Changepoints are a very common feature of Big Data that arrive in the form of a data stream. In this paper, we study high-dimensional time series in which, at certain time points, the mean structure changes in a sparse subset of the coordinates. The challenge is to borrow strength across the coordinates in order to detect smaller changes than could be observed in any individual component series...

In this paper, we introduce a new system of quasi variational inequalities. The projection technique is used to establish the equivalence between this new system of quasi variational inequalities and the fixed point problem. The fixed point formulation enables us to suggest some parallel projection iterative methods for solving the system of quasi variational inequalities. Convergence analysis ...

Weintroduceanewkindofmosaicing,where thepositionof the samplingstrip varies asa functionof the input camera location. The new images that are generated this way correspond to a new projection model defined by two slits, termed here the Crossed-Slits (X-Slits) projection. In this projection model, every 3D point is projected by a ray defined as the line that passes through that point and interse...

This paper presents a technique by which solutions to reflexive domain equations can be found in a certain category of complete metric spaces. The objects in this category are the (non-empty) metric spaces and the arrows consist of two maps: an isometric embedding and a non-distance-increasing left inverse to it. The solution of the equation is constructed as a fixed point of a functor over thi...

We study the universal groups of inverse semigroups associated with point sets and with tilings. We focus our attention on two classes of examples. The first class consists of point sets which are obtained by a cut and projection scheme (so-called model sets). Here we introduce another inverse semigroup which is given in terms of the defining data of the projection scheme and related to the mod...

A new techniques for proving the existence of fixed points of groups of isometric transformations is developed. It is used to find simpler proofs and real-case versions of previous results of the authors. In particular, we use the obtained fixed point theorem to show that a bounded representation in a separable, real or complex, Hilbert space which has an invariant indefinite quadratic form wit...

For a singularly perturbed convection-diffusion problem with exponential and characteristic boundary layers on the unit square a discretisation based on layer-adapted meshes is considered. The standard Galerkin method and the local projection scheme are analysed for a general class of higher order finite elements based on local polynomial spaces lying between Pp and Qp. We will present two diff...

3D motion tracking is a critical task in many computer vision applications. Unsupervised markerless 3D motion tracking systems determine the most relevant object in the screen and then track it by continuously estimating its projection features (center and area) from the edge image and a point inside the relevant object projection (namely, inner point), until the tracking fails. Existing reliab...

Many reverse engineering and inspection applications require generation of point clouds representing faces of physical objects. This paper describes a computational framework for constructing point clouds using digital projection patterns. The basic principle behind the approach is to project known patterns on the object using a digital projector. A digital camera is then used to take images of...

where xi,yi,zi represent the projective coordinates of a point p in the image space and Xw,Yw,Zw,1 represent the projective coordinates of a point P in world coordinates. The actual pixel location of the projected point p denoted (x,y) is ( xi zi , yi zi ). In (1), Mint and Mext are the projection matrices containing the parameters of the projection for the current camera system. Mint is termed...