Discrete image. Analog and discrete image view of graphic information

Images consisting of discrete elements each of which can only receive a finite number of distinguishable values \u200b\u200bthat change in the final time are called discrete. It should be emphasized that the elements of the discrete image, generally speaking, may have an unequal area and each of them may have an unequal number of distinguishable gradations.

As shown in the first chapter, the retina transmits discrete images to the highest departments of the visual analyzer.

Their apparent continuity is only one of the illusions of view. This "quantization" of initially continuous images is not determined by the constraints that are associated with the resolution of the optical system of the eye and not even the morphological structural elements of the visual system, but the functional organization of nervous networks.

The image is divided into discrete elements by recipe fields that combine one or another number of photoreceptors. Recipe fields produce primary selection of the useful light signal by spatial and temporal summation.

The central part of the retina (Fovaa) is occupied only by the columns, on the periphery outside the Fovaa, there are both columns and wands. Under nightlife conditions, the colummer fields in the central part of the retina have approximately the same value (about 5 "in the angular measure). The number of such fields in Fovaa, the angular dimensions of which are about 90", about 200. The main role in nightpoints is played by sticky fields. The rest of the retina surface. They have an angular size of about 1 ° all over the entire surface of the retina. The number of such fields in the retina is about 3 thousand. Not only detection, but also the viewing of weakly illuminated objects under these conditions is performed by peripheral sections of the retina.

With an increase in the illumination, the main role is started to play the other cumulative cells - columine receptive fields. In Fovaa, an increase in illumination causes a gradual decrease in the efficient value of the field, while the brightness of the order of 100 ASB does not reduce to one columination. On the periphery with increasing illumination gradually turn off (brake) sticky fields and the columns come into effect. Colummer fields on the periphery are like a fowel with the ability to decrease depending on the light energy falling on them. The greatest amount of colums that can have columine receptive fields with increasing illumination, grows from the center to the edges of the retina and at the angular distance of 50-60 ° from the center reaches approximately 90.

You can calculate that in the conditions of good day lighting The number of recipe fields reaches about 800 thousand. This value approximately corresponds to the number of fibers in the audience nerve of the person. The distinction (permission) of objects in daylight is carried out mainly by Fovtea, where the receptive field can be reduced to one columination, and the columns themselves are located most tight.

If the number of rigid cumulative cells can be determined in a satisfactory approximation, then there is no sufficient data to determine the number of possible conditions of recipe fields. Only some-estimates can be made based on the study of differential rapids of recipe fields. The threshold contrast in the foxal receptive fields in a certain working range of illumination has order 1. At the same time, the number of distinguishable gradations is small. In the entire range of perestroika, the colummer fowel recipe field differs 8-9 gradations.

The period of accumulation in the recipe field is the so-called critical duration - is determined by an average of about 0.1 seconds., But at high levels of lighting, it can seem to significantly decrease.

In fact, the model describing the discrete structure of the transmitted images should be even more complicated. It would be necessary to take into account the relationship between the size of the recipe field, thresholds and critical duration, as well as the statistical nature of visual thresholds. But so far there is no need for this. It is enough to present as a model of the image the set of the same in the area of \u200b\u200bthe elements, the angular sizes of which are smaller than the angular dimensions of the smallest-resolved part of the part, the number of distinguishable states of which are greater than the maximum number of distinguished gradations of brightness, and the time of the discrete change of which is smaller than the fracture period during critical Freight frequency flashes.

If you replace images of real continuous objects external world Such discrete images, the eye will not notice the substitution. * Consequently, discrete images of this kind contain at least no less information than the visual system perceives. **

* Color and volumetric images can also be replaced by a discrete model.
** The problem of replacing continuous images is discrete is important for film and television techniques. Temporary quantization underlies this technique. In the pulse-code television systems, the image, in addition, is divided into discrete elements and quantum on brightness.

In the previous chapter, we studied linear spatially invariant systems in a continuous two-dimensional area. In practice, we are dealing with images that have limited sizes and at the same time are counted in the discrete set of points. Therefore, the methods developed so far need to be adapted to expand and modify so that they can be applied in such a region. There are also several new moments that require careful consideration.

The countdown theorem indicates that under what conditions on a discrete set of values \u200b\u200bcan accurately restore a continuous image. We also learn what happens when conditions of its applicability are not performed. All this is directly related to the development of visual systems.

Methods requiring the transition to the frequency domain became popular in part due to quick calculation algorithms discrete transformation Fourier. However, care must be taken, since these methods assume the presence of a periodic signal. We will discuss how to meet this requirement and what leads to his violation.

7.1. Image size limit

In practice, images always have finite sizes. Consider a rectangular image of the width and height of Ya. Now there is no need to take integrals in the Fourier transformation in infinite limits:

It is curious that to restore the function, we do not need to know at all frequencies. Knowing that when it is a rigid restriction. In other words, a function other than zero only in a limited area of \u200b\u200bthe image plane contains much less information than a function that does not have this property.

To make sure that you will imagine that the screen plane is covered with copies of a specified image. In other words, we are expanding our image to periodic in both directions of the function

Here is the greatest integer that does not exceed x. Fourier transformation of such a multiplied image has the form

With appropriately selected convergence factors in UPR. 7.1 It is proved that

Hence,

how we see that is zero everywhere, except for a discrete dialing of frequencies in such a way as to find us enough to know at these points. However, the function is obtained from a simple cut-off of the area for which. Therefore, to restore it enough for us only for all this is a countable set of numbers.

Please note that the transformation of the periodic function turns out to be discrete. Reverse transformation can be represented as a row as

Another way to verify this is to consider the function as a function obtained by cutting some function for which inside the window. In other words, where the feature of the window is determined as follows.

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Laplas transformation - Laplace transformation Integrated conversion connecting the function of a complex alternating (image) with a real variable function (original). With it, the properties of dynamic systems are investigated and resolved ... ... Wikipedia

Laplace transformation

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GOST R 52210-2004: TV broadcast digital television. Terms and Definitions - Terminology GOST R 52210 2004: TV broadcast digital television. Terms and definitions of the original document: 90 (television) Demultiplexer: A device intended for separating the combined data streams of digital television ... ... Dictionary directory terms of regulatory and technical documentation

Compression video - (eng. Video Compression) Reducing the number of data used to represent the video stream. Video compression allows you to effectively reduce the stream required to transfer video through broadcasting channels, reduce space, ... ... Wikipedia

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