Repeating an arbitrary sequence of RF pulses and magnetic field gradients will eventually lead to a steady-state condition in any magnetic resonance system. While numerical methods can quantify this trajectory, analytic analysis provides significantly more insight and a means for faster calculation. Recently, an analytic analysis using homogeneous coordinates was published. The current work fur...

A modified formulation of Maxwell's equations is presented that includes a complex and nonlinear coordinate transform along one or two Cartesian coordinates. The added degrees of freedom in the modified Maxwell's equations allow one to map an infinite space to a finite space and to specify graded perfectly matched absorbing boundaries that allow the outgoing wave condition to be satisfied. The ...

A new method is presented for solving equivalence problems for the extended jet of nite order of the scale space corresponding to a 2-dimensional input image and the groups of spatially homogeneous aane and orthogonal transformations of local cartesian coordinate frames. By means of this method complete and irreducible sets of algebraic invariants are found that may describe any local and (or) ...

This paper presents a theoretical and experimental method for analyzing pneumatic transmission lines in the time-domain for a model pneumatic gantry robot. The objective is to develop pipeline simulators that can be implemented for modeling of fluid servo systems. After describe the model, the paper illustrates the experimental tests carried out on several different types of lines, and comparin...

The behaviour of critical points of Gaussian scale-space images is mainly described by their creation and annihilation. In existing literature these events are determined in so-called canonical coordinates. A description in a user-defined Cartesian coordinate system is stated, as well as the results of a straightforward implementation. The location of a catastrophe can be predicted with subpixe...

The calculation of the uncertainty in an estimated rotation requires a parametrization of the rotation group; that is, a unique mapping of the rotation group to a point in 3-D Euclidean space, R3. Numerous parametrizations of a rotation exist, including: (1) the latitude and longitude of the axis of rotation and the angle of rotation; (2) a representation as a Cartesian vector with length equal...

Background Quantitative MR myocardial strain analysis is typically performed using rectilinear or Cartesian grid tagging, and regional contractility is visually assessed by the deformation of the grid1. However, it is difficult to visually isolate circumferential and radial components of displacement and strain from parallel straight lines on short axis images. This study evaluates the potentia...

1992 Abstract We present a new method of multi-resolution image analysis that gives us the most concise set of local orthogonally invariant features of 2-dimensional input images. Solving the equivalence problem corresponding to a local jet and the group of orthogonal transformations of the cartesian coordinate frame we nd a complete and irreducible set of local algebraic invariants that may de...

We present an algorithm to process images of reflected Placido rings captured by a commercial videokeratoscope. Raw data are obtained with no Cartesian-to-polar-coordinate conversion, thus avoiding interpolation and associated numerical artifacts. The method provides a characteristic equation for the device and is able to process around 6 times more corneal data than the commercial software. Ou...

We present \surface frequency" representations, which describe how Cartesian positions on a surface vary with the intrinsic position along the surface. These representations are constructed using optimized coordinate values, individual sample weights, and an iterative transform algorithm. We then use surface frequency to monitor a deformable surface model and increase the number of samples when...