Understanding of image processing-Fourier transform

Most copy reference links:

http://blog.csdn.net/kofsky/article/details/2955823

1. Essence: Fourier transform is a method to map a time domain signal to the frequency domain.

Some signals mainly in the time domain performance of its characteristics, such as the process of capacitor charge and discharge, and some of the main signal in the frequency domain performance of its characteristics, such as mechanical vibration, human voice and so on. If the characteristics of the signal are mainly expressed in the frequency domain, then the corresponding time domain signal may appear disorganized, but it is very convenient to interpret in the frequency domain.  So we need to take Fourier transform for analysis. Gonzalez Edition < image processing > The explanation inside is very image: a proper analogy is to liken the Fourier transform to a glass prism. A prism is a physical instrument that decomposes light into different colors, and the color of each component is determined by its frequency (or wavelength). The Fourier transform can be regarded as a mathematical prism, the function based on frequency decomposition into different components. When we consider the light, we discuss its spectral or frequency spectrum. Similarly, Fourier transforms enable us to analyze a function by the frequency component.2. Key points:In the frequency domain, the greater the frequency, the faster the original signal changes, and the smaller the frequency, the more gentle the original signal. When the frequency is 0 o'clock, the DC signal is indicated, and there is no change. Therefore, the size of the frequency reflects the speed of the signal change. The high frequency component interprets the abrupt part of the signal, while the low frequency component determines the overall image of the signal. -------------Therefore, filtering is the main application of Fourier transform. In the image processing, the frequency domain reflects the intensity of the image in the spatial level, that is, the change of the image gray rate, that is, the gradient size of the image. To the image, the edge part of the image is the mutation part, the change is fast, so the reaction is high frequency component in the frequency domain, the noise of the image is high frequency part, and the low frequency component is the part of the image's smooth change. In other words, the Fourier transform provides an additional angle to observe the image, which can be transformed from the gray-scale distribution to the frequency distribution to observe the image characteristics. A written point is that the Fourier transform provides a free transition from airspace to frequency. For image processing, the following concepts are very important: image high-frequency components: Image mutation parts, in some cases refers to image edge information, in some cases refers to noise, more is a mixture of the two;
Low frequency component: the part of the image that changes gently, that is, the image contour information
High-pass filter: Allows the image to suppress low frequency components
Low-pass filter: In contrast to high-pass, allows the image to suppress HF components, low-frequency components through
Band-pass filter: The frequency of the image in a certain part of the passage, other too low or too high to suppress
There is also a band-stop filter, which is the inverse of the band-pass.3. Application:  Displacement: The Fourier transform amplitude of the shifted image is the same as the original image---------the camera or object moves up and down, and the Fourier transform amplitude is constant, we do not need to control the camera and target position precisely.   Frequency characteristics: f (at) Fourier transform to get 1/a*f (w/a)----------reduce the size of the image, such as long-range imaging, the frequency component will change linearly.   Overlay (linear): f (T1) +f (T2) Fourier transform F (W1) +f (W2)----------The use of frequency domain components to separate the image, the cloth infected with blood fingerprint as an example.   convolution theorem: Time domain convolution equivalence and frequency domain product----------doing template operations in the time domain is actually convolution the image. Therefore, the template operation of the image in the time domain is equivalent to the image in the frequency domain                   The         &NBS P                        /      filter processing. For example, a mean template, the frequency domain response to a low-pass filter, in the time domain for image filtering is equivalent to in the frequency domain of the graph                     &NBS P                          ,         &NB Sp   The frequency domain response of the mean template is used as a low-pass filter for the frequency response of the image.  

Image denoising is to suppress the noise part of the image. Therefore, if the noise is high frequency, from the frequency domain point of view, it is necessary to use a low-pass filter to the image processing. The low-pass filter can suppress the high frequency component of the image. But this situation often leads to the suppression of edge information. Common denoising templates include mean templates, Gaussian templates, and so on. Both filters suppress the high-frequency component of the image in the local area, and blur the edge of the image and suppress the noise. There is also a nonlinear filter-median filter. The median filter is very good to remove the impulse noise. Because the pulse point is the point of mutation, the output value after sorting, then the maximum point and the smallest point can be removed. Median filter has poor effect on Gaussian noise.

Salt and pepper noise: for salt and pepper use median filter can be very good removal. The mean value can also get some effect, but it will cause the blurring of edges.
Gaussian white Noise: white noise is distributed throughout the frequency domain, which seems to be more difficult.
Gonzalez image processing P185: Arithmetic mean filter and geometric mean filter (especially the latter) are more suitable for processing Gaussian or even random noise. Harmonic mean filter is more suitable for processing impulse noise.

Sometimes the feeling that image enhancement and image denoising is a contradictory process, image enhancement is often needed to enhance the edge of the image to achieve better display results, which need to increase the high-frequency components of the image. The image denoising is to eliminate the noise of the image, that is, the need to suppress high-frequency components. Sometimes these two refer to similar things. For example, when the noise is removed and the display of the image is significantly improved, the same is true at this point.
Common image enhancement methods include contrast stretching, histogram equalization, image sharpening and so on. The first two are the pixel-based transformations in the airspace, followed by the processing in the frequency domain. I understand that sharpening is directly on the image with high-pass filter after the component, that is, the edge effect of the image. Contrast stretch and histogram equalization are all to improve the contrast of the image, that is to make the image more obvious differences, I think, after such processing, the image should also enhance the high-frequency components of the image, making the image of the details of greater differences. It also introduces some noise

Understanding of image processing-Fourier transform