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a filtering spektrozonalnyh images

The filtering of images is fathomed as operation in which result the image of the same size gained from initial on some rules is gained.

Procedure of a filtering of difficult structured images is the most rational procedure, various aspects of a filtering are resulted in [51-56].

Let's observe the most used from them.

Linear filtering

The given type of a filtering finds wide application in optical systems of machining of the information. It is based on application of sweeping algorithms of convolution and the analysis of spectral ranges.

In the capacity of the linear hum filter the averaging filter which target value is the mean on a neighbourhood of a mask of the filter is used.

The given filtering can solve a problem of graininess of the image.

The linear filter can be written down as follows:

Where Gi, j - an element of a matrix of the image after a filtering; Ws, t - an element of a file of a kernel of convolution of the image, measuring m? ιr, Eij - an element of a matrix of the initial image.

Vinerovsky filtering

The given type of a filtering considers aprioristic value of statistical properties of noise on processed images that allows to raise their quality. In a basis it is assumed vinerovsky the filter used at local machining of images. If value of an average quadratic

Deviations intensivnostej pixels in local area of the image high the given filter carries out small smoothing and on the contrary: if value of an average quadratic deviation of intensity of pixels in local area low the filter should carry out the big smoothing.

Use of the given type of a filtering is more effective, than a usual linear filtering. Advantage is that it keeps edges and other parts of installations of the image. A deficiency vinerovskoj filterings is the big computing time.

Frequency filtering

The frequency filtering is based on the Fourier transforms which sense consists in representation of initial function in the form of the sum of trigonometrical functions of the various frequencies increased by set factors.

Use of a frequency filtering allows to process images in frequency area then without information loss to return to an initial aspect.

The space filtering

The space filtering is applied to the half-tone images presented in the form of two-dimensional matrixes. The principle of the space filtering consists in application of special operators to each point of the initial image. In the capacity of operators the right-angled or square matrixes named masks act. More often the mask represents a small two-dimensional file.

The co-ordinated filtering

The given type of a filtering is applied in machining of images to detection and allocation of installations on images.

In a case when the aspect of a detected image (scene) is known, the co-ordinated filtering is applied, that is the filters which have been adjusted precisely under the expected aspect of an image or a scene are used.

Inverse (return) filtering

The return filtering is applied to the optiko-electronic systems working with images on which there is a considerable quantity of external noise.

The given type of a filtering is applied in a case when the legitimate signal and the originated handicap have frequency composition close to each other.

Vejvlet-filtration

The term "vejvlet" (with English «a small wave») has appeared for the first time in the mid-eighties in connection with the analysis seismic and an audible signal. Now vejvlety studying of properties of turbulent fields, compression of great volumes of the information and in many other things cases have found wide application in problems of a pattern recognition, machining of various signals, the analysis of various images.

The main difference of vejvlet-transformation from widely used Fourier transform consists that it provides two-dimensional development of a signal, thus its frequency and co-ordinate are observed as independent variables that allows to carry out the signal analysis simultaneously in physical and frequency spaces.

In scientific researches which observe time-and-frequency dynamics of difficult processes and systems, it is often used continuous vejvlet - transformation. It is builted on use of analytical base-load functions [57-59]. Such aspect of vejvlet-transformation is evident and informative alternative, however has such deficiency as redundancy. Many factors contain the information which is doubled in others
Factors that leads to essential increase in a time for conducting of scalings. Speed of scaling continuous vejvlet - transformations essentially restricts possibility of machining of images real time.

In this connection there were algorithms of discrete vejvlet-transformation which considerably score on speed of scaling [60,61].

The given approaches on the basis of continuous vejvlet-transformation and discrete vejvlet-transformation have different principles of construction: or in the form of tables of values of factors of filters, or in a record analytic form.

Application of discrete vejvlet-transformation for digital machining and a filtering of images is more interesting approach on comparison with often used Fourier transform because there is a possibility of effective elimination of local handicapes. Discrete vejvlet - transformation makes image decomposition on components in different scales of observation [62].

The improved method of discrete vejvlet-transformation is the method of dual complex vejvlet-transformation. The given method provides independent scaling of two discrete vejvlet-transformations therefore the valid and imaginary parts of vejvlet-factors [63] are defined.

The spent experimental researches have shown, that the given method is modernisation of discrete vejvlet-transformation. It keeps all advantages of discrete vejvlet-transformation, but also in addition allows to work with amplitudes and phases of vejvlet-factors.

Despite development of various methods of digital machining of the images using vejvlet-transformation, the problem of sampling of a concrete way of a filtering remains actual.

As a whole machining of images includes two stages: preparative treatment which helps to improve properties of the initial image, and

The thematic machining which purpose is extraction of the information necessary for a user.

Any of procedures of machining of images leans against model of the class-room of images - the formalized description. The role of the given model consists in maintenance of the adequate description of properties of the class-room of images which will allow to carry out computing procedures further effectively.

In many cases real images can be presented model of a casual field in the form of the sum two component:

s (h,) = s1 (x, y) + S2 (x, y), (1.1)

Where s (h,) - a luminance field, h, at - the arguments defining an image plane, s 1 (h,) - slowly changing field of two variables, s 2 (h,) - a stationary field.

The model presented above well works with vejvlet-decomposition f (h,) as it can be presented in the form of the sum two component: where ι. i ', ⅞ - a set of factors, - casual fields with normal

Distribution, y (.v, y) - Fourier transform, - the residual function of threshold machining.

In the majority of problems in the capacity of base-load functions for implementation of discrete vejvlet-transformation apply vejvlety Dobeshi [64], for the first time 20th centuries used in 80-s' years. Procedures sweeping vejvlet - transformations on a basis vejvletov Dobeshi are used for conducting of various calculations.

In a case when the L / l ’, vejvlet Dobeshi represents function which is defined as follows:

Where L;..... - constant factors which fulfil

To condition

Let's observe algorithm of a filtering of images on the basis of discrete vejvlet-transformation.

1 step. Unitary passage of quadrature mirror-image filters by a signal x (i).

2 step. Thinning out of target images.

3 step. Resupply of the thinned out images on an entry of filters.

In spite of the fact that each of time rows has a range of frequencies twice less, than the image to a filtering, at return transformation to rebuild the initial image was possiblly thanks to presence of two sequences on exits of each of filters.

Magnitude of a threshold and alternative of the task of a threshold function strongly influence quality of a filtering of the image. Therefore important correctly to choose alternative of the task of a threshold function.

In drawings 1 three alternatives of the task of a threshold function for factors of vejvlet-transformation [65] are represented.

Drawing 1.12 - the threshold function Task at a vejvlet-filtration: an initial signal, rigid alternative of the task of a threshold function

Drawing 1.13 - the threshold function Task at a vejvlet-filtration: soft alternative of the task of a threshold function

Observing alternative 1.12а), it is possible to draw a leading-out that absence of correction of factors is observed.

For alternative 1.12б) function is set by a following aspect:


At such alternative invariable there are the most significant vejvlet - factors, and small factors are nulled.

For the alternative presented in drawing 1.13, the threshold function can be presented as follows

At work with images decomposition procedure on vejvletam provides transition from one-dimensional to two-dimensional implementation of discrete vejvlet-transformation. In the course of machining the initial image at each stage decomposes on four images of more smaller size.

To size up efficiency presented above approaches of sampling of the task of a threshold function, it is necessary to inject concept of an average quadric error (SKO)

Where x (i) - an initial signal with handicapes, y (i) - the filtered off signal, ∖x (i) - y (i) ∖ - a noise component.

SKO gives the chance to spend comparison of two signals and on its baseline to see all differences and similarities between two signals. Whether during each moment of a time there is an estimation of the gained errors from two signals without dependence there are on them handicapes or not then there is a process of its averaging. It is important, that the mean-square error does not depend on the space or time parametres of an initial signal.

Except an average quadric error at the analysis of images observe the relation a signal/noise

At the analysis of images of a relationship (1.6) - (1.7) it is necessary to write down as follows:

67

In any linear space it is necessary to define the distances computed through norm [66].

Let function i ', γr, (Λj1 (i ∈1 ζ {0], b to it forms a set of such functions, each of which is gained by shift operations and scaling of the same initial function ⅛ (v) ∈L2 (R k

Normalisation (1.8) secures, that the norm does not depend on parametres and and b.

Function / ' Ј2 (the L] will be called vejvletom at condition performance

Admissibilities:

Where ⅛ ‰) - function Fourier transform ⅛∙ ' (. γ).

The condition of an admissibility (1.9) leads to following property vejvleta:

That shows good localisation of function.

Let a prescribed function / (.

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A source: TITOV Dmitry Vitalevich. WORKING out And RESEARCH of METHODS, ALGORITHMS And HARDWARE COMPONENTS of MACHINING SPEKTROZONALNYH of IMAGES. The dissertation on competition of a scientific degree of a Dr.Sci.Tech. Kursk - 2018. 2018

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  1. a filtering zashumlennyh images at a preliminary stage of machining spektrozonalnyh images
  2. theoretical bases of a filtering spektrozonalnyh images at a predesign stage zashumlennyh images.
  3. the apparatus-oriented algorithm of the space filtering spektrozonalnyh images
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  9. CHAPTER 2. METHODS AND ALGORITHMS OF MACHINING SPEKTROZONALNYH OF IMAGES ON THE BASIS VEJVLET - TRANSFORMATIONS
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