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

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