The basic idea of linear Principal Component Analyses (PCA) consists in decorrelating coordinates by an orthogonal linear transformation. In this paper we generalize this idea to the nonlinear case. Simultaneously we will drop the usual restriction to gaussian distributions. The linearity and orthogonality condition of linear PCA is substituted with the condition of volume conservation in order...

The most common approach for geometric correction is the use of mapping polynomial. . It depends on selection of several clearly discernible points, called ground control points (GCPs), in the distorted image, and map them either to their true positions in ground coordinates (e.g. latitude, longitude) measured from a map, or to georeferenced image (corrected before), coordinates of correspondin...

The dynamics for a thin, closed loop inextensible Euler’s elastica moving in three dimensions are considered. The equations of motion for the elastica include a wave equation involving fourth order spatial derivatives and a second order elliptic equation for its tension. A Hasimoto transformation is used to rewrite the equations in convenient coordinates for the space and time derivatives of th...

Classical and quantum mechanics for an extended Heisenberg algebra with canonical commutation relations for position and momentum coordinates are considered. In this approach additional noncommutativity is removed from the algebra by linear transformation of phase space coordinates and transmitted to the Hamiltonian (Lagrangian). This transformation does not change the quadratic form of Hamilto...

This paper proposes a new design method for two-dimensional diamond-shaped IIR filters. The design starts from a desired 1D prototype filter, to which a frequency transformation is applied, which leads to the 2D filter with desired shape. The frequency transformation is derived by specifying the filter shape in polar coordinates in the frequency plane. The designed filters also have the useful ...

Similar to the spatial transformer network introduced in [1], we propose a 2-step procedure: (1) performing dense sampling from input volume (in 3D world coordinates) to output volume (in screen coordinates), and (2) flattening the 3D spatial output across disparity dimension. In the experiment, we assume that transformation matrix is always given as input, parametrized by the viewpoint α. Agai...

A solution of the problem of calculating cartesian coordinates from a matrix of interpoint distances (the embedding problem) is reported. An efficient and numerically stable algorithm for the transformation of distances to coordinates is then obtained. It is shown that the embedding problem is intimately related to the theory of symmetric matrices, since every symmetric matrix is related to a g...

Many problems solved in computer graphics, computer vision, visualization etc. require fast and robust computation of an area of a triangle or volume of a tetrahedron. These very often used algorithms are well known and robust if vertices coordinates of triangles or tetrahedrons are given in Euclidean coordinates. The homogeneous coordinates are often used for the representation of geometric tr...