Rotational Symmetries and Spherical Measure in Homogeneous Groups

Symmetries of Homogeneous Cosmologies

We reformulate the dynamics of homogeneous cosmologies with a scalar field matter source with an arbitrary selfinteraction potential in the language of jet bundles and extensions of vector fields. In this framework, the Bianchi— scalar field equations become subsets of the second Bianchi jet bundle, J , and every Bianchi cosmology is naturally extended to live on a variety of J . We are interes...

Rotational Symmetries a Quick Tutorial

The theory for operators describing rotational symmetries in image regions using orientation information was developed around 1981 by Granlund and Knutsson. It was however first mentioned in a patent from 1986, see [18, 17, 19]. An early related work is also [14]. For a more thorough description, see e.g. [15, 6, 4, 12]. See also [5, 3, 22, 2, 1, 21]. The theory describes modelling and detectio...

MAT301H1: Groups and Symmetries

Rotational and dihedral symmetries in Steinhaus and Pascal binary triangles

We give explicit formulae for obtaining the binary sequences which produce Steinhaus triangles and generalized Pascal triangles with rotational and dihedral symmetries.

Detecting Rotational Symmetries Using Normalized Convolution

Perceptual experiments indicate that corners and curvature are very important features in the process of recognition. This paper presents a new method to detect rotational symmetries, which describes complex curvature such as corners, circles, star, and spiral patterns. It works in two steps; first extract local orientation from a gray-scale or color image, second apply normalized convolution o...