A popular understanding of the spectrum obtained by Fourier transform of images

Fourier transform process ：

after Fourier transform and spectrum centering processing Spectrum of :

1. If the gray change on a line of the image is regarded as a discrete signal , Then the whole image can be regarded as a signal distributed on a two-dimensional plane , Therefore, images can be regarded as spatial signals . Fourier transform is to distribute the gray level of the image （ Spatial domain signal ） Transform to the frequency domain , It provides us with another perspective to observe the image .

2. Spectrum of image （ After the spectrum is centered ） The center point of is the lowest frequency , Take this point as the center of the circle , Points on different radii represent different frequencies . The image frequency here refers to the change speed of a gray curve in the original image ( That's not rigorous , But according to paragraph above 1 The angle of the point , It seems that it can also be understood in this way ).

3. The high-frequency part on the image spectrum represents the area where the gray level of the original image changes sharply , It means that there may be an edge in this area 、 outline 、 Details or noise information ; The low-frequency part represents the area where the gray level of the original image is basically unchanged or changes little , Represents the picture except the edge 、 outline 、 A large image area remaining in the high-frequency part such as detail or noise .( imagine , If you draw a portrait with black strokes on a white background , The gray scale between the black outline of the person you drew and the white background ( brightness ) The comparison must be great , Therefore, the gray change is more intense , So the high-frequency part of the image represents contour information ; But when you paint things , In red clothes, there is almost no grayscale change in large areas of red , Therefore, the low-frequency part represents a large area with uniform gray scale of the image )

4. The intensity of a point on the image spectrum indicates the amplitude of the corresponding gray-scale change curve at that frequency ( Gray peak ) Size , If the gray value of each point of the original image is 0, Then the corresponding spectrum has no bright spots .

for example , An all black image ( The gray peak is 0) The corresponding spectrum is also completely black

On the contrary, if the gray value of the original image is not 0 The point of , And the gray value changes uniformly , On the spectrum diagram, it is a spectrum diagram with a central bright spot . for example , The spectrum corresponding to a gray picture is as follows

  Draw a white line on a black background , There will be gray changes in the direction perpendicular to the white line , And the gray peak value is not 0, The corresponding spectrum diagram is as follows ：

  If there are more bright spots in the spectrum , It shows that the more gray areas in the original image , The more the image " complex "( Sharp ); If there are fewer bright spots in the spectrum , And more concentrated , It shows that there are less gray areas in the original image , The more the image " Simple "( soft ).

  The above pictures are from : Research on the characteristics of two-dimensional Fourier transform spectrum of image - xh6300 - Blog Garden

summary : The points on the spectrum and the points on the original image are not one-to-one correspondence , Each point on the spectrum represents the global information of the original image , The points on the spectrum map reflect the image area in the original image with the speed law of gray change ( There may be more than one ) And its gray peak （ Light and dark ） Information .

Reference resources :

Research on the characteristics of two-dimensional Fourier transform spectrum of image - xh6300 - Blog Garden

The image processing 2： Spectrum understanding of two-dimensional images _ Xiao Nami wants to work hard on her blog -CSDN Blog _ Two dimensional spectrum diagram

High frequency and low frequency components in the image _ Zangetsu _ Sina blog Understanding of image frequency _dzh_ Long road of cultivation _ Sina blog High frequency and low frequency components in the image _ Zangetsu _ Sina blog

  The frequency of the image _dengheCSDN The blog of -CSDN Blog _ Image frequency

Understand the low-frequency and high-frequency components in the image _Chaolei3 The blog of -CSDN Blog _ High frequency components