CN101170641A - A method for image edge detection based on threshold sectioning - Google Patents

Abstract

The invention provides an image edge detection method based on threshold segmentation. The method is a novel threshold segmentation algorithm capable of thresholding all points of the image one by one and then sorting. The statistical information of average gray-scale value of the pixel neighborhood region in the image is used as the reference of threshold setting of the point, and the variance of gray-scale value of pixel in the neighborhood region of the point is used as additional judgment condition, so that the overall binarization of the region information is considered comprehensively to ensure the image edge to be extracted as target point. Additionally, the size of structural element for calculating the average value and variance can be adjusted to select the structural elements with different sizes according to different demands. The method can define each pixel with a threshold value, and the overall binarization of region information is comprehensively considered. The invention has good effect of image segmentation and high accuracy of edge positioning.

Description

A kind of method for detecting image edge of cutting apart based on threshold value

Technical field

The invention belongs to image processing field, relate to a kind of edge detection method, particularly a kind of method for detecting image edge of cutting apart based on threshold value.

Background technology

Carrying out image threshold segmentation is a kind of widely used image Segmentation Technology.This method is at first determined a gray threshold that is among the gradation of image span, then with the gray value of each pixel in the image all with this threshold, and according to comparative result the pixel of correspondence is divided into two classes: the gray value of pixel is a class greater than threshold value, the gray value of pixel is another kind of less than threshold value, this two classes pixel generally belongs to the target and background two class zones in the image, has just played the effect of Region Segmentation so pixel classified according to threshold value.

Based on the cutting apart and be one of the most basic difficult problem of image segmentation of threshold value, its difficult point is choosing of threshold value.The whether appropriate effect decisive role that threshold value is selected to cutting apart.

In the image threshold method of classics, usually all being to get a threshold value, is image segmentation background and target two parts simply, is the situation of two spikes for histogram distribution, the effect of cutting apart is fine, and just not necessarily obtains good effect for complex image.Improved single threshold method has big Tianjin method (Otsu), the big Tianjin of two dimension method etc.Wherein, big Tianjin method is a kind of method of searching optimal threshold, and can do following understanding to big Tianjin method: in fact this mode is exactly to make inter-class variance value maximum, and the prospect that threshold value is partitioned into and background two parts have constituted entire image.Variance is the inhomogeneity a kind of tolerance of intensity profile, variance yields is big more, two parts difference that composing images is described is big more, when part target mistake is divided into background or part background mistake and is divided into target, the capital causes two parts difference to diminish, therefore, make and mean the misclassification probability minimum cutting apart of inter-class variance maximum.The threshold value that calculates like this can farthest split target and background, but this method just can not reach desirable effect for the situation that has a plurality of intensity profile targets in the image.

At top problem, the someone has proposed many threshold methods, and it is divided into a plurality of target and backgrounds according to histogrammic distribution with image, thereby a plurality of threshold values are set they is distinguished respectively.The threshold segmentation method that also has local block, it is divided into a plurality of zones uniformly with entire image, counts the histogram in each zone respectively, and provides its threshold value for each block.The difference of this method consideration of regional grey value profile is provided with different threshold values for different blocks, to a certain extent, has solved the shortcoming that single threshold is cut apart, but has been easy to generate " blocking effect ".

Above method comprises the image of complex information for a width of cloth, all is difficult to by one or several threshold values the information in the image all be extracted.This comes image information is extracted with regard to needing a kind of threshold value of algorithm all get to(for) each pixel in the image.

Summary of the invention

The purpose of this invention is to provide a kind of method for detecting image edge of cutting apart based on threshold value, utilize the structural element piece to image pointwise get neighborhood, count the average and the variance of grey scale pixel value in each neighborhood of pixels, for pixel in the image, with the grey scale pixel value average of this neighborhood as this threshold value, and introduce the interior grey scale pixel value variance of this vertex neighborhood as the further decision condition, thus edge of image is extracted, realize taking all factors into consideration the overall binaryzation of area information.This algorithm can suppress the influence of noise to segmentation effect effectively, realizes accurately cutting apart of edge, thereby and can carry out the objective contour that the parameter setting obtains different-effect according to various needs.

A kind of method for detecting image edge of cutting apart based on threshold value may further comprise the steps:

Step 1: image is carried out preliminary treatment, the one part of pixel point that gray scale is the highest in the image is removed, and carry out gray scale and stretch, existing grey scale pixel value is evenly distributed in 0～255 the scope as far as possible;

Step 2: with block structure the unit usually average and the variance of grey scale pixel value in the pixel neighborhood of a point in the statistical picture;

Step 3: the probability density function that utilizes target pixel points and background pixel point to distribute, obtain respectively according to the probability density function formula and background dot to be used as impact point to carry out probability that branch time-like mistake takes place and impact point and be used as background dot and carry out the probability that branch time-like mistake takes place, and then obtain the whole new probability formula that this point is made mistakes by mixing the probability density function definition;

Step 4: according to the whole new probability formula that this point is made mistakes, the equation about grey scale pixel value average in the neighborhood that is gone out by the gaussian density derivation of equation is found the solution, the gray average of neighborhood territory pixel that obtains each pixel is as the threshold value of this point;

Step 5: the gray value of usefulness current pixel point and described threshold ratio are, if gray value is less than the mean value of the grey scale pixel value in its neighborhood, and the variance of grey scale pixel value is greater than a set value in the neighborhood, this point is defined as boundary point, otherwise just belong to background parts, forward next pixel then to, return step 2, the point in image is been scanned all.

Comprise two gray level region of target and background in the block structure element in the described step 2 at most.

Size of structure element is big more in the described step 2, the marginal information that extracts is many more, the edge is also just thick more, it is accurately that one side is arranged in the inboard at edge and the outside, and an inaccurate side is along with the increase of size of structure element is grown along grey value profile direction from high to low, and operation time is also along with size of structure element becomes big and elongated simultaneously.

In the gaussian density formula of described step 4, the variance of the gaussian density of target pixel points is identical with the gaussian density variance of background pixel point.

In each pixel of described step 4, background pixel point is identical with the probability that target pixel points occurs.

In the described step 4, the mean value of the mean value of the gaussian density of the pixel grey scale mean value of each neighborhood of pixel points replacement target pixel points and the gaussian density of background pixel point is as this point (i, j) threshold value T _Ij, and $T_{\mathrm{ij}}=\frac{1}{(2m+1)(2n+1)}\underset{x=-m}{\overset{m}{\mathrm{\Σ}}}\underset{y=-n}{\overset{n}{\mathrm{\Σ}}}z(i+x,j+y),$ Wherein, wherein z (i, j) (i, the grey scale pixel value of j) locating, m, n all are natural numbers in order to be positioned in the image.

Introduce gray difference degree in the piece in the described step 5 and come the classification of limited images target, utilize the variance of the pixel value of current vertex neighborhood to realize as criterion:

${{\mathrm{\σ}}_{\mathrm{ij}}}^2=\frac{1}{(2m+1)(2n+1)}\underset{x=-m}{\overset{m}{\mathrm{\Σ}}}\underset{y=-n}{\overset{n}{\mathrm{\Σ}}}{(z(i+x,j+y)-T_{\mathrm{ij}})}^2,$

Wherein, wherein z (i, j) (i, the grey scale pixel value of j) locating, m, n all are natural numbers in order to be positioned in the image.

The advantage of a kind of method for detecting image edge of cutting apart based on threshold value of the present invention is:

(1) this method is to the neighborhood statistical information of each pixel in the image, and to all given threshold value of each pixel, thereby the overall binaryzation of area information is taken all factors into consideration in realization, and image segmentation is effective, the edge accurate positioning;

(2) size of structure element of computation of mean values and variance can be adjusted in this method, can select the structural element of different sizes according to different needs;

(3) this method can obtain different effects according to the difference of parameter setting, for the more image of details, can with neighborhood in the variance ratio set value Detla of grey scale pixel value be provided with lessly.For the very big image of noise effect, can be provided with Detla bigger.

Description of drawings

Fig. 1 is the flow chart of a kind of method for detecting image edge of cutting apart based on threshold value of the present invention;

Fig. 2 a is the Canny operator segmentation result figure of first frame in the common video clips " Claire ";

The figure as a result that the structural element that Fig. 2 b handles first frame employing 3 * 3 in the common video clips " Claire " for a kind of method for detecting image edge of cutting apart based on threshold value of the present invention is cut apart;

The figure as a result that the structural element that Fig. 2 c handles first frame employing 7 * 7 in the common video clips " Claire " for a kind of method for detecting image edge of cutting apart based on threshold value of the present invention is cut apart;

The figure as a result that the structural element that Fig. 2 d handles first frame employing 11 * 11 in the common video clips " Claire " for a kind of method for detecting image edge of cutting apart based on threshold value of the present invention is cut apart;

The figure as a result that the structural element that Fig. 2 e handles first frame employing 15 * 15 in the common video clips " Claire " for a kind of method for detecting image edge of cutting apart based on threshold value of the present invention is cut apart.

Embodiment

The present invention is described in further detail below in conjunction with accompanying drawing.

The present invention proposes a kind of method for detecting image edge of cutting apart based on threshold value.The standard that this method utilizes the gray value average statistical information of neighborhood of pixels in the image to be provided with as this threshold value, and introduce the interior grey scale pixel value variance of this vertex neighborhood as the further decision condition, making the impact point that extracts is edge of image.Good rim detection effect has been played in the accurate positioning of this method edge.

As shown in Figure 1, a kind of method for detecting image edge of cutting apart based on threshold value may further comprise the steps:

Step 1: image is carried out preliminary treatment.Can think that generally the target area is lower than the gray value of background area in the image.Therefore can suppose that gray value is the highest in the image one part of pixel point influences not quite for the result of image segmentation, so before handling, this part point is removed.

According to the histogram distribution situation, be taken in the total pixel number and arrange from high to low by gray value, come preceding 10% pixel, even f (z) is an image histogram distribution function (supposing that it is a continuous function), establish given threshold value T, make:

${\∫}_T^{255}f\left(z\right)\mathrm{dz}=\mathrm{sum}/10---\left(1\right)$

Wherein sum is a sum of all pixels in the image.Is 255 with gray value greater than the whole assignment of the pixel of T.

Next carry out gray scale then and stretch, obtain the minimum gray value G in the image _Min, for the gradation of image value be G a bit, the gray value after gray scale stretches is:

$G_{\mathrm{str}}=\frac{G-G_{\min }}{T-G_{\min }}\×255---\left(2\right)$

Existing grey scale pixel value is evenly distributed in 0～255 the scope as far as possible, can proves image, its information content (entropy) maximum with smooth histogram distribution.This handles and helps extracting more information in the cutting apart of back in step.

Step 2: for a pixel in the image, count the average and the variance of grey scale pixel value in its neighborhood, judge as this binaryzation to belong to the standard that target pixel points still is a background pixel point with the block structure element.

Suppose that (i j) is positioned at (i, the grey scale pixel value of j) locating in the image to z.For convenience of calculation, we choose the statistical information that the neighborhood territory pixel gray value of this pixel usually calculates in the block structure unit that is of a size of (2m+1) * (2n+1) pixel size, and comprise two gray level region of target and background in the block structure element at most, wherein m, n are natural numbers.The computing formula of average and variance is as follows respectively:

$T_{\mathrm{ij}}=\frac{1}{(2m+1)(2n+1)}\underset{x=-m}{\overset{m}{\mathrm{\Σ}}}\underset{y=-n}{\overset{n}{\mathrm{\Σ}}}z(i+x,j+y)---\left(3\right)$

${{\mathrm{\σ}}_{\mathrm{ij}}}^2=\frac{1}{(2m+1)(2n+1)}\underset{x=-m}{\overset{m}{\mathrm{\Σ}}}\underset{y=-n}{\overset{n}{\mathrm{\Σ}}}{(z(i+x,j+y)-T_{\mathrm{ij}})}^2---\left(4\right)$

Step 3: the probability density function that utilizes target pixel points and background pixel point to distribute, obtain respectively and background dot is used as impact point carries out probability that branch time-like mistake takes place and impact point and be used as background dot and carry out the probability that branch time-like mistake takes place, and then obtain the whole probability that this point is made mistakes.

Suppose that piece image only comprises two main gray level region.Make z represent gray-scale value.We regard these values as random quantity, and their histogram can be counted as the estimation p (z) of their probability density function (PDF).A bigger gray scale in the hypothetical probabilities density function (PDF) corresponding to background, and less one described the gray scale of target in the image.Describing the mixing probability density function that overall intensity changes in the image is:

p(z)＝P ₁p ₁(z)+P ₂p ₂(z) (3)

Here P ₁And P ₂Be the probability that two class pixels occur: P ₁Be the probability of object pixel, promptly pixel is the object pixel with value z; Equally, P ₂It is the probability that pixel belongs to background pixel.Suppose that any given pixel is not to belong to target to belong to background exactly, make:

P ₁+P ₂＝1 (4)

The main purpose that threshold value is cut apart is to select a T value, makes average error probability minimum when determining that a given pixel belongs to target or background.P ₁(z) and P ₂(z) be respectively the probability density function that object pixel and background pixel distribute, then a background dot be used as impact point and carried out the probability that branch time-like mistake takes place and be:

$E_1\left(T\right)={\∫}_{-\∞}^T{p}_2\left(z\right)\mathrm{dz}---\left(5\right)$

Equally, an impact point being used as background dot carries out the probability that branch time-like mistake takes place and is:

$E_2\left(T\right)={\∫}_T^{\∞}{p}_1\left(z\right)\mathrm{dz}---\left(6\right)$

The whole probability of to sum up, makeing mistakes is:

E(T)＝P ₂E ₁(T)+P ₁E ₂(T) (7)

Step 4: according to the whole new probability formula that this point is made mistakes, the equation that is gone out by the gaussian density derivation of equation is found the solution, the average gray of neighborhood territory pixel that obtains each pixel is as the threshold value of this point.

Desire to obtain wrong minimum threshold T, need be differentiated (use Leibnitz's rule) to T and made differential expression equal zero by formula (7), the result be:

P ₁p ₁(T)＝P ₂p ₂(T) (8)

The analysis expression that obtains a T need be known the equation of two probability density functions (PDF).Be not always can estimate in practice to these two density.Usually way is a density of utilizing parameter to become more readily available.One of main density of Shi Yonging is gaussian density in this case.At this moment:

$p\left(z\right)=\frac{p_1}{\sqrt{2\mathrm{\π}}{\mathrm{\σ}}_1}{e}^{-\frac{{(z-{\mathrm{\μ}}_1)}^2}{{{2\mathrm{\σ}}_1}^2}}+\frac{p_2}{\sqrt{2\mathrm{\π}}{\mathrm{\σ}}_2}{e}^{-\frac{{(z-{\mathrm{\μ}}_2)}^2}{{{2\mathrm{\σ}}_2}^2}}---\left(9\right)$

Here μ ₁And σ ₁ ²Be respectively the average and the variance of the gaussian density of target pixel points, μ ₂And σ ₂ ²Be respectively the average and the variance of the gaussian density of background pixel point.Formula (8) is brought in the formula (9), can obtains quadratic equation about T:

AT ²+BT+C＝0 (10)

Here:

A＝σ ₁ ²-σ ₂ ²B＝2(μ ₁σ ₂ ²-μ ₂σ ₁ ²)

$C={\mathrm{\μ}}_1{{\mathrm{\σ}}_2}^2-{\mathrm{\μ}}_2{{\mathrm{\σ}}_1}^2+{{4\mathrm{\σ}}_1}^2{{\mathrm{\σ}}_2}^2\ln \left(\frac{{\mathrm{\σ}}_2{P}_1}{{\mathrm{\σ}}_1{P}_2}\right)---\left(11\right)$

If the variance of the gaussian density of target pixel points is identical with the gaussian density variance of background pixel point, i.e. σ ²=σ ₁ ²=σ ₂ ², then above equation separate for:

$T=\frac{{\mathrm{\μ}}_1+{\mathrm{\μ}}_2}{2}+\frac{{\mathrm{\σ}}^2}{{\mathrm{\μ}}_1-{\mathrm{\μ}}_2}\ln \left(\frac{P_1}{P_2}\right)---\left(12\right)$

If the probability that background pixel point and target pixel points occur is identical, i.e. P ₁=P ₂, then optimum thresholding is the average of distribution average.

More than analyze and can be generalized in the fritter of image local.Therefore, can replace μ with the average gray of the neighborhood territory pixel of each pixel ₁And μ ₂Mean value, become this point (i, j) threshold value T _Ij, as shown in Equation (3) $T_{\mathrm{ij}}=\frac{1}{(2m+1)(2n+1)}\underset{x=-m}{\overset{m}{\mathrm{\Σ}}}\underset{y=-n}{\overset{n}{\mathrm{\Σ}}}z(i+x,j+y).$

Step 5: current pixel point is judged, judged that current some pixel belongs to boundary point or background, forward next pixel then to, return step 2, the point in image is been scanned all.

In a zone that has image object and background simultaneously, this regional pixel variance is bigger certainly; Simultaneously, only have target and only existing in the block of background, the pixel variance is less in the zone.And only carry out threshold decision, also may be categorized as image object to the image local sudden change that some noises and quantization error cause, so can quote the threshold value that the pixel value variance of the current vertex neighborhood of the interior gray difference degree of expression piece participates in weighing this point.

If (i, gray value j) is less than the mean value T of the grey scale pixel value in its neighborhood of formula (3) expression for this point _Ij, and the variances sigma of the interior grey scale pixel value of neighborhood of formula (4) expression _Ij ²Greater than set difference Detla, this point is defined as boundary point, otherwise just belongs to background, forward next pixel then to, forward step 2 to, the point in image is been scanned all, and the segmentation effect that obtains is exactly an edge of image.

Shown in Fig. 2 a, Fig. 2 b, choose first frame in the common video clips " Claire ", after cutting, obtain the image of 256 * 256 pixels, verify the segmentation effect of this algorithm.

In order to play the effect of contrast, shown in Fig. 2 a, select for use classical Canny operator that original image is cut apart.Adjust parameter through repeatedly testing, obtained the better effect that compares, this moment, parameter was 0.9,0.8,0.8 (being respectively the gaussian filtering standard variance, the ratio that ratio between low threshold value and the high threshold and high threshold account for total number of image pixels).Shown in Fig. 2 b, for using this method, the result that the structural element of employing 3 * 3 is cut apart original image.

From image as can be seen, the segmentation effect of this method has been compared remarkable advantages with the segmentation effect image of Canny operator, both edge accurate positionings, and the facial parts of Canny operator segmentation effect image is cut poor effect, be beyond recognition each position, as eye, nose, mouth etc.

Shown in Fig. 2 b, Fig. 2 c, Fig. 2 d, Fig. 2 e, the edge result who adopts the small scale structures element to be partitioned into is that single pixel is wide or wide near single pixel, but the result does not guarantee it is continuous; And adopt the large scale structural element to cut apart, the edge overstriking, but continuity makes moderate progress.

It is accurately that always there is the location of a side (inboard or the outside) at the edge, and an inaccurate side is along with the increase of size of structure element is grown along grey value profile direction from high to low, that is to say, if the grey value profile of the background area at place, image border is higher than the grey value profile of target area, the location in the outside is accurately, otherwise the location of inboard, edge is accurately.When needs obtain the continuous outline of target, can adopt the large scale structural element to cut apart.As can be seen from the figure: when size of structure element becomes big, can find that the Changing Pattern at the edge that extracts is grown to the inside, promptly the location in the outside, edge is accurately.

This method can be selected the structural elements of different sizes according to different needs, can obtain different effects according to the difference of parameter setting.For the set-point Detla that compares with the variance of grey scale pixel value in the neighborhood,, can be provided with Detla less if the details of image is more; If the noise effect of image is very big, can be provided with Detla bigger.

Claims (7)

1. method for detecting image edge of cutting apart based on threshold value is characterized in that this method may further comprise the steps:

Step 1: image is carried out preliminary treatment, the one part of pixel point that gray scale is the highest in the image is removed, and carry out gray scale and stretch, existing grey scale pixel value is evenly distributed in 0～255 the scope as far as possible;

Step 2: with block structure the unit usually average and the variance of grey scale pixel value in the pixel neighborhood of a point in the statistical picture;

Step 3: the probability density function that utilizes target pixel points and background pixel point to distribute, obtain respectively according to the probability density function formula and background dot to be used as impact point to carry out probability that branch time-like mistake takes place and impact point and be used as background dot and carry out the probability that branch time-like mistake takes place, and then obtain the whole new probability formula that this point is made mistakes by mixing the probability density function definition;

Step 4: according to the whole new probability formula that this point is made mistakes, the equation about grey scale pixel value average in the neighborhood that is gone out by the gaussian density derivation of equation is found the solution, the gray average of neighborhood territory pixel that obtains each pixel is as the threshold value of this point;

Step 5: the gray value of usefulness current pixel point and described threshold ratio are, if gray value is less than the mean value of the grey scale pixel value in its neighborhood, and the variance of grey scale pixel value is greater than a set value in the neighborhood, then this point is defined as boundary point, otherwise just belong to background parts, forward next pixel then to, return step 2, the point in image is been scanned all.

2. according to the described a kind of method for detecting image edge of cutting apart based on threshold value of claim 1, it is characterized in that: comprise two gray level region of target and background in the block structure element in the described step 2 at most.

3. according to the described a kind of method for detecting image edge of cutting apart based on threshold value of claim 1, it is characterized in that: size of structure element is big more in the described step 2, the marginal information that extracts is many more, the edge is also just thick more, it is accurately that one side is arranged in the inboard at edge and the outside, and an inaccurate side is along with the increase of size of structure element is grown along grey value profile direction from high to low, and operation time is also along with size of structure element becomes big and elongated simultaneously.

4. according to the described a kind of method for detecting image edge of cutting apart based on threshold value of claim 1, it is characterized in that: in the gaussian density formula of described step 4, the variance of the gaussian density of target pixel points is identical with the gaussian density variance of background pixel point.

5. according to the described a kind of method for detecting image edge of cutting apart based on threshold value of claim 1, it is characterized in that: in each pixel of described step 4, background pixel point is identical with the probability that target pixel points occurs.

6. according to the described a kind of method for detecting image edge of cutting apart based on threshold value of claim 1, it is characterized in that: in the described step 4, the mean value of the mean value of the gaussian density of the pixel grey scale mean value replacement target pixel points of each neighborhood of pixel points and the gaussian density of background pixel point, as this point (i, j) threshold value T _Ij, and $T_{\mathrm{ij}}=\frac{1}{(2m+1)(2n+1)}\underset{x=-m}{\overset{m}{\mathrm{\Σ}}}\underset{y=-n}{\overset{n}{\mathrm{\Σ}}}z(i+x,j+y),$ Wherein, wherein z (i, j) (i, the grey scale pixel value of j) locating, m, n all are natural numbers in order to be positioned in the image.

7. according to the described a kind of method for detecting image edge of cutting apart based on threshold value of claim 1, it is characterized in that: introduce gray difference degree in the piece in the described step 5 and come the classification of limited images target, utilize the variance of the pixel value of current vertex neighborhood to realize as criterion:

${{\mathrm{\σ}}_{\mathrm{ij}}}^2=\frac{1}{(2m+1)(2n+1)}\underset{x=-m}{\overset{m}{\mathrm{\Σ}}}\underset{y=-n}{\overset{n}{\mathrm{\Σ}}}{(z(i+x,j+y)-T_{\mathrm{ij}})}^2,$

Wherein, wherein z (i, j) (i, the grey scale pixel value of j) locating, m, n all are natural numbers in order to be positioned in the image.

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