Discussion on Image Frequency Processing

Abstract Three basic grids for FM screening are proposed, and the image is frequency-modulated based on the image area grid. In order to improve the image copy quality and make the image achieve the effect of frequency modulation, the tone matrix and the detail position matrix corresponding to the image area grid are also proposed, and the FM image is obtained through their logical operations.
Keywords image area grid; adjustment matrix; detail position matrix;

The two concepts of "amplitude" and "frequency" originally represent the characteristics of electromagnetic waves in communication technology. The frequency is defined as the number of wavelengths per unit time, and the amplitude is defined as the height of the waves. If you keep the amplitude of the wave constant and change the frequency, it is called frequency modulation; if you keep the same frequency and the amplitude changes, it is called amplitude modulation. When the image is screened, the network point is regarded as "wave", the frequency is the number of network points per unit length, and the amplitude represents the size of the network point. If an image has the same size of the Internet, and the distance between the dots changes, it is called the frequency modulation structure; if the distance between the dots is the same and the size of the dot is changed, the image is called the amplitude modulation structure (Figure 1).

Figure 1 Meaning of amplitude modulation and frequency modulation

The traditional network amplitude modulation has many disadvantages. Although the amplitude modulation of the dots can restore the printed image to a continuous modulated image in a certain sense, the fine dots cannot be stably transferred during the copying process, and when the dots start to be closed, the intermediate tone value breaks.
The amplitude-modulated image structure not only has a limited density range, but also its resolution is limited, and it is impossible to achieve the resolution of the photographic image (photographs generally reach 200 lp/cm).
In multi-color overlays, due to the overprinting of color separation screen images, a much larger graphical structure - "Moiré" than dots often appears. This phenomenon is not visually perceived only when the number of mesh lines is very high (approximately above 200 lp/cm) and is superimposed at the optimum mesh angle.
Due to the above three defects, it is determined that the amplitude modulation of the dot can only simulate the photographic manuscript more closely. In order to make the replicas comparable to the quality of the photographs, we explored theoretically and practically the structure of FM images.

1 Considerations for FM Image Grids In the printing process, the larger the dots, the more stable the printing process, and the fine dots will cause various transfer problems. Therefore, micro structures smaller than the minimum printable point (11 μm in diameter on smooth paper and 20 μm in diameter on rough paper) should not appear during printing.
It is not necessary to be below the minimum printable point, because the "color particles" of the photo image can also reach this size. The silver salt image has a smaller "positive color granule" at the bright spot, while the dark spot also has a smaller "negative color granule" due to the color granule expansion. So in printing, both the positive and negative points should have the same minimum diameter. The entire image should be divided into the same area elements at the time of recording. Each area element is either inked (positive dots) or not inked (negative dots). The area elements can only be several times larger than the minimum printable point because they are larger than the smallest printable point on the one hand and the highest possible number of recording lines on the other hand. We call this selected minimum printable point a recording grid.
In photographic images, different tones are achieved by frequency modulation. In the bright spot, a smaller image area contains less silver particles, and in the shadow area, the same size image area has more silver particles. Similarly, the smaller the number of recording grids in which the brighter parts of the printed image are inked, the more darker the parts are the more inked recording grids. So the principle of photometric modulation can also be used to print images.
In order to obtain the gradation of the photographic image, we divide it into the same size image area. The number of silver grains in each image area is used as the tone value, and the density range is independent of the size of the image area. At the lowest density, no silver particles appear in this image area; at the highest density, the image area becomes completely dark. This extreme case also exists in printed images, and the density range of the FM image structure is limited only by the density of the field and the density of uninked white paper.
The fineness of the recording grid depends on the minimum printable point of the transfer process, and the size of the image area is closely related to the tone level. In extreme cases, the image area consists of only one record grid. This grid is either inking or not inked, so there are only two tone levels when recording. We can make the area contain any number of record grids. If an image area consists of K record grids, then the tone progression Z of the image area is: Z=K+1
The number of gradation steps should at least render the printed image visually indistinguishable from the rest, thereby showing a continuous effect. The human eye can generally distinguish 70 tones. Therefore, at least 100 tone levels are required for printed images to avoid a step transition.
We can not change the size of the image area in an image, that is, divide the image into a grid of regions by the size of the image area. If the image area grid is superimposed with the recording grid, the image is divided into two grids at the time of recording. That is, the grid of the image area is first divided, and then the image area is further subdivided by the recording grid (Figure 2). . If the recording grid width is 25 μm, the corresponding image area grid width should be at least 250 μm (since at least 100 tone levels are required).

At first glance, the grid of the image of the FM image structure is similar to the image structure of the AM screen. However, we can choose a much lower number of grid lines (eg, 40 lp/cm) than the number of screened grid lines (about 50-80 lp/cm). Of course, the resolution of the FM structure will not be reduced as a result. Because from the consideration of this article, the resolving power of the structure of the frequency modulation image has nothing to do with the size of the image area, so it has nothing to do with the fineness of the area grid. The grid of regions can be understood as a mesh that is dependent on the reproduction of the tone level and therefore cannot be compared with the mesh of the amplitude modulated image structure. The resolution of the FM image structure mainly depends on the resolution used to scan the original. Scanning is the same as the scanning of the AM structure. The original must be divided into tiny image points so that the image can be divided into image grids (see Figure 2). However, the scanning resolution of the FM and AM structures is significantly different. The resolving power of photographic images is generally more than 200 lp/cm. To achieve this resolving power of the FM image, it is necessary to use a fine scan image point grid scan. Therefore, the mesh of the image of the FM image structure is significantly higher than that of the AM structure.
From the above, it is known that the image area can be subdivided by the recording grid, and likewise, an image area grid can be subdivided into the scanning image point grid. Therefore, we have established the modulation processing of FM images on the basis of image processing (see the section “Overlapping image areas with different details”).
Scanning the mesh of points can achieve the fineness of the recorded mesh. At this time, each image point can be recorded in two levels. It can be either an inked point or an inkless point. We can make the grid width of the scanning point twice as large. Then each grid of the image points contains 4 recording grids, and the number of tone levels per pixel is 5 (in Figure 7 each pixel contains 9 record grids). In this way, on the one hand, the number of gradations in the mesh of pixels divided by the resolution of the photographic image is similar, and on the other hand, the scanning resolution can be appropriately reduced.

2 The relationship between tone reproduction and resolution The scanned image data is the brightness of the original. With computer processing (see experimental section), the input luminance value can be converted to the print recording point output. The scanning dot mesh divides the original into cells and the recording grid is used to restore the brightness value of each cell. In amplitude-modulated images, the fineness Ls of the grid of scanning spots must match the fineness Lr and tone progression n of the recording grid, ie Ls=Lr/n.
In FM image structure, not only the number of tonal orders exceeds the critical resolution of the human eye (above 100), but also the resolving power of resolution is achieved. This requires that the fineness of the scanning spot mesh reaches 200 lp/cm or more (for example, 250 lp/cm), and the fineness of the recording grid reaches 500 lp/cm. There are only 5 levels that can be copied at this time. However, we can achieve the necessary number of tone levels in the FM image structure by processing the image area. The size of the image area, that is, the number of grids of scanned image points contained in the image area can be arbitrarily selected. For example (see Figure 6), an image area contains 6 x 6 grids of scan pixels. Each scan grid contains only 9 grids, and only 10 levels can be copied. The area contains 324 record grids. If the image area is used as a processing unit, 324 recording grids can replicate 325 tone levels. Of course, we can also design the area to replicate only 100 tone levels.
3 Considerations for Image Detail Restoration

There are many details on an image. We can distinguish and evaluate an image detail based on luminance difference and detail contour. It is important to distinguish image details when using frequency modulation because each detail has a frequency corresponding to the tone when recording.
In the image data stored after the original is optically scanned, an image detail can be expressed in such a way that n adjacent pixels having the same tone value or the same density value belong to the same image detail. Consider, for example, an image area consisting of 8 x 8 pixels. In the image database it is a matrix containing 8 x 8 luminance values. Each image detail can be distinguished based on the brightness value of each image point (Figure 3). The image points contained in each image detail have approximately the same brightness value and are adjacent to each other. The scope of a detail is the distribution of the positions of the pixels it contains in the matrix. The gradation value of a detail is the average value of the brightness of the pixels it contains.
When the original is photoelectrically scanned, the noise is not completely eliminated, and the luminance values ​​of the pixels in the same detail obtained by scanning are different from each other. At this time, the outline of the detail is discriminated such that the difference between the luminance of the pixel belonging to a certain detail and the luminance of the median is far smaller than the difference between the luminance of the other pixels and the luminance of the median. Therefore, as long as the noise is small, the maximum difference between the median brightness of the details and the brightness of the pixels belonging to that detail can be given.

4 Avoiding "Moiré" considerations in FM images The arrangement of printed dots in a FM image structure depends on the tone value, matching the distance between printed dots to the tone value. However, a regular arrangement of printing dots may occur when the tone value is constant, resulting in "moiré" in multi-color printing. To avoid this situation, we overlap the frequency modulation grid with a random grid to simulate the image structure of the photographic original.
The silver particles are randomly distributed on the photographic continuous tone image. The random distribution of printing points can theoretically be achieved by means of a random auxiliary matrix. For example, in a 4×4 matrix, 16 numbers such as 1, 2, ..., 16 are randomly distributed in 16 grids to form a random matrix (Figure 4).

The random matrix in FIG. 4 corresponds to one detail consisting of four image points. A critical value is found by comparing the random elements in the random matrix with the gradation values. A random number less than the critical value is the printed point, which constitutes a print matrix. This example corresponds to the tone value. Select 1, 2, and 3 from the random matrix as the position of the printing point in the printing matrix, and the remaining points are not colored.
This method is based on the comparison of random numbers with tone signals and is used in inkjet printers. Its disadvantage is that the distribution of printed dots is entirely determined by the distribution of random numbers, so it may be due to the low degree of randomness, the accumulation of printed dots, or the unsightly structure due to the small change in the position of random numbers.
To avoid this situation, we use the principle of frequency modulation as much as possible. According to the area percentage of a detail, the details are divided into several blocks. The number of printing points in a detail is np, the number of recording points is nr, and the number of sub-blocks is ni. Then: ni=nr/np Then, only one random number is taken as the printing point in each sub-block. For example, the detail adjustment F=25%, nr=16, np=F·nr=25%×16=4 (four printing points), ni=nr/np=16/4=4, the image details are divided into Four blocks, each block containing four record points, one record point (random number) in each block as a printing point (Figure 5).
If the area percentage of a certain detail is small, random numbers can be generated for a few recording points in a block, and random elements are not given to other elements (such as edge points of a block), so that the distribution of printed dots can be made more uniform.