Granular Pressure and the Thickness of a Layer Jamming on a Rough Incline

Dense granular media have a compaction between the random loose and random close packings. For these dense media the concept of a granular pressure depending on compaction is not unanimously accepted because they are often in a "frozen" state which prevents them to explore all their possible microstates, a necessary condition for defining a pressure and a compressibility unambiguously. While periodic tapping or cyclic fluidization have already being used for that exploration, we here suggest that a succession of flowing states with velocities slowly decreasing down to zero can also be used for that purpose. And we propose to deduce the pressure in \emph{dense and flowing} granular media from experiments measuring the thickness of the granular layer that remains on a rough incline just after the flow has stopped.Comment: 10 pages, 2 figure

Fast and Accurate Camera Covariance Computation for Large 3D Reconstruction

Estimating uncertainty of camera parameters computed in Structure from Motion (SfM) is an important tool for evaluating the quality of the reconstruction and guiding the reconstruction process. Yet, the quality of the estimated parameters of large reconstructions has been rarely evaluated due to the computational challenges. We present a new algorithm which employs the sparsity of the uncertainty propagation and speeds the computation up about ten times \wrt previous approaches. Our computation is accurate and does not use any approximations. We can compute uncertainties of thousands of cameras in tens of seconds on a standard PC. We also demonstrate that our approach can be effectively used for reconstructions of any size by applying it to smaller sub-reconstructions.Comment: ECCV 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

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

A QCQP Approach to Triangulation

Triangulation of a three-dimensional point from at least two noisy 2-D images can be formulated as a quadratically constrained quadratic program. We propose an algorithm to extract candidate solutions to this problem from its semidefinite programming relaxations. We then describe a sufficient condition and a polynomial time test for certifying when such a solution is optimal. This test has no false positives. Experiments indicate that false negatives are rare, and the algorithm has excellent performance in practice. We explain this phenomenon in terms of the geometry of the triangulation problem.Comment: 14 pages, to appear in the proceedings of the 12th European Conference of Computer Vision, Firenze, Italy, 7-13 October 201

Distance Optimization and the Extremal Variety of the Grassmann Variety

The approximation of a multivector by a decomposable one is a distance-optimization problem between the multivector and the Grassmann variety of lines in a projective space. When the multivector diverges from the Grassmann variety, then the approximate solution sought is the worst possible. In this paper, it is shown that the worst solution of this problem is achieved, when the eigenvalues of the matrix representation of a related two-vector are all equal. Then, all these pathological points form a projective variety. We derive the equation describing this projective variety, as well as its maximum distance from the corresponding Grassmann variety. Several geometric and algebraic properties of this extremal variety are examined, providing a new aspect for the Grassmann varieties and the respective projective spaces

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