A low bit rate video codec that employs bi-directional motion compensation with geometric transforms is given. The improvement achieved by using bi-directional motion vectors is analysed and the performance of the codec at a bit rate of 48 kbit/s is compared against the H.261 video codec.

A low bit rate video codec that employs bidirectional motion compensation with geometric transforms is given. The improvement achieved by using bi-directional motion vectors is analysed and the performance of the codec at a bit rate of 48 kbit/s is compared against the H.261 video codec.

The motion rotors, or motors, are used to model Euclidean motion in 3D conformal geometric algebra. In this chapter we present a technique for estimating the motor which best transforms one set of noisy geometric objects onto another. The technique reduces to an eigenrotator problem and has some advantages over matrix formulations. It allows motors to be estimated from a variety of geometric da...

In this paper a geometric approach to the special relativity (SR) is used that called "invariant relativity" (ISR). ISR it considered in four-dimensional (4D) spacetime physical laws are geometric, coordinate-free relationships between 4D quantities. It mathematicaly proved electric and magnetic fields properly defined vectors on spacetime. According first proof dimension of vector field determ...

Abstract: The divergence function in information geometry, and the discrete Lagrangian in discrete 1 geometric mechanics each induce a differential geometric structure on the product manifold QˆQ. 2 We aim to investigate the relationship between these two objects, and the fundamental role that 3 duality, in the form of Legendre transforms, play in both fields. By establishing an analogy between...

We present robust algorithms for set operations and Euclidean transformations of curved shapes in the plane using approximate geometric primitives. We use a refinement algorithm to ensure consistency. Its computational complexity is O(n log n + k) for an input of size n with k = O(n) consistency violations. The output is as accurate as the geometric primitives. We validate our algorithms in flo...

The geometric constructions are performed on (semi) Riemannian manifolds and vector bundles provided with nonintegrable distributions defining nonlinear connection structures induced canonically by metric tensors. Such spaces are called nonholonomic manifolds and described by two equivalent linear connections also induced unique forms by a metric tensor (the Levi Civita and the canonical distin...

Two methods are proposed for correct and verifiable geometric reasoning using finite precision arithmetic. The first method, data normalization, transforms the geometric structure into a configuration for which all finite precision calculations yield correct answers. The second method, called the hidden variable method, constructs configurations that belong to objects in an infinite precision d...

We introduce a highly error resistant method of extracting Itô processes as applied to market data. This method is inspired by an AI method known as Hough transforms (HT). The HT method has been used in extracting geometric shape patterns from noisy and corrupted image data. We use this method to extract simultaneously logistic geometric Brownian motion trends from simulated price histories dat...

We present a formula that turns power series into series of functions. This formula serves two purposes: first, it helps to evaluate some power series in a closed form; second, it transforms certain power series into asymptotic series. For example, we find the asymptotic expansions for λ > 0 of the incomplete gamma function γ(λ,x) and of the Lerch transcendent Φ(x,s,λ). In one particular case, ...