The Moving Object Detection and Research Effects of Noise on Images Based on Cellular Automata With a Hexagonal Coating Form and Radon Transform

Methods for image identification based on the Radon transform using hexagonal-coated cellular automata in the chapter are considered. A method and a mathematical model for the detection of moving objects based on hexagonal-coated cellular automata are described. The advantages of using hexagonal coverage for detecting moving objects in the image are shown. The technique of forming Radon projections for moving regions in the image, which is designed for a hexagonal-coated cellular automata, is described. The software and hardware implementation of the developed methods are presented. Based on the obtained results, a hexagonal-coated cellular automata was developed to identify images of objects based on the Radon transform. The Radon transform allowed to effectively extract the characteristic features of images with a large percentage of noise. Experimental analysis showed the advantages of the proposed methods of image processing and identification of moving objects.

Using Few Radon Projections to Recover 3-D NMR Spectrum

Given a regular binary function f on R2 with compact support D, we use translation to form a new binary function g from f so that the image representation of g (x, y) is made up of non-overlapping copies of D. Thus, g is made up of discrete entities that are surrounded by regions of space. We devise a procedure that can determine the translation parameters using a minimum number of Radon projections g of g . This model is a mathematical abstraction of an application of the Radon transform in Spectroscopy.Keywords: Radon transforms, transformation of an image, Back projection.

On Tomography with Limited Data

We give an algorithm for reconstructing a density function f in the plane from limited number of Radon projections on a range of angles −𝝋∗<𝝋<𝝋∗ together with a few well selected angles outside this range. In doing so, we assume that f is subjected to a linear transformation that produces g, and actually recover g. Interpolation is a basic tool in our calculations

Linear Transformation Recognition Using Radon Transform

Given two regular functions (images) f and g on R2 where g is formed from f by a general linear transformation, g(x) = f (Ax + b). We present a procedure to determine the transformation ‘parameters’ A and b using Radon projections of f and only two projections of g. We use these projections together with simple facts on matrix vector multiplication to recover the matrix A. The assumptions we have here are: f is nonnegative and A is nonsingular. Commonly used transformations in image processing such as rotation, scaling and others are special cases of our approach.