final results demonstrate a proof-of-concept deformation application based on the open-source surgery simulation Simulation Open Framework Architecture toolkit. Conclusions: To summarize, we present a deformable multisurface model that embeds a shape statistics force, with applications to surgery planning and simulation