http://opencv.org/
OpenCV is released under a BSD license and hence it’s free for both academic and commercial use. It has C++, C, Python and Java interfaces and supports Windows, Linux, Mac OS, iOS and Android. OpenCV was designed for computational efficiency and with a strong focus on real-time applications. Written in optimized C/C++, the library can take advantage of multi-core processing. Adopted all around the world, OpenCV has more than 47 thousand people of user community and estimated number of downloads exceeding 6 million. Usage ranges from interactive art, to mines inspection, stitching maps on the web or through advanced robotics.
OpenCV Wiki
http://code.opencv.org/projects/opencv/wiki
OpenCV (Open Source Computer Vision) is a library of programming functions for realtime computer vision. It uses a BSD license and hence it's free for both academic and commercial use. It has C++, C, Python and Java (Android) interfaces and supports Windows, Linux, Android, iOS and Mac OS. It has more than 2500 optimized algorithms. Adopted all around the world, OpenCV has nearly 7 million downloads growing by nearly 200K/month. Usage ranges from interactive art, to mines inspection, stitching maps on the web on through advanced robotics.
OpenCV Q&A
http://answers.opencv.org/questions/
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Discrete Fourier Transform
http://docs.opencv.org/doc/tutorials/core/discrete_fourier_transform/discrete_fourier_transform.html
Goal
We’ll seek answers for the following questions:
- What is a Fourier transform and why use it?
- How to do it in OpenCV?
- Usage of functions such as: copyMakeBorder(), merge(), dft(), getOptimalDFTSize(), log() and normalize() .
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Fourier transform - Wikipedia
https://en.wikipedia.org/wiki/Fourier_transform
The Fourier transform, named after Joseph Fourier, is a mathematical transform with many applications in physics and engineering. Very commonly it transforms a mathematical function of time, f(t), into a new function, sometimes denoted by or F, whose argument is frequency with units of cycles/s (hertz) or radians per second. The new function is then known as the Fourier transform and/or the frequency spectrum of the function f.
The Fourier transform is also a reversible operation. Thus, given the function one can determine the original function, f. (See Fourier inversion theorem.) f and are also respectively known as time domain and frequency domain representations of the same "event".
Most often perhaps, f is a real-valued function, and is complex valued, where a complex number describes both the amplitude and phase of a corresponding frequency component. In general, f is also complex, such as the analytic representation of a real-valued function. The term "Fourier transform" refers to both the transform operation and to the complex-valued function it produces.
In the case of a periodic function (for example, a continuous but not necessarily sinusoidal musical sound), the Fourier transform can be simplified to the calculation of a discrete set of complex amplitudes, called Fourier series coefficients.
Also, when a time-domain function is sampled to facilitate storage or computer-processing, it is still possible to recreate a version of the original Fourier transform according to the Poisson summation formula, also known as discrete-time Fourier transform. These topics are addressed in separate articles. For an overview of those and other related operations, refer to Fourier analysis or List of Fourier-related transforms.
Discrete-time Fourier transform - Wikipedia
https://en.wikipedia.org/wiki/Discrete-time_Fourier_transform
In mathematics, the discrete-time Fourier transform (DTFT) is one of the specific forms of Fourier analysis. As such, it transforms one function into another, which is called the frequency domain representation, or simply the "DTFT", of the original function (which is often a function in the time-domain). The DTFT requires an input function that is discrete. Such inputs are often created by digitally sampling a continuous function, like a person's voice.
The DTFT frequency-domain representation is always a periodic function. Since one period of the function contains all of the unique information, it is sometimes convenient to say that the DTFT is a transform to a "finite" frequency-domain (the length of one period), rather than to the entire real line.
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