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His postdoctoral work at Trinity College Dublin and at the University of Geneva concentrated on the then-emerging field of digital watermarking. He published seminal papers on image transform domain watermarks and, in particular, rotation and translation invariant watermarks based on the Fourier transform. [2]
Phase correlation is an approach to estimate the relative translative offset between two similar images (digital image correlation) or other data sets.It is commonly used in image registration and relies on a frequency-domain representation of the data, usually calculated by fast Fourier transforms.
PST operated on an astronomical image reveals the accuracy of the method in enhancing sharp and faint features. PST edge detection on lightbulb image Feature enhancement in an image (St Paul's Cathedral, London) using phase stretch transform (PST). Left panel shows the original image and the right panel shows the detected features using PST.
Formally, the optical transfer function is defined as the Fourier transform of the point spread function (PSF, that is, the impulse response of the optics, the image of a point source). As a Fourier transform, the OTF is generally complex-valued; however, it is real-valued in the common case of a PSF that is symmetric about its center.
The equation of a 1-D Gabor wavelet is a Gaussian modulated by a complex exponential, described as follows: [3] = / ()As opposed to other functions commonly used as bases in Fourier Transforms such as and , Gabor wavelets have the property that they are localized, meaning that as the distance from the center increases, the value of the function becomes exponentially suppressed.
Block diagram of the (forward) generalized lifting scheme transform. Generalized lifting scheme is a dyadic transform that follows these rules: Deinterleaves the input into a stream of even-numbered samples and another stream of odd-numbered samples. This is sometimes referred to as a lazy wavelet transform. Computes a prediction mapping. This ...
An example application of the Fourier transform is determining the constituent pitches in a musical waveform.This image is the result of applying a constant-Q transform (a Fourier-related transform) to the waveform of a C major piano chord.
Image registration or image alignment algorithms can be classified into intensity-based and feature-based. [3] One of the images is referred to as the moving or source and the others are referred to as the target, fixed or sensed images. Image registration involves spatially transforming the source/moving image(s) to align with the target image.