The fundamental question as to whether thin intergranular films can adopt an equilibrium thickness in polycrystalline ceramics is addressed. Two continuum approaches are presented, one based on interfacial energies and the other on the force balance normal to the boundary. These indicate that there will exist a stable thickness for the intergranular film and that it will be of the order of 1 nm...

We consider the fundamental matrix solution associated to piecewise smooth differential systems of Filippov type, in which the vector field varies discontinuously as solution trajectories reach one or more surfaces. We review the cases of transversal intersection and of sliding motion on one surface. We also consider the case when sliding motion takes place on the intersection of two or more su...

The low-rank matrix completion problem is a fundamental machine learning and data mining problem with many important applications. The standard low-rank matrix completion methods relax the rank minimization problem by the trace norm minimization. However, this relaxation may make the solution seriously deviate from the original solution. Meanwhile, most completion methods minimize the squared p...

José Henrique Brito12 [email protected] Christopher Zach4 [email protected] Kevin Köser3 [email protected] Manuel João Ferreira2 [email protected] Marc Pollefeys3 [email protected] 1 Instituto Politécnico do Cávado e do Ave Barcelos, Portugal 2 Universidade do Minho Guimarães, Portugal 3 Computer Vision and Geometry Group ETH Zurich, Switzerland 4 Machine Learning and Perc...

The epipolar geometry is a key point in computer vision and the fundamental matrix estimation the unique way to compute it. This article surveys several methods of fundamental matrix estimation. All the different methods have been programmed and their accuracy analysed using synthetic and real images. A discussion justified with experimental results is given and the code is available in Interne...

The normalized eight-point algorithm is broadly used for the computation of the fundamental matrix between two images given a set of correspondences. However, it performs poorly for low-size datasets due to the way in which the rank-two constraint is imposed on the fundamental matrix. We propose two new algorithms to enforce the rank-two constraint on the fundamental matrix in closed form. The ...