There are many applications that are not naturally based on the orthogonal co-ordinate systems, like ultrasound imaging, astronomy, mechanical computations etc. In many cases it is necessary to transform the problem formulation to the orthogonal co-ordinate system, where the problem is solved, transform the solution back and visualize the solution. The polar, spherical or cylindrical co-ordinat...

Two new design techniques for adaptive orthogonal block transforms based on vector quantization (VQ) codebooks are presented. Both techniques start from reference vectors that are adapted to the characteristics of the signal to be coded, while using different methods to create orthogonal bases. The resulting transforms represent a signal coding tool that stands between a pure VQ scheme on one e...

The rays # and 4 are said to be orthogonal (denoted by (I,$ 4) = 0) if (I,$ 4) = 0 and non-orthogonal (denoted by (9 4) # 0) if (+, 4) # 0. This definition is independent of the choice of I/I E +Q and #J E 4. The rays Ilr,, . . . , a,%k are said to be independent if and only if I,!J~, . . . , +!I~ are linearly independent. This definition does not depend on the choice of I,!+ E +&, i = 1,. . . ...

In this paper, new adaptive medical image coding technique based orthogonal polynomials transformation is proposed. The input image is first applied with the proposed orthogonal polynomials based modified zero crossing algorithm for edge detection since it is not sensitive to noise and surface irregularities. Then the scan filling algorithm is used to separate the foreground that contains the m...

In this paper we consider the following problem in computational geometry which has applications in VLSI oorplan design and image processing. Given an orthogonal polygon P (i.e. edges are either vertical or horizontal) with n ver-tices and a positive integer m < n, determine an orthogonal polygon Q with less than or equal to m vertices such that ERROR(P; Q) is minimized, where ERROR(P; Q) is de...

This paper presents a method for using objects in a scene to define the reference frame for 3-D reconstruction. We first present a simple technique to calibrate an orthographic projection from four non-coplanar reference points. We then show how the observation of two additional known scene points can provide the complete perspective projection. When used with a known object, this technique per...

We describe BrainSync, an orthogonal transform that allows direct comparison of resting fMRI (rfMRI) time-series across subjects. For this purpose, we exploit the geometry of the rfMRI signal space to propose a novel orthogonal transformation that synchronizes rfMRI time-series across sessions and subjects. When synchronized, rfMRI signals become approximately equal at homologous locations acro...

This thesis provides an explicit construction of a quantum Goppa code for any hyperelliptic curve over a non-binary field. Hyperelliptic curves have conjugate pairs of rational places. We use these pairs to construct self-orthogonal classical Goppa codes with respect to a weighted inner product. These codes are also self-orthogonal with respect to a symplectic inner product and therefore define...