RU2695417C1 - Method for noise-immune gradient selection of object contours on digital halftone images - Google Patents

Abstract

FIELD: data processing.

SUBSTANCE: invention relates to image processing and can be used in photo, video, optical-location and optical-electronic equipment when solving tasks of pattern recognition by their contours on images. Method's essence consists in that, taking into account the noise level of the image, the smoothing coefficient is selected, coefficients of smoothing cubic B-splines are calculated along each line and each column of the image. Then two matrices G^x and G^y component of the brightness gradient at each point of the image by summation of smoothing parabolic B-splines with coefficients of smoothing cubic B-splines found earlier for rows and columns. Further, a brightness gradient module is determined at each point of the image. After that, contours of the object are formed by converting a brightness gradient module, during which elements on the new white matrix are selected with black colour, the modulus of the gradient for which in the image coordinates exceeds the transformation threshold.

EFFECT: high rate of extracting contours of halftone images in conditions of pulse interference.

1 cl, 3 tbl, 5 dwg

Description

The invention relates to the field of digital image processing and can be used in photo, video, optical-location and optical-electronic equipment in solving problems of pattern recognition by their contours in digital images.

The necessary conditions for a contour to pass through some point of a digital grayscale image are as follows:

- a sharp change in brightness at a given point compared to at least one of the neighboring points;

- the presence of at least two neighboring points comparable in brightness with the point in question.

In this regard, most of the known methods for selecting contours in digital grayscale images are based on the calculation of the gradient modulus over the entire area of the digital image using the approximations of the first derivative — local finite brightness differences. In this case, the approximate components of the gradient are calculated using a sliding window (mask) moving throughout the image. In this case, the brightness of the image pixels falling into the sliding window is multiplied by the mask coefficients, and then summed [1 - Gonzalez R., Woods R. Digital image processing. -M .: Technosphere, 2005, 1072 pp .; 2 - Gonzalez R., Woods R., Eddins S. Digital image processing in MATLAB.-M .: Technosphere, 2006, 616 pp .; 3 - Pratt W. Digital image processing: Transl. From English. - M .: Mir, 1982. Book 2. 480s .; 4 - Gdansky N.I., Marchenko Yu.A. Gradient way to highlight the contours of objects on a halftone raster image matrix. // RF patent №2325044 for the invention. IPC H04N1 / 409, G06K9 / 46. Will declare. Gdansky N.I., Marchenko Yu.A. Patent. MGUIE. - No. 2007106412/09; declared 02/21/2007; publ. 05/20/2008.].

Currently, several types of masks are known: Roberts, Prewitt, Sobel, Shcharr, etc. The Roberts mask is the simplest because it has a size of 2x2 pixels. The masks of Prewitt, Sobel and Shcharr have a dimension of 3x3 pixels and differ in the values of the coefficients. It should be noted that similar masks for calculating the components of the brightness gradient using finite differences are used as part of more complex contouring algorithms. One of the best such algorithms is the Canny border detector, which uses, in particular, the Sobel mask. The disadvantages of the methods for isolating the contours of images based on the use of sliding windows and determining the components of the brightness gradient using finite differences are their rather strong sensitivity to noise belonging to the class of pulsed arising due to many phenomena during digital conversion and transmission of images (affected pixels).

Other methods for isolating the contours of objects in images include methods based on calculating the approximations of second derivatives — operators of the Laplacian and Gaussian type, or operators using varieties of Laplace masks. A correlation mask is also known, the coefficients of which are proportional to the corresponding correlation coefficients of image elements. In the case where there is no correlation between the image elements, the mask does not affect the image; in the opposite case, the correlation coefficient is unity, this mask reduces to the Laplace mask [Pratt W. Digital image processing: Trans. from English - M .: Mir, 1982. Book 2, 480c., C.500-508.]. These methods, due to the intersection of the zero level of the straight line connecting the ambiguous second derivatives, make it possible to obtain a more accurate position of the contour, but they are more sensitive to various noises, including pulsed than gradient ones, and also have the disadvantage associated with the detection of numerous false closed curves.

Also known are methods of isolating the contours of objects in images that are farther from the proposed method, which are based on approximating brightness differences and statistical methods, for example, a method based on local polynomial approximation [5 - Sherstobitov AI, Marchuk VI, Timofeev DV, Voronin VV, Egiazarian KO Local feature descriptor based on 2D local polynomial approximation kernel indices. Image Processing: Algorithms and Systems XII, edited by Karen O. Egiazarian, Sos S. Agaian, Atanas P. Gotchev, Proceedings of SPIE Vol. 9019 (SPIE, San Francisco, WA 2014) 901908, DOI: 10.1117 / 12.2041610.]. However, the disadvantage of methods based on the approximation of brightness differences is the sensitivity to the presence of pulsed noise on the digital image matrix.

It should be noted that increasing the stability of the known methods for distinguishing image contours is possible due to preliminary image correction associated with smoothing the image brightness. However, this approach can lead not only to the elimination of impulse noise, but also to the loss of some useful information about the image circuit.

и

компонент градиента яркости в каждой точке изображения путем обратного вейвлет преобразования, в котором в качестве ядра преобразования используют аналитические функции, описывающие производные используемых вейвлетов обратного преобразования по соответствующим координатам. После этого определяют модуль градиента яркости в каждой точке изображения, и формируют контуры объекта путем порогового преобразования модуля градиента яркости, в процессе которого на новой белой матрице черным цветом выделяют элементы, модуль градиента, для которых в соответствующих координатах изображения превышает порог преобразования.Closest to the technical nature of the claimed method is a method of noise-resistant gradient separation of the contours of objects in digital halftone images [6 - Bezuglov DA, Mishchenko S.E., Kuzin A.P. The method of noise-resistant gradient selection of the contours of objects in digital grayscale images // RF Patent No. 2648954, IPC G06K 9/48. Will declare. and patented. Rostov branch of the RTA - No. 2016104498/08; declared 02/10/2016; publ. 08/15/2017 Bull. No. 23], taken as a prototype, which consists in first calculating the direct wavelet transform of the rows and columns of a digital grayscale image, and then forming two matrices

and

a component of the brightness gradient at each point in the image by means of an inverse wavelet transform, in which analytical functions are used as the transformation kernel, which describe the derivatives of the inverse transform wavelets used in the corresponding coordinates. After that, the brightness gradient module is determined at each point in the image, and the object contours are formed by threshold conversion of the brightness gradient module, during which elements, the gradient module, for which in the corresponding image coordinates exceed the conversion threshold, are highlighted in black on a new white matrix.

The disadvantage of the prototype method is that the calculation of the direct wavelet transform of rows and columns of a digital grayscale image is computationally expensive. In addition, this method demonstrates poor resistance to impulse noise.

The problem to which the invention is directed, is the creation of means for selecting the contours of grayscale images in the conditions of impulse noise, satisfying the requirements for high speed image processing.

The technical result is to increase the speed of separation of the contours of grayscale images in the conditions of pulsed interference.

и

компонент градиента яркости в каждой точке изображения путем суммирования сглаживающих параболических B-сплайнов с найденными ранее коэффициентами сглаживающих кубических B-сплайнов для строк и столбцов соответственно. Далее определяют модуль градиента яркости в каждой точке изображения. После этого формируют контуры объекта путем порогового преобразования модуля градиента яркости, в процессе которого на новой белой матрице черным цветом выделяют элементы, модуль градиента для которых в соответствующих координатах изображения превышает порог преобразования.To solve this technical problem, we propose a method for noise-resistant gradient-based contouring of objects in digital grayscale images, which consists in the fact that, first, taking into account the level of noise, a smoothing coefficient is selected, and smoothing cubic B-splines are calculated along each row and each column of the image. Then two matrices are formed

and

components of the brightness gradient at each point in the image by summing the smoothing parabolic B-splines with the coefficients of smoothing cubic B-splines found earlier for the rows and columns, respectively. Next, determine the modulus of the brightness gradient at each point in the image. After that, the object contours are formed by the threshold conversion of the brightness gradient module, during which elements are selected in black on a new white matrix, the gradient module for which in the corresponding image coordinates exceeds the conversion threshold.

Thus, the proposed method has the following distinctive features and the sequence of its implementation from the prototype method, which are shown in table 1.

Table 1

Prototype method The proposed method 1. Given the level of image noise, a smoothing factor is selected 2. Calculate the coefficients of the smoothing cubic B-splines along each row and each column of the image 1. Calculate the direct wavelet transform of the rows and columns of a digital halftone image

и

компонент градиента яркости в каждой точке изображения
2.1 путем обратного вейвлет-преобразования, в котором в качестве ядра преобразования используют аналитические функции, описывающие производные используемых вейвлетов обратного преобразования по соответствующим координатам2. Form two matrices

and

luminance gradient component at each image point
2.1 by the inverse wavelet transform, in which analytical functions are used as the transformation kernel, which describe the derivatives of the inverse transform wavelets used in the corresponding coordinates 3. Form two matrices

and

component of the brightness gradient at each point in the image by
3.1 summation of smoothing parabolic B-splines with previously found coefficients of smoothing cubic B-splines for rows and columns, respectively 3. Determine the modulus of the gradient of brightness at each point in the image 4. Determine the modulus of the gradient of brightness at each point in the image 4. The contours of the object are formed by a threshold conversion of the brightness gradient module, during which elements are selected in black on a new white matrix, the gradient module for which in the corresponding image coordinates exceeds the conversion threshold 5. The contours of the object are formed by a threshold transformation of the brightness gradient module, during which elements are selected in black on a new white matrix, the gradient module for which in the corresponding image coordinates exceeds the conversion threshold

From the table 1 comparison of the sequences of the prototype method and the proposed method shows that in the proposed method the following operations are introduced:

- taking into account the level of noise in the image, a smoothing factor is selected;

- calculate the coefficients of the smoothing cubic B-splines along each row and each column of the image.

And also the execution mode of one operation is changed:

и

компонент градиента яркости в каждой точке изображения формируют путем суммирования сглаживающих параболических B-сплайнов с найденными ранее коэффициентами сглаживающих кубических B-сплайнов для строк и столбцов соответственно.- two matrices

and

the brightness gradient component at each image point is formed by summing the smoothing parabolic B-splines with the coefficients of smoothing cubic B-splines found earlier for the rows and columns, respectively.

The introduction of two operations and changing the mode of one operation allows to achieve a technical result, namely, increasing the speed of formation of the contours of grayscale images in the conditions of impulse noise.

The present invention is not known from the analysis of the prior art, and information sources containing information about similar technical solutions having features similar to those distinguishing the claimed solution from the prototype, as well as properties that match the properties of the proposed solution, are therefore not known, therefore, that it has significant differences follows from them in an unobvious way and, therefore, meets the criteria of “novelty” and “inventive step”.

The essence of the proposed method is disclosed by figures 1-5.

In FIG. 1 is a structural diagram of a device that implements the proposed method of noise-tolerant gradient selection of the contours of objects in digital grayscale images.

In FIG. Figure 2 shows the original digital grayscale image (Fig. 2a) and the result of selecting the contours of this image in the absence of noise (Fig. 2b).

In FIG. Figure 3 shows test digital grayscale images with impulse noise superimposed on them (in Fig. 3a, impulse noise “broken pixels” with a probability of 0.5 is superimposed on the original image, and “salt-pepper” with a probability of 0.5 in Fig. 3b) .

In FIG. Fig. 4 shows images illustrating the results of the contouring in noisy images using the Sobel mask (the results in Fig. 4a correspond to impulse noise “dead pixels” with a probability of 0.5, and in Fig. 4b - “salt-pepper” with a probability of 0.5 )

In FIG. 5 shows the results of the selection of the contours of the proposed method (the results in Fig. 5a correspond to impulse noise “broken pixels” with a probability of 0.5, and in Fig. 5b - “salt-pepper” with a probability of 0.5).

When implementing this method, the following sequence of operations is performed:

- taking into account the level of image noise, a smoothing factor of 1 is selected;

- calculate the coefficients of the smoothing cubic B-splines along each row and each column of the image - 2;

и

компонент градиента яркости в каждой точке изображения путем суммирования сглаживающих параболических B-сплайнов с найденными ранее коэффициентами сглаживающих кубических B-сплайнов для строк и столбцов соответственно − 3;- form two matrices

and

the brightness gradient component at each image point by summing the smoothing parabolic B-splines with the coefficients of smoothing cubic B-splines found earlier for the rows and columns, respectively - 3;

- determine the modulus of the brightness gradient at each point in the image - 4;

- form the contours of the object by a threshold conversion of the brightness gradient module, during which elements are selected in black on a new white matrix, the gradient module for which in the corresponding image coordinates exceeds the transformation threshold - 5.

Before considering the operation of the device for the selection of circuits to justify the method, we state the following.

размером

. Тогда строке изображения может быть поставлена в соответствие некоторая функция

. В области

входные данные можно представить в виде совокупности

равноотстоящих отсчетов координат

с шагом

, заданных так, что Let the image matrix be given

the size

. Then some function can be associated with the image line.

. In the area of

input data can be represented as a set

equidistant coordinate samples

in increments

defined so that

;

(1)

;

(one)

.and corresponding image brightness values

.

Imagine the input signal as a spline approximation in the basis of smoothing cubic normalized B-splines of defect 1 [7 Zavyalov Yu.S., Kvasov BI, Miroshnichenko B.JI. Methods of spline functions. -M.: Science, 1980. 350 p.]

(2)

(2)

− коэффициент

-го сплайна;Where

- coefficient

spline;

(3)

(3)

(4)

(four)

− координаты середины носителя

-сплайна;

- coordinates of the middle of the medium

-spline;

− степень сплайна.

- degree of spline.

и осуществим привязку коэффициентов сплайна к середине соответствующего носителя. Тогда для этого участка, с учетом (4), выражение (5) примет вид [7]:Let's consider now a site

and bind the spline coefficients to the middle of the corresponding carrier. Then for this section, taking into account (4), expression (5) will take the form [7]:

(5)

(five)

, тогда выражение (5) можно представить в виде:We introduce the normalized coordinate

, then expression (5) can be represented as:

(6)

(6)

в виде:After simple arithmetic transformations, we obtain an analytical expression for the spline in the segment

as:

(7)

(7)

We find the spline coefficients from the solution of the functional minimization problem [8 Lapchik M.P. Numerical methods.-M: Academy, 2008, 381 pp.]:

(8)

(eight)

− коэффициент сглаживания; Where

- smoothing coefficient;

− значение сплайна в точке

;

- spline value at a point

;

− модуль второй производной сплайна.

- module of the second derivative of the spline.

.The smoothing coefficient is chosen equal to the value of the standard deviation of the noise in the image. If the statistical characteristics of the noise are unknown, then the effect of noise smoothing is observed at

.

Given the representation of the spline in the form (7), functional (8) can be represented in the form

(9)

(9)

представляет собой линейную функцию от

:In view of (7)

is a linear function of

:

(10)

(ten)

, откудаAt nodal points

from where

(11)

(eleven)

(12)

(12)

продифференцируем (9) по каждому элементу вектора

и приравняем к нулю полученное выражение. Например, первое уравнение можно записать в видеTo form the resulting system of equations for unknown coefficients

we differentiate (9) for each element of the vector

and equate the resulting expression to zero. For example, the first equation can be written as

(13)

(13)

получим систему уравнений видаAfter differentiation for each of the coefficients

we get a system of equations of the form

, (14)

, (14)

− квадратная семидиагональная матрица ранга

;Where

- square semidiagonal matrix of rank

;

− вектор правых частей, который строится на основе входного массива

.

- the vector of the right parts, which is based on the input array

.

были получены в виде:In the work [9 Bezuglov D.A., Krutov V.A., Shvachko O.V. The method of signal differentiation using spline approximation // Fundamental Research, 2017, No. 4-1, P.24-28] nonzero matrix elements

were obtained as:

(15)

(15)

(16)

(sixteen)

(17)

(17)

, (18)

, (18)

был записан в виде:and vector

was written as:

. (19)

. (nineteen)

всегда хорошо обусловлена, что обеспечивает существование единственного решения системы уравнений. При этом матрица

зависит только от коэффициента сглаживания. Это позволяет найти обратную матрицу

и использовать ее для расчета искомых коэффициентов всех строк и столбцов изображения по формулеAnalysis of the system of equations allows us to conclude that the matrix

always well-conditioned, which ensures the existence of a unique solution to a system of equations. Moreover, the matrix

depends only on the smoothing coefficient. This allows you to find the inverse matrix

and use it to calculate the desired coefficients of all rows and columns of the image according to the formula

. (20)

. (20)

и

, которые в каждой строке хранят массивы коэффициентов сглаживающих кубических

-сплайнов, аппроксимирующих распределения яркости вдоль строк и столбцов входного изображения

соответственно. Например, матрица

в строке с номером

содержит вектор коэффициентов сплайна

, найденных в результате решения системы уравнений (14) по распределению яркости вдоль соответствующей строки матрицы

, а матрица

в строке с номером

содержит вектор коэффициентов сплайна

, найденных по данным соответствующего столбца матрицы

.A system of equations of the form (14) can be solved for each row and column of the image. As a result, we obtain the matrices

and

which in each line store arrays of smoothing cubic coefficients

splines approximating the brightness distribution along the rows and columns of the input image

respectively. For example, the matrix

in line with number

contains a vector of spline coefficients

found as a result of solving the system of equations (14) by the brightness distribution along the corresponding row of the matrix

, and the matrix

in line with number

contains a vector of spline coefficients

found from the corresponding matrix column

.

, может быть записан в виде:Given expression (7), a spline describing the derivative of the one-dimensional function

can be written as:

(21)

(21)

-сплайном.This spline is called smoothing parabolic.

Spline.

It follows that the components of the brightness gradient of the input image can be found by the formulas:

(22)

(22)

(23)

(23)

As in the prototype, the brightness gradient module will be found by the formula

. (24)

. (24)

In this case, the threshold transformation is described by the relation:

(25)

(25)

− значение порога.Here

Is the threshold value.

As an example, we consider the problem of selecting contours in a digital grayscale image under conditions of pulsed noise. It should be noted that the prototype method provides effective suppression of noise distributed according to the normal law, and is not intended to highlight contours in a noisy image. In this regard, the efficiency of the proposed method for the selection of contours was carried out in comparison with the method of selecting contours, which was widely used, based on the use of the Sobel mask (“Canny” border detector). Comparison of the proposed method and the prototype method will produce speed.

исходного полутонового изображения, в котором отсутствовали шумы, обрабатывалась детектором границ «Canny». В результате было получено изображение контуров

, соответствующее матрице яркости

при отсутствии шумов. Изображения, соответствующие матрицам

и

приведены на фиг.2 (фиг. 2а и 2б соответственно).The following algorithm was used to form test images. Brightness matrix

The original halftone image, in which there was no noise, was processed by the “Canny” border detector. As a result, the image of the contours was obtained.

corresponding to the brightness matrix

in the absence of noise. Matrix Matched Images

and

are shown in figure 2 (Fig. 2A and 2B, respectively).

). В качестве модели шума использовался импульсный шум «битые пиксели» и «соль-перец» с вероятностью

. В результате были получены изображения, которым соответствуют матрицы яркости

, представленные на фиг. 3 (фиг. 3а и 3б соответственно).Next, noise was added to the original digital grayscale image (matrix

) As a noise model, impulse noise “broken pixels” and “salt-pepper” was used with probability

. As a result, images were obtained that correspond to brightness matrices

shown in FIG. 3 (Figs. 3a and 3b, respectively).

контуров, по результатам обработки оператором Собеля зашумленных изображений, представленных на фиг. 3 (фиг. 4а отражает результаты выделения контуров изображения на фиг. 3а, а фиг. 4б − фиг. 3б).In FIG. 4 are matrices

contours, according to the results of processing by the Sobel operator of the noisy images presented in FIG. 3 (Fig. 4a reflects the results of the selection of the image outlines in Fig. 3a, and Fig. 4b - Fig. 3b).

An analysis of the obtained images allows us to conclude that the Sobel operator is inoperative for selecting contours in images obtained under pulsed noise conditions.

контуров, полученные при помощи предлагаемого способа с использованием сплайн дифференцирования. Изображение на фиг.5а соответствует модели шумов «битые пиксели», а на фиг. 5б − «соль-перец». Приведенные на фиг. 5 изображения подтверждают работоспособность предлагаемого способа выделения контуров при наличии импульсных шумов.In FIG. 5 shows images of matrices

contours obtained using the proposed method using spline differentiation. The image in FIG. 5a corresponds to the “dead pixel” noise model, and in FIG. 5b - “salt and pepper”. Referring to FIG. 5 images confirm the efficiency of the proposed method for the allocation of circuits in the presence of impulse noise.

In order to quantify the effectiveness of the proposed method in comparison with the prototype used three indicators.

, полученными предлагаемым способом, а также способом прототипа и изображением контура

, полученным при отсутствии шумов.The first was that the standard deviation (RMS) between the contour images was determined

obtained by the proposed method, as well as the prototype method and the contour image

obtained in the absence of noise.

RMS assessment was carried out according to the formula:

. (26)

. (26)

отношения сигнал/шум (ОСШ), рассчитываемую по формулам:The second indicator is an estimate

signal-to-noise ratio (SNR) calculated by the formulas:

, (27)

, (27)

, (28)

, (28)

− максимальное значение яркости в полутоновых изображениях, которое обычно равно 255.Where

- The maximum brightness value in grayscale images, which is usually equal to 255.

The values of the third indicator to assess the effectiveness of the proposed method for suppressing impulse noise is obtained using the ratio

; (29)

; (29)

- СКО фона; Where

- DIS standard;

(30)

(thirty)

на исследуемом изображении

,- the average value of the background; n1, m1- coordinates of the selected background area in size

on the test image

,

. (31)

. (31)

и значениях коэффициента сглаживания

приведены в таблице 2. Аналогичные результаты, относящиеся к импульсному шуму «соль-перец», представлены в таблице 3.The results of this comparison as applied to the model of impulse noise of the “broken pixel” type for various noise probabilities

and smoothing coefficient values

are shown in table 2. Similar results related to impulse noise "salt-pepper" are presented in table 3.

table 2

Indicator 1, the ESR gain, dB Noise probability Spline function smoothing factor five ten 50 100 0.3 1.8 2.01 2.22 2.23 0.5 2.03 2,31 2.6 2.64 0.7 2.13 2.42 2.75 2.79 Indicator 2, peak SNR gain, dBr Noise probability Spline function smoothing factor five ten 50 100 0.3 3.47 4.09 5.22 5.48 0.5 3.76 4,57 5.87 6.32 0.7 3.97 4.85 6.45 6.87 Indicator 3, the gain in the ratio of peak signal to noise on the standard deviation of the SNRF background, dB Noise probability Spline function smoothing factor five ten 50 100 0.3 5.23 6.08 8.11 8.9 0.5 5.41 6.34 8.15 8.94 0.7 5.63 6.65 8.73 9,4

Table 3

Indicator 1, the ESR gain, dB Noise probability Spline function smoothing factor five ten 50 100 0.2 2.15 2.28 2,33 2,33 0.3 2,51 2.69 2.83 2.81 0.5 2.95 3.23 3,5 3.53 0.7 3.22 3,55 3.92 3.96 Indicator 2, peak SNR gain, dBr Noise probability Spline function smoothing factor five ten 50 100 0.2 4.86 5.43 5.94 6.06 0.3 5.13 5.77 6.57 6.56 0.5 5,4 6.15 7.16 7.44 0.7 5.65 6.46 7.78 8.07 Indicator 3, the gain in the ratio of peak signal to noise on the standard deviation of the SNRF background, dB Noise probability Spline function smoothing factor five ten 50 100 0.2 6.05 6.93 8.7 9.59 0.3 6.17 7.08 9 9.69 0.5 6.07 7.05 8.99 9.79 0.7 6.12 7.14 9.32 10.12

We estimate the gain of the proposed method in comparison with the prototype method in terms of speed.

размером MЧM.Let the square matrix define the distribution of image brightness

size MCHM.

Moreover, the direct discrete wavelet transform for rows and columns in the prototype method is carried out according to the formulas

, (32)

, (32)

(33)

(33)

respectively.

− вейвлет.Here

- wavelet.

при реализации прямого вейвлет-преобразования будет равен:In this case, the amount of computational cost

when implementing a direct wavelet transform, it will be equal to:

. (34)

. (34)

.In expression (34), it is taken into account that

.

If the derivative corresponds to the selected wavelet type, then the inverse transformation, which allows obtaining the components of the brightness gradient of the original image, can be found by the formulas

(35)

(35)

(36)

(36)

− коэффициент нормировки для обратного вейвлет-преобразования (для приведенных соотношений данный коэффициент равен единице).Where

Is the normalization coefficient for the inverse wavelet transform (for the given relations, this coefficient is equal to unity).

операций. С учетом того, что модуль градиента яркости изображения будем определять по формуле (19) итоговое количество операций для выделения контуров будет составлятьInverse transformation will also require

operations. Taking into account the fact that the brightness gradient modulus of the image will be determined by formula (19), the total number of operations for selecting contours will be

. (37)

. (37)

раз решить систему линейных уравнений размерностью

вида (14). Для обращения матрицы такой системы уравнений потребуется порядка

операций. Так как коэффициенты матрицы совпадают для всех строк и столбцов, то матрицу

необходимо обратить один раз. Так как матрицу можно обратить заранее, для всех вычислений используется одна матрица, изменяется только правая часть системы уравнений (14). Для вычисления контура необходимо еще

операций. В результате общее число операций при реализации предлагаемого способа составитTo implement the proposed method for selecting contours using spline approximation, it is necessary

times solve a system of linear equations of dimension

type (14). To invert the matrix of such a system of equations, an order of

operations. Since the coefficients of the matrix are the same for all rows and columns, the matrix

need to draw once. Since the matrix can be inverted in advance, for all calculations one matrix is used, only the right-hand side of the system of equations (14) changes. To calculate the contour

operations. As a result, the total number of operations during the implementation of the proposed method will be

. (38)

. (38)

It follows that the gain in computational efficiency equal to the ratio of the number of operations in the prototype method and the proposed method will be equal to:

(39)

(39)

. В этом случаеUsually,

. In this case

. (40)

. (40)

выигрыш составит

раз.For example, when

the gain is

time.

Thus, the methods known to the authors for isolating contours in grayscale images are ineffective in conditions of impulse noise, and the prototype method that provides the solution to the problem of isolating contours in noisy images is able to deal with Gaussian noise and has a low speed. On the contrary, the proposed method is resistant to impulse noise and can increase the speed of the selection of the contours of grayscale images.

Consider the operation of the device for the selection of circuits that implements the method.

и

и

компонент градиента яркости изображения (БВКГ) 3 и 4, блок определения модуля градиента яркости изображения (БОМГ) 5, блок порогового преобразования (БПП) 6.The structure of the contouring device (Fig. 1) includes blocks for determining the coefficients of the splines of the original image (BOX) 1 and 2, blocks for computing matrices

and

and

a component of the brightness of the image image (BVKG) 3 and 4, a unit for determining a module of a gradient of image brightness (BOMG) 5, a threshold transformation unit (BPP) 6.

The general input of the device is the inputs of the BOX 1 and the BOX 2, the output of the BOX 1 is connected to the input of the BVKG 3, the output of which is connected to the first input of the BOMG 5, the output of the BOX 2 is connected to the input of the BVKG 4, the output of which is connected to the second input of the BOMG 5, the output of the BOMG 5 connected to the input of the BPP 6, the output of which is the output of the device.

The device operates as follows.

цифрового полутонового изображения. В БОКС 1 осуществляют вычисление коэффициентов сплайнов

из решения

систем линейных уравнений вида (14) по формуле (15) для каждой строки входной матрицы

. Полученные коэффициенты сплайнов с выхода БОКС 1 поступают на вход БВКГ 3, в котором преобразование сигналов осуществляют по формуле (21). На выходе БВКГ 3 формируют двумерную матрицу

, элементы которой содержат значения производных яркости в каждой точке изображения вдоль строки. Данные сигналы поступают на первый вход БОМГ 5. The inputs of BOX 1 and BOX 2 receive a two-dimensional distribution of the brightness of the signal specified by the brightness matrix

digital halftone image. In BOX 1, spline coefficients are calculated

from decision

systems of linear equations of the form (14) by the formula (15) for each row of the input matrix

. The obtained spline coefficients from the output of BOX 1 are fed to the input of the BVCH 3, in which the signals are converted according to the formula (21). At the output of BVKG 3 form a two-dimensional matrix

, the elements of which contain the derivatives of brightness at each point in the image along the line. These signals are fed to the first input of BOMG 5.

систем линейных уравнений вида (14) по формуле (20) для каждого столбца матрицы

. Полученные коэффициенты сплайнов с выхода БОКС 2 поступают на вход БВКГ 4, в котором преобразование сигналов осуществляют по формуле (21). На выходе БВКГ 4 формируют двумерную матрицу

, элементы которой содержат значения производных яркости в каждой точке изображения вдоль строки. Данные сигналы поступают на второй вход БОМГ 5. В БОМГ 5 осуществляют процедуру расчета модуля градиента яркости по формуле (24). В результате получают двумерную матрицу

, описывающую распределение модуля градиента яркости входной матрицы

, соответствующее каждому ее элементу. Матрица

поступает на вход БПП 6, в котором осуществляют формирование двумерной матрицы контуров

по формуле (20). Полученная матрица поступает на выход устройства, где может быть визуализирована или сохранена в памяти ЭВМ.In BOX 2, the spline coefficients are calculated from the solution

systems of linear equations of the form (14) according to the formula (20) for each column of the matrix

. The obtained spline coefficients from the output of BOX 2 are fed to the input of the BVCH 4, in which the signals are converted according to the formula (21). At the output of BVKG 4 form a two-dimensional matrix

, the elements of which contain the derivatives of brightness at each point in the image along the line. These signals are fed to the second input of BOMG 5. In BOMG 5, the procedure for calculating the brightness gradient module by the formula (24) is carried out. The result is a two-dimensional matrix

describing the distribution of the brightness gradient modulus of the input matrix

corresponding to each of its elements. Matrix

enters the input of the BPP 6, in which the formation of a two-dimensional matrix of contours

by the formula (20). The resulting matrix is sent to the output of the device, where it can be visualized or stored in the computer memory.

As blocks 1-6 of the considered image processing device, those described in [10 - Ayficher E.S., Jervis B.U. Digital signal processing: a practical approach. 2nd edition. - M.: Williams, 2004. 992 p .; 11 - Kupriyanov M.S., Matyushkin B.L. Technical support for digital signal processing. Directory. - M.: Science and Technology, 2000. 752 pp.], As well as any similar technical devices known from the prior art (programmable and non-programmable processors for digital signal and image processing) that implement the corresponding mathematical functions (15) - (20).

In BOX 1 and BOX 2, the operation of multiplying the matrix by a vector is performed. This operation is similar to convolutional filtering, which is widely used in digital signal processing devices [10], [11].

In BVKG 3 and BVKG 4, to calculate the gradient components, matrix-matrix multiplication operations are performed, which is also common in digital signal processing devices [10], [11].

BOMG 5 and BPP 6 can be implemented similarly to the prototype method in accordance with the description in the sources [10], [11].

The above materials confirm compliance with the criterion of "industrial applicability" of the proposed method.

This means that the technical result of the invention is to increase the speed of selection of the contours of grayscale images in the conditions of pulsed interference.

Claims (1)

Method of noise-tolerant gradient selection of contours of objects in digital grayscale images, in which two matrices are formed

and

components of the brightness gradient at each point in the image, determine the module of the brightness gradient at each point in the image, form the contours of the object by threshold conversion of the module of the brightness gradient, during which elements are selected in black on a new white matrix, the gradient module for which in the corresponding coordinates of the image exceeds the conversion threshold characterized in that before the formation of the matrices

and

the components of the brightness gradient, taking into account the level of noise in the image, select the smoothing coefficient and calculate the smoothing coefficients of the cubic B-splines along each row and each column of the image, and two matrices

and

the brightness gradient component at each image point is formed by summing the smoothing parabolic B-splines with the coefficients of smoothing cubic B-splines found earlier for the rows and columns, respectively.

Images