Paper 54: Understanding of Image frequency

I have been thinking about a problem, after the image enhancement, which aspects of the most significant features, reasoning, no fruit and finally! Looking through a paper, based on Fidelity (VIF) Enhancement image quality evaluation, the article points out that no reference quality evaluation can be considered from three aspects: average gradient (AG), Information entropy (IE), Space frequency (SF). These characteristics are not very comprehensive, the effect is not necessarily good, the results of the test on the database is not very ideal, based on the space frequency, research:

1, what is the frequency of the image:

The different frequency information has different function in the image structure . The main component of the image is the low frequency information, which forms the basic gray level of the image, and the decision function of the image structure is small; if information determines the basic structure of the image and forms the main edge structure of the image, the high frequency information forms the edge and detail of the image. is the further enhancement of the image content in the intermediate frequency information.

The Fourier transform can be used to obtain the image spectrum graph:

The image on the left is the original, and the right is the spectrogram.

• the frequency of images is an indicator of the intensity of gray changes in the image, and is the gradient of the gray level in the plane space. such as: a large area of the desert in the image is a region of slow gray-scale changes, the corresponding frequency value is very low, and for the Surface attribute transformation of the sharp edge region in the image is a sharp change in the area of gray, the corresponding frequency value is higher.

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 image changes slowly. part is the low frequency component . 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.

• The image is a two-dimensional Fourier transform to get the spectrum map , is the image gradient distribution map , of course, the spectrum of the points on the image and the points on the map does not exist one by one corresponding relationship , even in the case of non-shift frequency is not. Fourier spectrum Map We see the bright and dark light, is actually like a certain point and the neighborhood point difference between the strength , that is, the size of the gradient, that is, the frequency of the point size (so understand that the low-frequency part of the image refers to the lower gradient point, High-frequency section opposite).

So what is the spatial frequency (⊙o⊙) of the image?

2, the spatial frequency of the image:

definition: spatial frequency domain. English: Spatial frequency domain. Encyclopaedia: With the spatial frequency (i.e. wave number) as an independent variable to describe the characteristics of the image, you can decompose an image cell value in the spatial change into a linear superposition of the Jianzhen function with different amplitude, space frequency and phase, and the composition and distribution of various spatial frequency components in the image are called spatial spectrum. This decomposition, processing, and analysis of spatial frequency characteristics of images is called spatial frequency domain processing or wave number domain processing. and the time domain and the frequency domain are similar to each other, and the spatial domain and the spatial frequency domain can be converted to each other.

The spatial frequency of an image refers to the number of days of the week in which the images or stimuli in each degree of view are bright and dark as sine modulated grid bars. It is a concept that describes the working characteristics of a vision system, which is based on the theoretical analysis of vibrational waveforms presented by mathematician J.-b.-j Fourier in 19th century. Initially in physical optics, the spatial frequency refers to the number of gratings per millimeter, in lines/millimeters. 60 's introduction of visual research. The wide application of this concept provides a new way for the research of visual characteristics, graphic perception, transmission of visual system signals and processing of information.
When using spatial frequencies to describe the characteristics of a vision system, the size of the grid space frequency and the contrast of the grid bar itself are important factors. The contrast of the bar graph is (highest brightness-lowest brightness)/(maximum brightness + minimum brightness). Adjusts the contrast of a spatial frequency grid, which is the contrast threshold for the spatial frequency when the observer can have a correct resolution of 50%. The inverse of the threshold value is the contrast sensitivity of the observer to the spatial frequency. Experimental measurement, the human eye contrast threshold is changed with the change of spatial frequency, that is, the function of spatial frequency, called the comparative susceptibility function (CSF). Because it is similar to the modulation transfer function (MTF) of an optical system, it is also called MTF. Observers with normal visual acuity were most sensitive to grids of 3 or 4 weeks per degree of view, and decreased susceptibility above or below this frequency. If the space frequency exceeds 60 weeks per degree of view, no matter how much the contrast increases, you cannot see the grid bar. The frequency at which the grid is not visible is called the cutoff frequency, which can be used as an indicator of visual sharpness.
　　1968 F.W Campbell and J. Robson proved that there are many channels in the human visual system, and that each channel has a different area of space frequency modulation. They also estimate the effective bandwidth of each channel, which is the multi-channel theory of vision. This theory was later confirmed by many experiments. The visual experiment also proves that each frequency channel is also sensitive to the direction of the grid bar. L. Maffei and other electrophysiological experiments have also shown that there are neurons in the visual cortex that are sensitive to different spatial frequencies, so he believes that the vision system is a Fourier analyzer. H.R. Weilson from the heterogeneity of the distribution of retinal cells, a four-channel theory is proposed. He believes that there are 4 frequencies at each point of the retina, and the sensitivity of these 4 frequencies varies. Later he added 4 channels to 6 frequency channels.

Paper 54: Understanding the image frequency