Image spectrum decentralization

1. The research of digital image sometimes needs to transform to frequency for processing, such as filtering
however, the spectrum obtained by direct two-dimensional DFT transformation of digital image is that the high frequency is in the middle and the low frequency is in the four corners. In order to concentrate the energy and facilitate the use of filters, the shift property of two-dimensional DFT can be used to centralize the spectrum.

2. After Fourier transform, the DC components of the image are concentrated on the four corners of the image, and then moved from the four corners to the central region of the spectrum after center translation processing. For details, you can see the description of FFT shift function in MATLAB

4. Digital image is an image represented by two-dimensional digital group, and its digital unit is pixel. The proper application of digital image usually needs the knowledge of the relationship between digital image and the phenomenon, that is, geometry and photometry or sensor calibration. The field of digital image processing is to study their transformation algorithm.

5. The most intensive part of the spectrum map is the value or core of the most pixels in the image, which is the more important part of the current image. The adjustment of this part should be careful, because slight adjustment may cause great changes.

6. The analysis of phase spectrum of spectrum obtained by Fourier transform of seismic signal after filtering:
1. The basic wavelet of seismic record can also be described by these three elements. Formation filtering characteristics include energy transfer, reflection interference, scattering and absorption, which are related to formation physical properties and structure. These factors all have the function of reconstructing the seismic wave phase spectrum. When the seismic wave passes through the strata with different lithology, its phase difference is different, that is to say, the change of seismic wave characteristics can indirectly reflect the change of strata physical properties
2. Fourier transform transforms the time-domain signal which is difficult to process into the frequency-domain signal which is easy to analyze. Some tools can be used to process these frequency-domain signals. Finally, these frequency domain signals can be transformed into time domain signals by inverse Fourier transform
3. The frequency of an image is an indicator of the intensity of gray changes in the image, and it is the gradient of gray in the plane space. In the region of slow gray change, the corresponding frequency value is very low; The frequency value is higher in the region with sharp gray change
4. The spectrum map obtained by two-dimensional Fourier transform is the distribution map of image gradient. The bright spots with different light and shade seen on the Fourier spectrum map are actually the difference between a certain point in the image and the neighboring points, that is, the size of the gradient, that is, the frequency of the point. The low-frequency part of the image refers to the point with low gradient, while the high-frequency part is opposite. If the gradient is large, the brightness of the point is strong, otherwise the brightness is weak. In this way, we can see the energy distribution of the image by observing the spectrum after Fourier transform. If there are more dark points in the spectrum, then the actual image is softer (because the difference between each point and the neighborhood is not big, and the gradient is relatively small). On the contrary, if there are more bright points in the spectrum, then the actual image must be sharp, The boundary is clear and the pixels on both sides of the boundary are quite different.

7. y=fft(x,number);%number是x的长度
n=0:length(y)-1;
f=fs*n/length(y);%fs是x的采样频率
plot(f,abs(y));

8. In frequency domain, the larger the frequency is, the faster the original signal changes; The higher the frequency is, the smoother the original signal is.
when the frequency is 0, it means that the DC signal does not change. Therefore, the frequency reflects the speed of the signal change. The high frequency component explains the abrupt part of the signal, while the low frequency component determines the overall image of the signal.
in image processing, the frequency domain reflects the intensity of the image gray change in the spatial domain, that is, the speed of the image gray change, For an image, the edge part of the image is a mutation part, which changes quickly, so the response is high frequency component in frequency domain; The noise of image is mostly high frequency part; In other words, Fourier transform provides another angle to observe the image, which can transform the image from gray distribution to frequency distribution to observe the characteristics of the image, The main reason is that the four corner position after transformation just corresponds to the low-frequency component of the image, and generally speaking, the energy of the image is concentrated on the low-frequency component, so the amplitude of the low-frequency position after transformation will be larger, and the display will be brighter

9. The so-called spectrum analysis is actually in the transform domain analysis, spectrum analysis is one of the various transformation methods (two-dimensional FFT analysis, discrete cosine transform, etc.), image spectrum analysis is the image of two-dimensional time domain signal through two-dimensional FFT analysis into spatial spectrum analysis