CN101908208B - Self-adaptive confirming method of smooth wave-filtering spatial scale facing to picture edge detection - Google Patents

Abstract

The invention discloses an adaptive determination method of smoothing filter space scale oriented to image edge detection. The present invention can adaptively determine the best smoothing filter spatial scale for each pixel in the image, that is, the smoothing filter spatial scale of the pixel in the large-area smooth and uniform area is relatively large, while the smoothing filter spatial scale of the pixel in the edge of the image is relatively large. The smoothing filter spatial scale is relatively small. The adaptive determination of the smoothing filter spatial scale of each pixel in the image can be combined with the edge detection or smoothing filter of grayscale or color images, which can effectively eliminate the interference of independently distributed Gaussian white noise or spatially correlated texture noise in the image, and at the same time Keep the edges of the image from being blurred, and can be applied in the textile printing and dyeing industry.

Description

Self-adaptation towards the smooth wave-filtering spatial scale of Image Edge-Detection is determined method

Technical field

The present invention relates to a kind of picture signal treatment technology, the self-adaptation that relates in particular to a kind of smooth wave-filtering spatial scale towards Image Edge-Detection is determined method.

Background technology

A problem that had not solved is how to determine the smooth wave-filtering spatial scale of each pixel in Image Edge-Detection or smothing filtering, in the traditional images edge detection method, as Canny operator [1] (J.Canny, " A computational approach to edge detection; " IEEE Trans.On Pattern Analysis andMachine Intelligence, 8 (6): 679-698,1986), entire image adopts same smooth wave-filtering spatial scale, but interference of noise in the very difficult removal of images effectively of this method keeps edge of image can not be filtered ripple again simultaneously.

Though also having the researchist to adopt the whole bag of tricks is that each pixel is determined corresponding smooth wave-filtering spatial scale in the image, as Jeong and Kim[2] (H.Jeong and C.I.Kim, " Adaptive determinationof filter scales for edge detection; " IEEE Trans.On Pattern Analysis and MachineIntelligence, 14 (5): 579-585,1992) propose the employing regularization method and optimize the filtering space scale that the energy function of metric space is determined each pixel in the image; And Lindeberg[3] (T.Lindeberg, " Edgedetection and ridge detection with automatic scale selection; " in Proc.of CVPR, 1996) suggestion is that characteristics of image detects the space scale of determining feature detection etc. by the local maximum of seeking normalization feature amplitude at metric space.But all there is weak point in these methods, the gradient descending method that is adopted in the energy function optimizing process is absorbed in the local optimum point, Jeong and Kim[2] smooth wave-filtering spatial scale of each pixel is initialized as 3 in the method that proposes, and then slowly increase, but such space scale is excessive for the pixel that is in the image border, causes that easily crossing filtering because of the image border blurs; Lindeberg[3] then need the space partial derivative of higher order of each pixel in the computed image in the method, and for being subjected to the noise image, especially towards the textile printing and dyeing image of the texture noise that is subjected to space correlation, because signal to noise ratio (S/N ratio) is very low in the image, the calculating of image partial derivative of higher order is insecure.

Summary of the invention

The object of the present invention is to provide a kind of self-adaptation of the smooth wave-filtering spatial scale towards Image Edge-Detection to determine method, if utilized pixel to drop in the even smooth region of image, each sub regions in this zone then, as the left side, right-hand part, the sample mean of the first half and Lower Half gray scale or color is that whole area grayscale or color mean value one does not have estimation partially, under the situation of given confidence level 1-α, judge the left side that this is regional, right-hand part, whether the gray scale of the first half and Lower Half or the sample mean of color drop on whole area grayscale or the corresponding fiducial interval of color mean value.Can select to select best smooth wave-filtering spatial scale adaptively for each pixel in the set for smooth wave-filtering spatial scale at one group according to these characteristics.

The step of the technical solution used in the present invention is as follows:

(1) set a discrete values set selecting smooth wave-filtering spatial scale for each pixel in the image, the numerical value in this discrete set is to arrange from big to small;

(2) the image smoothing wave filter is a moving window, and according to grating lattice scan mode point by point scanning view picture input picture, input picture is gray level image or coloured image, and described smooth wave-filtering spatial scale is exactly the radius r of this moving window;

(3) when moving window scans a pixel, when promptly the center of moving window rests on this pixel, from gathering, the selective discrete values of above-mentioned smooth wave-filtering spatial scale gets the radius r of a numerical value as moving window according to order;

(4) calculate the mean value that drops on interior all pixel gray scales of this moving window or color, and the variance of gray scale or color:

$\stackrel{\‾}{c}(x,y)=\frac{1}{{(2r+1)}^2}\underset{x^{\′}=x-r}{\overset{x+r}{\mathrm{\Σ}}}\underset{y^{\′}=y-r}{\overset{y+r}{\mathrm{\Σ}}}c(x^{\′},y^{\′})---\left(1\right)$

${\mathrm{\σ}}^2(x,y)=\frac{1}{{(2r+1)}^2}\underset{x^{\′}=x-r}{\overset{x+r}{\mathrm{\Σ}}}\underset{y^{\′}=y-r}{\overset{y+r}{\mathrm{\Σ}}}{(c(x^{\′},y^{\′})-\stackrel{\‾}{c}(x,y))}^2---\left(2\right)$

(x wherein, y) volume coordinate of central pixel point in the expression moving window, r represents the radius of described moving window, r is a unit with pixel interval in the digital picture, (x ', y ') expression drops on that (x y) is the center, and radius is the volume coordinate of the moving window interior pixel point of r with pixel, c (x ', y ') expression is positioned at the gray scale or the color of pixel (x ', y ')

(x y) is the center, and radius is the mean value of interior all pixel gray scales of the moving window of r or color, σ with pixel in expression ²(x, y) variance of all pixel gray scales or color in the described moving window of expression;

(5) calculating drops on described moving window left side respectively, right-hand part, and the mean value of the first half and Lower Half pixel gray scale or color:

${\stackrel{\‾}{c}}_L(x,y)=\frac{1}{(2r+1)r}\underset{x^{\′}=x-r}{\overset{x-1}{\mathrm{\Σ}}}\underset{y^{\′}=y-r}{\overset{y+r}{\mathrm{\Σ}}}c(x^{\′},y^{\′})---\left(3\right)$

${\stackrel{\‾}{c}}_R(x,y)=\frac{1}{(2r+1)r}\underset{x^{\′}=x+1}{\overset{x+r}{\mathrm{\Σ}}}\underset{y^{\′}=y-r}{\overset{y+r}{\mathrm{\Σ}}}c(x^{\′},y^{\′})---\left(4\right)$

${\stackrel{\‾}{c}}_U(x,y)=\frac{1}{(2r+1)r}\underset{x^{\′}=x-r}{\overset{x+r}{\mathrm{\Σ}}}\underset{y^{\′}=y-r}{\overset{y+1}{\mathrm{\Σ}}}c(x^{\′},y^{\′})---\left(5\right)$

${\stackrel{\‾}{c}}_D(x,y)=\frac{1}{(2r+1)r}\underset{x^{\′}=x-r}{\overset{x+r}{\mathrm{\Σ}}}\underset{y^{\′}=y+1}{\overset{y+r}{\mathrm{\Σ}}}c(x^{\′},y^{\′})---\left(6\right)$

Here With

Expression drops on described moving window left side respectively, right-hand part, and the mean value of the first half and Lower Half pixel gray scale or color is if input picture is a gray level image, then

With

It all is scalar; If input picture is a coloured image, then

With

Be vector, each vector all has three components, and is promptly red, green and blue component;

(6) press the definition of α quantile in the t distribution on the statistics, check described moving window left side, right-hand part, the mean value of the first half and Lower Half pixel gray scale or color, promptly With

The mean value that whether drops on whole slide window gray scale or color is in confidence level is fiducial interval under the 1-α:

$P\left\{\right|\frac{{\stackrel{\&OverBar;}{c}}_j^i(x,y)-{\stackrel{\&OverBar;}{c}}^i(x,y)}{{\mathrm{\&sigma;}}^i(x,y)/\sqrt{n}}|<z_{\mathrm{\&alpha;}/2}\}=1-\mathrm{\&alpha;}---\left(7\right)$

If input picture is a gray level image, subscript i=1 here is because have only a gray-scale value on each pixel in the image, and when input picture is coloured image, here subscript i represents redness corresponding in color mean value or the color variance, green or blue component, and

Middle subscript j then represents it is described moving window left side, right-hand part, the first half or Lower Half, n represents to drop on described moving window left side, right-hand part, the number of pixel in the first half or the Lower Half, if described moving window is a square, n numerical value then just equals (2r+1) r, according to given α numerical value, obtains z by the inquiry of t distribution table _α/2Numerical value;

(7) if described moving window left side, right-hand part, the mean value of the first half and Lower Half pixel gray scale or color, promptly

With

In each component, all satisfy formula (7), judge that then (x y) drops on a length of side and is the homogeneous area of (2r+1), jumps to step (9) for the pixel at place, described moving window center;

(8) if described moving window left side, right-hand part, the mean value of the first half and Lower Half pixel gray scale or color, promptly

With

In each component have one not satisfy formula (7), the image-region that current moving window place is described is not a homogeneous area, then next than the radius r of fractional value as moving window according to order selection from the alternative discrete values set of above-mentioned smooth wave-filtering spatial scale from big to small, repeat above-mentioned steps (4) then to step (6);

(9) the current moving window radius r of getting is as the smooth wave-filtering spatial scale of the pixel at place, moving window center;

(10) described moving window moves on to next pixel according to the grating lattice scanning sequency, and repeating step (3) is to step (9), and all pixels are all determined smooth wave-filtering spatial scale separately in image.

The beneficial effect that the present invention has is:

This self-adaptation determines that the smooth wave-filtering spatial scale of each pixel can be incorporated in the rim detection or smothing filtering of gray scale or coloured image in the image, independent distribution white Gaussian noise or space correlation texture interference of noise in the removal of images effectively, keep the edge in the image can not blured excessively simultaneously, can be applied in the textile printing and dyeing industry.

Description of drawings

Accompanying drawing is a process flow diagram of the present invention.

Embodiment

As shown in drawings, workflow of the present invention is as follows:

(1) input one width of cloth numerical imaging.

(2) the given discrete values set that can select smooth wave-filtering spatial scale for each pixel in the image, as 6,5,4,3,2,1}.

(3) input confidence level 1-α is 0.05 as the α value.

(4) the image smoothing wave filter is a square moving window, and the radius r of moving window is equal to smooth wave-filtering spatial scale.

(5) maximal value desirable according to the radius r of moving window, as 6 in this example, image is done symmetry expansion up and down accordingly, if the width of input picture and highly be respectively Width and Height, expand the width of back image so and highly be respectively Width+2r and Height+2r, can be earlier the row of image be carried out the symmetry expansion, and then row are carried out symmetry expand, promptly

$I_{\mathrm{row}-\mathrm{ext}}^c(i,j)=\left\{\begin{array}{c}{I}^c(i,r+2-j);1\&le;i\&le;\mathrm{Height},1\&le;j\&le;r\\ I^c(i,j-r);1\&le;i\&le;\mathrm{Height},r+1\&le;j\&le;r+\mathrm{Width}\\ I^c(i,2\mathrm{Width}+r-j);1\&le;i\&le;\mathrm{Height},r+\mathrm{Width}+1\&le;j\&le;2r+\mathrm{Width}\end{array}\right.---\left(1\right)$

$I_{\mathrm{ext}}^c(i,j)=\left\{\begin{array}{c}{I}_{\mathrm{row}-\mathrm{ext}}^c(w+2-i,j);1\&le;i\&le;w,1\&le;j\&le;2w+\mathrm{Width}\\ I_{\mathrm{row}-\mathrm{ext}}^c(i-w,j);w+1\&le;i\&le;w+\mathrm{Height},1\&le;j\&le;2w+\mathrm{Width}\\ I_{\mathrm{row}-\mathrm{ext}}^c(2\mathrm{Height}+w-i,j);w+1+\mathrm{Height}\&le;i\&le;2w+\mathrm{Height},1\&le;j\&le;2w+\mathrm{Width}\end{array}\right.---\left(2\right)$

Here I ^cBe a certain component of expression input picture,, just have only one-component if input picture is a gray level image; If input picture is a coloured image, then at redness, green or the blue component of rgb color space.Here (i, j) volume coordinate of pixel in the image of back is expanded in expression.

Be to component I ^cThe symmetry expansion of line direction, and

Be

Again column direction is carried out symmetry expansion back image on the basis.

Perhaps also can be earlier the row of image be carried out the symmetry expansion, and then row is carried out symmetry expand, promptly

$I_{\mathrm{col}-\mathrm{ext}}^c(i,j)=\left\{\begin{array}{c}{I}^c(r+2-i,j);1\&le;i\&le;r,1\&le;j\&le;\mathrm{Width}\\ I^c(i-r,j);r+1\&le;i\&le;r+\mathrm{Height},1\&le;j\&le;\mathrm{Width}\\ I^c(2\mathrm{Height}+r-i,j);r+\mathrm{Height}+1\&le;i\&le;2r+\mathrm{Height},1\&le;j\&le;\mathrm{Width}\end{array}\right.---\left(3\right)$

$I_{\mathrm{ext}}^c(i,j)=\left\{\begin{array}{c}{I}_{\mathrm{col}-\mathrm{ext}}^c(i,r+2-j);1\&le;i\&le;2r+\mathrm{Height},1\&le;j\&le;r\\ I_{\mathrm{col}-\mathrm{ext}}^c(i,j-r);1\&le;i\&le;2r+\mathrm{Height},1+r\&le;j\&le;r+\mathrm{Width}\\ I_{\mathrm{col}-\mathrm{ext}}^c(i,2r+\mathrm{Width}-j);1\&le;i\&le;2r+\mathrm{Height},r+1+\mathrm{Width}\&le;j\&le;2r+\mathrm{Width}\end{array}\right.---\left(4\right)$

Wherein

Be to component I ^cSymmetry expansion on column direction, and Be

On the basis line direction is carried out image after the symmetry expansion, the expanded images that two kinds of symmetrical extended modes obtain is the same.

(6) moving window is according to inner the work from top to bottom of grating lattice scan mode image after expansion, zigzag scanning from left to right, promptly remove the image inside of moving window maximum radius size frame, the size of expanded images inside is the same with the original size of input picture.

(7) when moving window scans a pixel, when promptly the center of moving window rests on this pixel, get the current radius r of a numerical value according to order as moving window from the alternative discrete values set of above-mentioned smooth wave-filtering spatial scale;

(8) calculate the mean value that drops on this moving window interior pixel point gray scale or color, and gray scale or color variance

$\stackrel{\&OverBar;}{c}(x,y)=\frac{1}{{(2r+1)}^2}\underset{x^{\&prime;}=x-r}{\overset{x+r}{\mathrm{\&Sigma;}}}\underset{y^{\&prime;}=y-r}{\overset{y+r}{\mathrm{\&Sigma;}}}c(x^{\&prime;},y^{\&prime;})---\left(5\right)$

${\mathrm{\&sigma;}}^2(x,y)=\frac{1}{{(2r+1)}^2}\underset{x^{\&prime;}=x-r}{\overset{x+r}{\mathrm{\&Sigma;}}}\underset{y^{\&prime;}=y-r}{\overset{y+r}{\mathrm{\&Sigma;}}}{(c(x^{\&prime;},y^{\&prime;})-\stackrel{\&OverBar;}{c}(x,y))}^2---\left(6\right)$

(x wherein, y) volume coordinate of central pixel point in the expression moving window, r represents the current numerical value r that gets radius of described moving window, r is a unit with pixel interval in the digital picture, (x ', y ') expression drops on that (x y) is the center, and radius is the volume coordinate of the moving window interior pixels point of r with pixel, c (x ', y ') expression is positioned at the gray scale or the color of pixel (x ', y ') (x y) is the center, and radius is the mean value of interior all pixel gray scales of the moving window of r or color, σ with pixel in expression ²(x, y) variance of inner all pixel gray scales of the described moving window of expression or color.If input picture is a gray level image, then

And σ ²(x y) is scalar; If input picture is a coloured image, then

And σ ²(x y) is vector, and each vector all has three components, and is promptly red, green and blue component.

(9) calculating drops on described moving window left side respectively, right-hand part, and the mean value of the first half and Lower Half pixel gray scale or color:

${\stackrel{\&OverBar;}{c}}_L(x,y)=\frac{1}{(2r+1)r}\underset{x^{\&prime;}=x-r}{\overset{x-1}{\mathrm{\&Sigma;}}}\underset{y^{\&prime;}=y-r}{\overset{y+r}{\mathrm{\&Sigma;}}}c(x^{\&prime;},y^{\&prime;})---\left(7\right)$

${\stackrel{\&OverBar;}{c}}_R(x,y)=\frac{1}{(2r+1)r}\underset{x^{\&prime;}=x+1}{\overset{x+r}{\mathrm{\&Sigma;}}}\underset{y^{\&prime;}=y-r}{\overset{y+r}{\mathrm{\&Sigma;}}}c(x^{\&prime;},y^{\&prime;})---\left(8\right)$

${\stackrel{\&OverBar;}{c}}_U(x,y)=\frac{1}{(2r+1)r}\underset{x^{\&prime;}=x-r}{\overset{x+r}{\mathrm{\&Sigma;}}}\underset{y^{\&prime;}=y-r}{\overset{y+1}{\mathrm{\&Sigma;}}}c(x^{\&prime;},y^{\&prime;})---\left(9\right)$

${\stackrel{\&OverBar;}{c}}_D(x,y)=\frac{1}{(2r+1)r}\underset{x^{\&prime;}=x-r}{\overset{x+r}{\mathrm{\&Sigma;}}}\underset{y^{\&prime;}=y+1}{\overset{y+r}{\mathrm{\&Sigma;}}}c(x^{\&prime;},y^{\&prime;})---\left(10\right)$

Here

With

Expression drops on described moving window left side respectively, right-hand part, and the mean value of the first half and Lower Half pixel gray scale or color is if input picture is a gray level image, then

With

Be scalar, and if input picture is a coloured image, then

With

Be vector, each all has three components, and is promptly red, green and blue component.

(10) press the definition of α quantile in the statistics t distribution, check described moving window left side, right-hand part, the mean value of the first half and Lower Half pixel gray scale or color, promptly

With

Whether drop in the fiducial interval that confidence level is 1-α:

$P\left\{\right|\frac{{\stackrel{\&OverBar;}{c}}_j^i(x,y)-{\stackrel{\&OverBar;}{c}}^i(x,y)}{{\mathrm{\&sigma;}}^i(x,y)/\sqrt{n}}|<z_{\mathrm{\&alpha;}/2}\}=1-\mathrm{\&alpha;}---\left(11\right)$

If input picture is a gray level image, subscript i=1 here is because have only a gray-scale value on each pixel in the image, and when input picture is coloured image, here subscript i represents corresponding redness in color mean value or the color variance, green or blue component, and

Middle subscript j then represents it is described moving window left side, right-hand part, the first half or Lower Half, n represents to drop on described moving window left side, right-hand part, the number of pixel in the first half or the Lower Half, if described moving window is a square, n numerical value then just equals (2r+1) r, according to given α numerical value, can obtain z by the inquiry of statistics t distribution table _α/2Numerical value.

(11) if described moving window left side, right-hand part, the mean value of the first half and Lower Half pixel gray scale or color, promptly

With In each component, all satisfy formula (11), judge that then (x y) drops on a length of side and is the homogeneous area of (2r+1), jumps to step (13) for the pixel at place, described moving window center.

(12) if described moving window left side, right-hand part, the mean value of the first half and Lower Half pixel gray scale or color, promptly

With

In each component have one not satisfy formula (11), the image-region that current moving window place is described is not a homogeneous area, then next than the radius r of fractional value as moving window according to order selection from the alternative discrete values set of above-mentioned smoothing filter space scale from big to small, repeat above-mentioned steps (8) then to (10).

(13) the current moving window radius r of getting is as the smooth wave-filtering spatial scale of the pixel at place, moving window center.

(14) described moving window moves on to next pixel according to the grating lattice scanning sequency, and repeating step (7) is to step (13), and all pixels are all determined smooth wave-filtering spatial scale separately in image.

(15), can be incorporated in Image Edge-Detection or the smothing filtering according to the smooth wave-filtering spatial scale of each pixel.If in conjunction with method for detecting image edge, can be earlier image be carried out smothing filtering according to the smooth wave-filtering spatial scale of each pixel the best based on gradient; On the basis of removing picture noise, the space derivative of computed image; Be steps such as local non-maximum value inhibition and hysteresis threshold processing then, just can obtain edge of image.

Claims (1)

1. an adaptive method for determining the smoothing filter spatial scale facing image edge detection, characterized in that the steps of the method are as follows: (1) Set a discrete value set for each pixel in the image to select a smoothing filter spatial scale, and the values in this discrete set are arranged from large to small; (2) The image smoothing filter is a sliding window, which scans the entire input image point by point according to the raster lattice scanning method, the input image is a grayscale image or a color image, and the smoothing filter spatial scale is the radius of the sliding window r; (3) When the sliding window scans to a pixel point, that is, when the center of the sliding window stays at the pixel point, a numerical value is taken as the radius r of the sliding window in order from the set of discrete numerical values for selection of the above-mentioned smoothing filter spatial scale; (4) Calculate the average value of the grayscale or color of all pixels falling within the sliding window, and the variance of the grayscale or color: $\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\underset{{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; r</span>}}{\overset{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; r</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; r</span>}}{\overset{\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; r</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$ ${\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\underset{{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; r</span>}}{\overset{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; r</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; r</span>}}{\overset{\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; r</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$ Wherein (x, y) represents the spatial coordinates of the central pixel in the sliding window, r represents the radius of the sliding window, r is in the pixel pitch in the digital image, and (x', y') represents the distance between pixels (x, y) is the center, the spatial coordinates of the pixel in the sliding window with a radius of r, c(x', y') represents the grayscale or color of the pixel (x', y'),

Indicates the average value of the grayscale or color of all pixels in the sliding window with the pixel (x, y) as the center and radius r, σ ² (x, y) represents the grayscale or color of all pixels in the sliding window Variance; (5) Calculate the average value of pixel grayscale or color falling on the left half of the sliding window, the right half, the upper half and the lower half respectively: ${\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; c</span>}}}_{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; r</span>}}\underset{{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; r</span>}}{\overset{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; r</span>}}{\overset{\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; r</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$ ${\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; c</span>}}}_{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; r</span>}}\underset{{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; r</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; r</span>}}{\overset{\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; r</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$ ${\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; c</span>}}}_{\mathrm{<span\; class="notranslate">\; u</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; r</span>}}\underset{{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; r</span>}}{\overset{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; r</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; r</span>}}{\overset{\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$ ${\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; c</span>}}}_{\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; r</span>}}\underset{{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; r</span>}}{\overset{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; r</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; r</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$ here

and

Represents the average value of the grayscale or color of the pixels falling in the left half, right half, upper half and lower half of the sliding window, if the input image is a grayscale image, then

and

are scalars; if the input image is a color image, then

and

are vectors, and each vector has three components, namely red, green and blue components; (6) According to the definition of the α quantile point on the t distribution in statistics, check the left half of the sliding window, the right half, the average value of the grayscale or color of the pixel points in the upper half and the lower half, that is

and Whether it falls within the confidence interval of the mean value of the grayscale or color of the entire sliding window at a confidence level of 1-α: $P\left\{\right|\frac{{\stackrel{\&OverBar;}{c}}_j^i(x,\mathrm{the\; y})-{\stackrel{\&OverBar;}{c}}^i(x,\mathrm{the\; y})}{{\mathrm{\&sigma;}}^i(x,\mathrm{the\; y})/\sqrt{\mathrm{no}}}|<z_{\mathrm{\&alpha;}/2}\}=1-\mathrm{\&alpha;}---\left(7\right)$ If the input image is a grayscale image, the superscript i=1 here, because there is only one grayscale value on each pixel in the image, and when the input image is a color image, the superscript i here represents the color average or color variance corresponding red, green or blue components, while

The middle subscript j indicates that it is the left half, the right half, the upper half or the lower half of the sliding window, and n indicates that it falls on the left half, the right half, the upper half or the lower half of the sliding window The number of pixels in the middle, if the sliding window is a square, the n value is just equal to (2r+1)r, according to the given α value, the value of z _α/2 is obtained by querying the t distribution table; (7) If the left half of the sliding window, the right half, the average value of pixel grayscale or color in the upper half and lower half, that is and

Each component in all satisfies the formula (7), then it is judged that the pixel point (x, y) where the center of the sliding window is located falls in a uniform area with a side length of (2r+1), skip to step (9) ; (8) If the left half of the sliding window, the right half, the average value of pixel grayscale or color in the upper half and lower half, that is

and

If one of the components in α does not satisfy the formula (7), it means that the image area where the current sliding window is located is not a uniform area, then select from the discrete value set of the above smoothing filter spatial scale in order from large to small. A smaller value is used as the radius r of the sliding window, and then returns to step (4); (9) The radius r taken by the current sliding window is used as the smoothing filter spatial scale of the pixel at the center of the sliding window; (10) The sliding window is moved to the next pixel according to the scanning order of the raster lattice, and steps (3) to (9) are repeated until all pixels in the image have determined their respective spatial scales for smoothing and filtering.

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