Robust Image Watermark Using Radon Transform and Bispectrum Invariants

A digital image is a numeric representation of a two-dimensional image. Depending on whether the image resolution is fixed, it may be of vector or raster type. Without qualifications, the term 'digital image' usually refers to raster images also called bitmap images. In mathematics, the Radon transform in two dimensions, named after the Austrian mathematician Johann Radon, is the integral transform consisting of the integral of a function over straight lines. The transform was introduced by Johann Radon, who also provided a formula for the inverse transform. Radon further included formulas for the transform in three-dimensions, in which the integral is taken over planes. In mathematics, in the area of statistical analysis, the bispectrum is a statistic used to search for nonlinear interactions. The Fourier transform of the second-order cumulant, i.e. , the autocorrelation function, is the traditional power spectrum. The Fourier transform of C3(t1, t2) is called the bispectrum or bispectral density. Applying the convolution theorem allows fast calculation of the bispectrum . A watermark is a recognizable image or pattern in paper that appears as various shades of lightness/darkness when viewed by transmitted light (or when viewed by reflected light, atop a dark background), caused by thickness or density variations in the paper. There are two main ways of producing watermarks in paper, the dandy roll process, and the more complex cylinder mould process. Radon is a chemical element with the atomic number 86, and is represented by the symbol Rn. It is a radioactive, colorless, odorless, tasteless noble gas, occurring naturally as the decay product of uranium or thorium. Its most stable isotope, Rn, has a half-life of 3.8 days. Radon is one of the densest substances that remains a gas under normal conditions. It is also the only gas that only has radioactive isotopes, and is considered a health hazard due to its radioactivity. In mathematics, an invariant is a property of a class of mathematical objects that remains unchanged when transformations of a certain type are applied to the objects. The particular class of objects and type of transformations are usually indicated by the context in which the term is used. For example, the area of a triangle is an invariant with respect to isometries of the Euclidean plane. The phrases 'invariant under' and 'invariant to' a transformation are both used. Medical imaging is the technique and process used to create images of the human body (or parts and function thereof) for clinical purposes or medical science (including the study of normal anatomy and physiology). Although imaging of removed organs and tissues can be performed for medical reasons, such procedures are not usually referred to as medical imaging, but rather are a part of pathology. In machine learning, pattern recognition is the assignment of a label to a given input value. An example of pattern recognition is classification, which attempts to assign each input value to one of a given set of classes (for example, determine whether a given email is 'spam' or 'non-spam'). However, pattern recognition is a more general problem that encompasses other types of output as well. Source.


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Last Modified: January 27, 2014 @ 12:00 am