• Graphic images from analog (continuous) form to digital (discrete) are converted by spatial sampling.
• Spatial discretization of an image can be compared to building an image from a mosaic ( a large number small multi-colored glasses).
• The image is divided into separate small elements (dots, or pixels), and each element can have its own color (red, green, blue, etc.).

• The most important characteristic of the quality of a raster image is the resolution.
• The resolution of a bitmap image is determined by the number of dots both horizontally and vertically per unit length of the image.
• The smaller the dot size, the greater the resolution and, accordingly, the higher the image quality.
• 1 inch = 2.54 cm

• During the sampling process, different color palettes can be used, i.e. sets of colors in which image points can be painted.
• Each color can be considered as a possible state of the point.
• Number of colors N in the palette and the amount of information I , required to encode the color of each point are related and can be calculated by the formula:

2 = 2 i= 2 1 = 2 i = i=1 bit.

Color depth, (bits)

The number of colors in the palette N

2 24 =16 777 216

• The image quality on the monitor screen depends on the spatial resolution and color depth.
• The spatial resolution of a monitor screen is defined as the product of the number of image lines by the number of dots per line. The monitor can display information with various spatial resolutions (800 x 600, 1024 x 768, 1152 x 864 and above).

• The greater the spatial resolution and color depth, the higher the image quality.
• AT operating systems it is possible to select the required and technically possible graphics mode for the user.

• The information volume of the required video memory can be calculated by the formula:
• where I- information volume of video memory in bits;
• X Y- the number of dots in the image (X - the number of dots horizontally, Y- vertically);
• I- color depth in bits per point.

• Example: the required amount of video memory for graphics mode with a spatial resolution of 800 x 600 pixels and a color depth of 24 bits is:
• 1 P = I*X*Y = 24 bits x 800 x 600 = 11,520,000 bits = = 1,440,000 bytes = 1,406.25 KB ~ 1.37 MB.

• The quality of information displayed on the monitor screen depends on the screen size and pixel size. Knowing the screen diagonal size in inches (15", 17", etc.) and the screen pixel size (0.28 mm, 0.24 mm or 0.20 mm), you can estimate the maximum possible spatial resolution of the monitor screen.

The cardinal problem of numerical modeling of migration processes is discretization in space and time. In spatial discretization, the finite difference method (FDM) and the finite element method are most often used.

Processing of graphic information

Coding and processing of graphic and multimedia information

Spatial Discretization

Graphical information can be presented in analog and discrete forms. An example of an analog representation of graphic information is a painting canvas, the color of which changes continuously, and a discrete one is an image printed with an inkjet printer and consisting of separate dots of different colors.

Graphic images from analog (continuous) form to digital (discrete) are converted by spatial discretization. Spatial discretization of an image can be compared to the construction of an image from a mosaic (a large number of small multi-colored glasses). The image is divided into separate small elements (dots, or pixels), and each element can have its own color (red, green, blue, etc.).

Pixel- the minimum area of ​​the image for which you can independently set the color.

As a result of spatial discretization, graphic information is presented in the form bitmap, which is formed from a certain number of lines containing, in turn, a certain number of points (Fig. 1.1).

Resolution. The most important characteristic of the quality of a raster image is the resolution.

Resolutionbitmap is defined by the number of dots both horizontally and vertically per unit length of the image.

The smaller the dot size, the greater the resolution (more raster lines and dots per line) and, accordingly, the higher the image quality. The resolution value is usually expressed in terms of dpi(dot per inch - dots per inch), i.e., in the number of dots in an image strip one inch long (1 inch = 2.54 cm)

Spatial discretization of continuous images stored on paper, photo and film can be done by scanning. Currently, digital photo and video cameras are becoming more widespread, which capture images immediately in a discrete form.

The quality of bitmaps resulting from scanning depends on the resolution of the scanner, which manufacturers indicate with two numbers (for example, 1200 x 2400 dpi)

Scanning is performed by moving a strip of photosensitive elements along the image. The first number is optical resolution scanner and is determined by the number of photosensitive elements on one inch of the strip. The second number is hardware resolution; it is determined by the number of "microsteps" that the strip of photosensitive elements can take, moving one inch along the image.

Color depth. The sampling process can use different color palettes, i.e. sets of colors in which image points can be painted. Each color can be considered as a possible state of the point. The number of colors N in the palette and the amount of information I required to encode the color of each point are related and can be calculated by the formula:

In the simplest case (black and white image without grayscale), the color palette consists of only two colors (black and white). Each dot of the screen can take one of two states - "black" or "white", therefore, by formula (1.1) it is possible to calculate how much information is needed to encode the color of each dot.

or why the resolution of the file must be at least twice the lineature of the raster

A characteristic feature of modern printing systems processing of halftone originals is that both the spatial discretization of the image and the quantization of its tone by level are carried out in them at least twice. Spatial discretization is the replacement of an image whose tone changes arbitrarily in the X and Y coordinates with an image composed of separate sections - zones within which this parameter is averaged. In the general case, as already mentioned, the sampling frequency should be at least twice the frequency of the harmonic component of the original image to be reproduced on the copy. This position is illustrated schematically in Fig. 1 (a), at position a) of which the original continuous message is a sinusoidal oscillation u(t) with period T. The spectrum of such a signal consists of a constant component and the first harmonic:

u \u003d U 0 + U l sin (27tt / T)

Rice. one.

The original signal (a), its sample values ​​and the modulation depth (%) at zero (b), opposite (c) and intermediate (d) phase of the sampling frequency.

At the zero phase of discrete readings U D period T/2 the depth of their modulation by the first harmonic of the original signal is zero, and information about the frequency is completely lost. Only the average value is transmitted U 0 the original signal (see Fig. 1, b). With a change in the phase of counts by half of their period, the modulation depth turns out to be equal to 100% (see Fig. 1, c). Intermediate between the considered phases of readings are accompanied by distortions in the amplitude and phase of the first harmonic, although, as the graph in Fig. 1(d), information about its frequency is preserved. At least one-dimensional (in one of the coordinates) discretization of images accompanies the process of electro-optical analysis. In analog reproduction systems and in television, an optical parameter, which is a function of the coordinates of the original or the transmitted scene, is converted into the amplitude of an electrical signal that changes at the output of the photoelectric cell in time during progressive reading (scanning). The spectrum of spatial frequencies of the image in the direction transverse to the horizontal scanning direction is limited by the frequency of decomposition into lines. Due to the finite dimensions of the scanning spot (aperture), this spectrum is also limited along the lines by a frequency reciprocal of this spot. The second reason for limiting the frequency spectrum and sampling the image along the line is the video signal modulation of the amplitudes, phases or frequencies of an additional electromagnetic wave - the carrier frequency necessary for signal transmission, for example, in television or in analog remote (using electrical communication channels) reproduction. Two-dimensional (in both coordinates) sampling and quantization take place during the so-called analog-to-digital conversion of the video signal, as a result of which the set of spatial samples of the tone value can be represented by some array of numbers written, for example, in binary code. This representation allows you to abstract from the real scanning time and perform functional transformations of tone, color, small details, contours and other image content as operations on the numbers of this array. For such purposes, PCs are now effectively used.
Spatial discretization also accompanies rasterization - the representation of an image in the form of a set of sealed and blank elements, the relative area of ​​which is determined by the tone or color of the corresponding sections of the original. In this case, as already mentioned, the frequency of the first sampling associated with electro-optical analysis and analog-to-digital conversion is taken, as a rule, in twice exceeding the lineature of the polygraphic raster, or rather, the frequency of the raster function, within the period of which one or another number of raster dots and spaces is formed. If this condition is met, then when reproducing a system of periodic strokes of an arbitrary spatial phase, the sizes of neighboring points will at least slightly differ from each other in all cases except for one: when the strokes themselves are shifted by exactly half a period relative to decomposition element 1 and the raster cell. On the print, instead of strokes, a uniform field of identical raster dots with a relative area of ​​50% is formed (see Fig. 2, d), since the reflectance of the original, averaged over the area of ​​the reading spot I, has the same (intermediate) value for all elements of the raster. In the reference zone 7, each time there is half a stroke and half a space (see Fig. 2, c). This case is similar to that shown in Fig. 1(b).

Rice. 2.
The strokes of the frequency 0.51 in the raster grating of the L lineature at the same (a) and opposite (b) phases; their raster copies: b, d - with reading element 1 equal to the lineature pitch; e - at readings of 2 twice as small raster steps.

In all other spatial phases, the stroke contrast on reproduction turns out to be higher, since the values ​​of neighboring readings and the sizes of the raster dots formed in accordance with them differ. The maximum difference occurs in the opposite extreme case, when, as shown in Fig. 2 (a, b), the strokes of frequency 0.51 coincide in phase with the raster grating. Here there is an analogy with the case illustrated in Fig. 1 (a, c). They are transmitted in a raster twice the lineature, equal to L lines / cm, without loss of contrast. The guarantee of transmission of strokes with full contrast, regardless of their spatial phase, is provided by a decomposition frequency that is twice the raster lineature, as Fig. 2 (e). Since at least two spatial discretizations of the image take place in polygraphic reproduction, it follows from the above simplified example that a two-fold decomposition frequency margin must be provided twice. The first time you have to do this is when choosing the screen lineature, if the task is to reproduce certain spatial frequencies of the original on the print. A second margin of 2, this time in relation to the selected lineature value, is set for the scan rate of the original. For example, to reproduce strokes that have a frequency of 4 lines / mm on the original, a print lineature of 80 lines / cm (~ 200dpi) is required (as well as the corresponding paper smoothness and other print parameters). It is necessary to read such an original when scanning at a frequency of 16 lines / mm (~ 400ppi). The degree of destruction of contours and fine details in the raster process is somewhat reduced if the sampling frequency, in accordance with the provisions of the sampling theory, is twice the raster lineature (see Fig. 3, e, f).

Rice. 3.
« Funnel (a) and random (b) distribution of weight values; images of contour 1, which separates on the original sections with absorption 0.94 and 0.04, based on one (c, d), four (e, f) and 64 (g, h) readings per raster period;
2 - analysis reference zone

The section of the original intersected by the contour is represented in this case by four counts of different values. Four fragments of the corresponding section of the copy are formed according to different signs of the “alphabet” of dots. The shape of the area printed inside the area is modulated by the geometry of the contour, and the latter is rendered with greater graphical accuracy and sharpness. This effect is clearly illustrated by the model in Fig. 4 (d) in comparison with those presented in fig. 4(b, c).

Rice. 4.
Line elements (a) of a halftone original and their bitmap copies using:

• one (b, c, e) and four (d, f) samples in the period of the raster function;
• unsharp masking of a numeric array (c);
• shifts of raster dots (e) and their fragments (e) on the contours.

The accuracy of the full contrast contour transfer further increases with the increase in the reading frequency of the original and turns out to be at the level of the resolution of the output device, when each synthesis element in the original video array corresponds to an independent multilevel reading (see Fig. 3, g, h). The reference zones, as a rule, are almost an order of magnitude larger than the dimensions of the synthesis elements and cannot be significantly reduced. Otherwise, excessively, on average by two orders of magnitude, the already large volumes of illustration files, amounting to tens and hundreds of megabytes, increase. Accordingly, the capacity of storage devices, the time for processing and exchanging video information between various modules and workstations of pre-press systems, the transmission time or the occupied bandwidth for remote reproduction increase. In practice, they are limited to only a twofold excess of the sampling rate over the lineature, which corresponds to the examples in Fig. 3 (e, f) and fig. 4(d). Such modes and reproduction systems are conditionally referred to as coarse scan / fine print systems (coarse reading / clear printing). The number of readings equal to the number of synthesis subelements, i.e. fine scan / fine print modes, are found only in continuous tone output devices or inkjet digital printing with relatively small image formats, low input / output resolutions (about 12-24 lines /mm (300-600dpi)) and in this regard, low lineatures.

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