219 research outputs found
Deep Modeling of Growth Trajectories for Longitudinal Prediction of Missing Infant Cortical Surfaces
Charting cortical growth trajectories is of paramount importance for
understanding brain development. However, such analysis necessitates the
collection of longitudinal data, which can be challenging due to subject
dropouts and failed scans. In this paper, we will introduce a method for
longitudinal prediction of cortical surfaces using a spatial graph
convolutional neural network (GCNN), which extends conventional CNNs from
Euclidean to curved manifolds. The proposed method is designed to model the
cortical growth trajectories and jointly predict inner and outer cortical
surfaces at multiple time points. Adopting a binary flag in loss calculation to
deal with missing data, we fully utilize all available cortical surfaces for
training our deep learning model, without requiring a complete collection of
longitudinal data. Predicting the surfaces directly allows cortical attributes
such as cortical thickness, curvature, and convexity to be computed for
subsequent analysis. We will demonstrate with experimental results that our
method is capable of capturing the nonlinearity of spatiotemporal cortical
growth patterns and can predict cortical surfaces with improved accuracy.Comment: Accepted as oral presentation at IPMI 201
Stress and Strain in Flat Piling of Disks
We have created a flat piling of disks in a numerical experiment using the
Distinct Element Method (DEM) by depositing them under gravity. In the
resulting pile, we then measured increments in stress and strain that were
associated with a small decrease in gravity. We first describe the stress in
terms of the strain using isotropic elasticity theory. Then, from a
micro-mechanical view point, we calculate the relation between the stress and
strain using the mean strain assumption. We compare the predicted values of
Young's modulus and Poisson's ratio with those that were measured in the
numerical experiment.Comment: 9 pages, 1 table, 8 figures, and 2 pages for captions of figure
A Fisher-Rao metric for paracatadioptric images of lines
In a central paracatadioptric imaging system a perspective camera takes an image of a scene reflected in a paraboloidal mirror. A 360° field of view is obtained, but
the image is severely distorted. In particular, straight lines in the scene project to circles in the image. These distortions make it diffcult to detect projected lines using standard image processing algorithms. The distortions are removed using a Fisher-Rao metric which is defined on the space of projected lines in the paracatadioptric image. The space of projected lines is divided into subsets such that on each subset the Fisher-Rao metric is closely approximated by the Euclidean metric. Each subset is sampled at the vertices of a square grid and values are assigned to the sampled points using an adaptation of the trace transform. The result is a set of digital images to which standard image processing algorithms can be applied.
The effectiveness of this approach to line detection is illustrated using two algorithms, both of which are based on the Sobel edge operator. The task of line detection is reduced to the task of finding isolated peaks in a Sobel image. An experimental comparison is made between these two algorithms and third algorithm taken from the literature and
based on the Hough transform
Macro deformation and micro structure of 3D granular assemblies subjected to rotation of principal stress axes
This paper presents a numerical investigation on the behavior of three dimensional granular materials during continuous rotation of principal stress axes using the discrete element method. A dense specimen has been prepared as a representative element using the deposition method and subjected to stress rotation at different deviatoric stress levels. Significant plastic deformation has been observed despite that the principal stresses are kept constant. This contradicts the classical plasticity theory, but is in agreement with previous laboratory observations on sand and glass beads. Typical deformation characteristics, including volume contraction, deformation non-coaxiality, have been successfully reproduced. After a larger number of rotational cycles, the sample approaches the ultimate state with constant void ratio and follows a periodic strain path. The internal structure anisotropy has been quantified in terms of the contact-based fabric tensor. Rotation of principal stress axes densifies the packing, and leads to the increase in coordination numbers. A cyclic rotation in material anisotropy has been observed. The larger the stress ratio, the structure becomes more anisotropic. A larger fabric trajectory suggests more significant structure re-organization when rotating and explains the occurrence of more significant strain rate. The trajectory of the contact-normal based fabric is not centered in the origin, due to the anisotropy in particle orientation generated during sample generation which is persistent throughout the shearing process. The sample sheared at a lower intermediate principal stress ratio (b=0.0) (b=0.0) has been observed to approach a smaller strain trajectory as compared to the case b=0.5 b=0.5 , consistent with a smaller fabric trajectory and less significant structural re-organisation. It also experiences less volume contraction with the out-of plane strain component being dilative
A Fisher-Rao Metric for curves using the information in edges
Two curves which are close together in an image are indistinguishable given a measurement, in that there is no compelling reason to associate the measurement with one curve rather than the other. This observation is made quantitative using the parametric version of the Fisher-Rao metric. A probability density function for a measurement conditional on a curve is constructed. The distance between two curves is then defined to be the Fisher-Rao distance between the two conditional pdfs. A tractable approximation to the Fisher-Rao metric is obtained for the case in which the measurements are compound in that they consist of a point x and an angle α which specifies the direction of an edge at x. If the curves are circles or straight lines, then the approximating metric is generalized to take account of inlying and outlying measurements. An estimate is made of the number of measurements required for the accurate location of a circle in the presence of outliers. A Bayesian algorithm for circle detection is defined. The prior density for the algorithm is obtained from the Fisher-Rao metric. The algorithm is tested on images from the CASIA Iris Interval database
Effects of Friction and Disorder on the Quasi-Static Response of Granular Solids to a Localized Force
The response to a localized force provides a sensitive test for different
models of stress transmission in granular solids. The elasto-plastic models
traditionally used by engineers have been challenged by theoretical and
experimental results which suggest a wave-like (hyperbolic) propagation of the
stress, as opposed to the elliptic equations of static elasticity. Numerical
simulations of two-dimensional granular systems subject to a localized external
force are employed to examine the nature of stress transmission in these
systems as a function of the magnitude of the applied force, the frictional
parameters and the disorder (polydispersity). The results indicate that in
large systems (typically considered by engineers), the response is close to
that predicted by isotropic elasticity whereas the response of small systems
(or when sufficiently large forces are applied) is strongly anisotropic. In the
latter case the applied force induces changes in the contact network
accompanied by frictional sliding. The larger the coefficient of static
friction, the more extended is the range of forces for which the response is
elastic and the smaller the anisotropy. Increasing the degree of polydispersity
(for the range studied, up to 25%) decreases the range of elastic response.
This article is an extension of a previously published letter [1].Comment: 21 pages (PDFLaTeX), 24 figures (some of them bitmapped to save
space); submitted to Phys. Rev.
- …