CN103390280A - Rapid threshold segmentation method based on gray level-gradient two-dimensional symmetrical Tsallis cross entropy - Google Patents

Abstract

The invention relates to a rapid threshold segmentation method based on gray level-gradient two-dimensional symmetrical Tsallis cross entropy, aims at the problems that approximate assumption exists in a conventional gray level-average gray level histogram and a whole solution space is required to be searched by calculation, so that segmentation is inaccurate and the efficiency is not high, and provides improved two-dimensional symmetrically Tsallis cross entropy threshold segmentation and a rapid recursive method thereof. The threshold segmentation method is higher in universality and accurate in segmentation; in order to realize accurate segmentation of a gray image, a new gray level-gradient two-dimensional histogram is adopted, and a two-dimensional symmetrical Tsallis cross entropy theory with a superior segmentation effect is combined with the histogram, so that the gray level image segmentation accuracy is effectively improved; the requirement for on-line timeliness of an industrial assembly line is met at the same time, a novel rapid recursive algorithm is adopted, and redundant calculation is reduced; and after a gray level image of the industrial assembly line is processed, the inside of an image zone is uniform, the contour boundary is accurate, the texture detail is clear, and at same time, good universality is provided.

Description

The Fast Threshold dividing method of intensity-based-gradient two-dimensional symmetric Tsallis cross entropy

Technical field

The present invention relates to the image segmentation field in machine vision, specifically refer to the quickly and accurately threshold segmentation method of a kind of two-dimensional symmetric Tsallis cross entropy realization of intensity-based-histogram of gradients to the industrial flow-line gray level image.

Background technology

Image segmentation is the treatment technology in early stage of graphical analysis and vision detection system, and Threshold segmentation is that a kind of use is the most general, processing is the most effective, realizes the simplest image partition method.The result of Threshold segmentation directly affects subsequent characteristics and extracts the precision of identifying with target, so Threshold sementation is in occupation of vital status.On industrial flow-line, Threshold sementation has application very widely: as the character recognition on workpiece, bearing dustproof cover surface defects detection, the detection of solar battery panel slight crack, magnetic tile surface defect detection, cereal appearance quality detection etc.The Halcon machine vision software of Germany MVTec company provides numerous cases of Threshold segmentation,, as the detection of zigzag fashion defect, bga chip encapsulation inspection, the detection of mechanograph peak etc., has reached subpixel accuracy.

Under the industrial environment of harshness, be used for the captured image of non-contact detecting and tend to be subject to the interference of the factors such as noise, uneven illumination, therefore how choosing optimal threshold becomes the key of cutting apart.For this problem, Chinese scholars has been carried out broad research, has proposed multiple threshold segmentation method.Traditional classic algorithm one dimension Otsu method is because of the limited requirement that can not meet industrial Accurate Segmentation of applicable situation.In order to strengthen noise immunity and to promote the effect of cutting apart, existing large quantity algorithm considers that not only the half-tone information of pixel also considers other relevant information of pixel, as the average of pixel neighborhood, intermediate value, variance, gradient etc., algorithm can be divided pixel in the higher dimensional space of these variablees.

Threshold segmentation method based on entropy concept (such as Shannon entropy, minimum cross entropy, Tsallis entropy etc.) is the focus of Recent study.Li and Brink have successively introduced minimum cross entropy criterion,, because the targets to different sizes can produce preferably segmentation effect and realize simply, have been subject to extensive concern.Sahoo and Arora have proposed two-dimentional Tsallis entropy Research on threshold selection, although segmentation effect increases, real-time is poor, can't be applied to industry spot.Tang Yinggan etc. combine minimum cross entropy and Tsallis entropy to derive two-dimentional minimum Tsallis cross entropy Research on threshold selection, but do not meet the tolerance symmetry, and real-time is still poor.Wu's one congruence has proposed two-dimentional Tsallis gray scale entropy Research on threshold selection,, although the method has reflected the homogeneity of gray scale in class, do not reflect the difference degree of quantity of information between two probability distribution, so segmentation effect need improve still.Based on two-dimensional symmetric Tsallis cross entropy Research on threshold selection, not only can characterize the difference degree between image before and after cutting apart, meet the symmetric requirement of distance metric, and can make the uniform gray level of cutting apart target and background inside in rear image.In order further to improve the real-time of Threshold Segmentation Algorithm and to cut apart accuracy, the researchist has proposed some methods such as oblique point-score, decomposition method, accurate point-score, straight-line method, polygometry, for the present invention has established theoretical foundation massively.

Summary of the invention

The object of the invention is to that segmentation precision is not high for existing in existing method, universality is strong, real-time high not, in original two dimensional Tsallis entropy method, tiltedly divide on the basis of Tsallis entropy method and contrast original two dimensional Otsu method, two-dimentional Tsallis gray scale entropy method, propose the Threshold sementation of the two-dimensional symmetric Tsallis cross entropy of intensity-based-histogram of gradients, develop that a kind of segmentation performance is superior, universality is strong, be applicable to the threshold segmentation method in the higher industrial flow-line of requirement of real-time.

The inventive method is based on following consideration: intra-zone homogeneity, edge contour and the grain details of image is that the performance of Threshold segmentation embodies, in order fully to highlight these information, on the basis of original gray level-average gray level two-dimensional histogram, new Gray Level-Gradient two-dimensional histogram is proposed.The inventive method combines its two-dimensional histogram and two-dimensional symmetric Tsallis cross entropy theory, and, by novel quick recurrence method, realizes accurate, Fast Segmentation to gray level image.

The technical scheme of Fast Threshold dividing method that the present invention is based on Gray Level-Gradient two-dimensional symmetric Tsallis cross entropy is as follows:

(1) Real-time Obtaining industrial flow-line gray level image p (x, y), process by adopting the stronger intermediate value 4 angular domain templates of adaptability to carry out filtering to gray level image, obtains filtered image g (x, y), and the maximum gray scale H of image after calculation of filtered;

(2) ask for the absolute difference of gray level after pixel grayscale and its filtering, thereby obtain the neighborhood gradient, and calculate maximum neighborhood gradient W;

(3) set up the Gray Level-Gradient two-dimensional histogram, the two-dimensional histogram horizontal ordinate is that mean value, the ordinate of gray level after pixel grayscale and its filtering is the neighborhood gradient of this pixel, note h (i, j) represent the frequency that this two tuple occurs, try to achieve the joint probability p (i, j) of its generation;

(4) passing threshold vector (t, s) is divided into lower-left area 0, lower right area 1, right regions 2,3 four parts of top left region to two-dimensional histogram, and as shown in Figure 1, area 0 is corresponding with impact point; Zone 1 is corresponding with background dot; Marginal point between zone 2 and zone 3 corresponding target and backgrounds and the noise spot in image;

(5) the total two-dimensional symmetric Tsallis cross entropy of target and background two classes, i.e. criterion function:

$\mathrm{\Φ}(t,s)=\frac{1}{q-1}\left\{\underset{i=0}{\overset{t}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)\right[{{\mathrm{\μ}}_{\mathrm{oi}}}^{1-q}(t,s)i^q+{{\mathrm{\μ}}_{\mathrm{oi}}}^q(t,s)i^{1-q}+{{\mathrm{\μ}}_{\mathrm{oj}}}^{1-q}(t,s)j^q+{{\mathrm{\μ}}_{\mathrm{oj}}}^q(t,s)j^{q-1}]+$

$\underset{i=t+1}{\overset{H}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)[{{\mathrm{\μ}}_{\mathrm{bi}}}^{1-q}(t,s)i^q+{{\mathrm{\μ}}_{\mathrm{bi}}}^q(t,s)i^{1-q}+{{\mathrm{\μ}}_{\mathrm{bj}}}^{1-q}(t,s)j^q+{{\mathrm{\μ}}_{\mathrm{bj}}}^q(t,s)j^{1-q}]\}$

Relevant definition amount is respectively:

$\left\{\begin{array}{c}{\mathrm{\α}}_{\mathrm{oi}}(t,s)=\underset{i=0}{\overset{t}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)i^q\\ {\mathrm{\α}}_{\mathrm{oj}}(t,s)=\underset{i=0}{\overset{t}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)j^q\end{array}\right.$ $\left\{\begin{array}{c}{\mathrm{\β}}_{\mathrm{oi}}(t,s)=\underset{i=0}{\overset{t}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)i^{1-q}\\ {\mathrm{\β}}_{\mathrm{oj}}(t,s)=\underset{i=0}{\overset{t}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)j^{1-q}\end{array}\right.$

$\left\{\begin{array}{c}{\mathrm{\α}}_{\mathrm{bi}}(t,s)=\underset{i=t+1}{\overset{H}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)i^q\\ {\mathrm{\α}}_{\mathrm{bj}}(t,s)=\underset{i=t+1}{\overset{H}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)j^q\end{array}\right.$ $\left\{\begin{array}{c}{\mathrm{\β}}_{\mathrm{bi}}(t,s)=\underset{i=t+1}{\overset{H}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)i^{1-q}\\ {\mathrm{\β}}_{\mathrm{bj}}(t,s)=\underset{i=t+1}{\overset{H}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)j^{1-q}\end{array}\right.$

(6) probability of statistics target class and background classes generation is respectively p _o(t, s) and p _b(t, s), the mean vector of target class and background classes is respectively

And μ _b(t, s)=[μ _bi(t, s), μ _bj(t, s)] ^T.Adopt novel quick recurrence method to calculate target class p _o(t, s), α _oi(t, s), α _oj(t, s), β _oi(t, s), β _oj(t, s),

With

Have 7 correlatives altogether.With p _o(t, s) is example:

If note

There is following recursion formula:

$P_s\left(t\right)=\underset{j=0}{\overset{s-1}{\mathrm{\Σ}}}p(t,j)+p(t,s)=p_{s-1}\left(t\right)+p(t,s)$

$p_o(t,s)=\underset{i=0}{\overset{t}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)=\underset{i=0}{\overset{t-1}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)+\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(t,j)=p_o(t-1,s)+p_s\left(t\right)$

(7) the approximate hypothesis of abandoning tradition two-dimensional histogram, 7 of background classes correlatives, with p _b(t, s) is example: p _b(t, s)=p _o(H, s)-p _o(t, s);

(8) adopt the value of the mode comparison two-dimensional symmetric Tsallis cross entropy formula of tabling look-up, corresponding best threshold vector (t when obtaining maximal value ^*, s ^*).

Beneficial effect of the present invention: the present invention adopts intermediate value 4 angular domain templates to carry out filtering to gray level image, improve the difference of centre of neighbourhood grey scale pixel value and institute's reference pixel gray-scale value, this template has the effect of mean filter and medium filtering concurrently simultaneously, so this template has stronger adaptability; The present invention adopts the Gray Level-Gradient two-dimensional histogram, and this histogram makes not only that to cut apart the image border profile accurate, and grain details is clear, and has very strong noise immunity, and the target and background intra-zone is more even.Divide in the two-dimensional histogram zone, considered the internal point of target and background comprehensively, the maximal value of neighborhood shade of gray is generally less, needs the solution space of traversal greatly to dwindle, and has improved the real-time of algorithm; The present invention adopts new two-dimensional histogram and through the pervasive two-dimensional symmetric Tsallis cross entropy strong, superior performance of a large amount of tests, combines, further improved the quality that gray level image is cut apart, and, by novel quick recurrence method, further improved real-time.

Description of drawings

Schematic diagram is divided in Fig. 1 Gray Level-Gradient two-dimensional histogram zone.

Fig. 2 overall flow figure of the present invention.

Embodiment

For making the purpose, technical solutions and advantages of the present invention clearer, below in conjunction with instantiation, and with reference to accompanying drawing, the specific embodiment of the present invention is elaborated, the present invention is including but not limited to example.

As shown in Figure 2, be overall flow figure of the present invention, concrete steps are as follows:

The first step:

(1.1) utilize intermediate value 4 angular domain templates to carry out filtering and noise reduction to the industrial flow-line gray level image f (x, y) that collects, this template is as follows:

$A=\left(\begin{array}{ccc}1& 0& 1\\ 0& 0& 0\\ 1& 0& 1\end{array}\right)$

At first quicksort is carried out in the gray-scale value of the pixel on 4 angles of each pixel in gray level image, then to the mean value of second and the 3rd value after sorting as the output, thereby obtain filtered image g (x, y).The maximum average value H=max[(f (x, y) of gray level+g (x, y) after calculating pixel gray level and its filtering again)/2].

(1.2) ask for the absolute difference of gray level after pixel grayscale and its filtering, use | f (x, y)-g (x, y) | expression, thus obtain the neighborhood gradient, and calculate maximum neighborhood gradient W=max (| f (x, y)-g (x, y) |).

Second step:

(2.1) set up gray level-gradient two-dimensional histogram, the two-dimensional histogram horizontal ordinate is that mean value, the ordinate of gray level after pixel grayscale and its filtering is the neighborhood gradient of this pixel.If with h (i, j) represent this two tuple ([f (x, y)+g (x, y)]/2=i, | f (x, y)-g (x, y) |=frequency that j) occurs, the joint probability of its generation:

$p(i,j)=\frac{h(i,j)}{M\×N}$

Here M * N is total pixel number of image, i=0, and 1 ... H; J=0,1 ..., W, H and W are respectively maximum mean value and maximum shade of gray.

The 3rd step: if (t, s) is the threshold vector of choosing, (t, s) the two-dimensional histogram plane figure is divided into four parts, as shown in Figure 1, after the pixel grayscale of area 0 and its filtering, the mean value of gray level is less, and the neighborhood gradient is also less, and is therefore corresponding with impact point; After the pixel grayscale in zone 1 and its filtering, the mean value of gray level is larger, and the neighborhood gradient is also less, and is therefore corresponding with background dot; Zone 2 and zone 3 have larger neighborhood gradient, therefore the marginal point between corresponding target and background and the noise spot in image.

(3.1) probability of target class and background classes generation is respectively:

$P_o(t,s)=\underset{i=0}{\overset{t}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j),p_b(t,s)=\underset{i=t+1}{\overset{H}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)$

(3.2) mean vector of target class and background classes is respectively:

${\mathrm{\μ}}_o(t,s)={[{\mathrm{\μ}}_{\mathrm{oi}}(t,s),{\mathrm{\μ}}_{\mathrm{oi}}(t,s)]}^T={[\frac{\underset{i=0}{\overset{t}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)i}{p_o(t,s)},\frac{\underset{i=0}{\overset{t}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)j}{p_o(t,s)}]}^T$

${\mathrm{\μ}}_b(t,s)={[{\mathrm{\μ}}_{\mathrm{bi}}(t,s),{\mathrm{\μ}}_{\mathrm{bj}}(t,s)]}^T={[\frac{\underset{i=t+1}{\overset{H}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)i}{p_b(t,s)},\frac{\underset{i=t+1}{\overset{H}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)j}{p_b(t,s)}]}^T$

If note $\stackrel{\‾}{{\mathrm{\μ}}_{\mathrm{oi}}}(t,s)=\underset{i=0}{\overset{t}{\mathrm{\Σ}}}\underset{s=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)i,\stackrel{\‾}{{\mathrm{\μ}}_{\mathrm{oj}}}(t,s)=\underset{i=0}{\overset{t}{\mathrm{\Σ}}}\underset{s=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)j,$ The mean vector of background and target two classes can be calculated as follows:

${\mathrm{\μ}}_o(t,s)={[{\mathrm{\μ}}_{\mathrm{oi}}(t,s),{\mathrm{\μ}}_{\mathrm{oj}}(t,s)]}^T={[\frac{\stackrel{\‾}{{\mathrm{\μ}}_{\mathrm{oi}}}(t,s)}{p_o(t,s)},\frac{\stackrel{\‾}{{\mathrm{\μ}}_{\mathrm{oj}}}(t,s)}{p_o(t,s)}]}^T$

${\mathrm{\μ}}_b(t,s)={[{\mathrm{\μ}}_{\mathrm{bi}}(t,s),{\mathrm{\μ}}_{\mathrm{bj}}(t,s)]}^T={[\frac{\stackrel{\‾}{{\mathrm{\μ}}_{\mathrm{oi}}}(H,s)-\stackrel{\‾}{{\mathrm{\μ}}_{\mathrm{oi}}}(H,s)}{p_o(H,s)-p_o(t,s)},\frac{\stackrel{\‾}{{\mathrm{\μ}}_{\mathrm{oj}}}(H,s)-\stackrel{\‾}{{\mathrm{\μ}}_{\mathrm{oj}}}(t,s)}{p_o(H,s)-p_o(t,s)}]}^T$

The 4th step:

(4.1) the symmetrical Tsallis cross entropy of objective definition class:

$H_o^q(t,s)={[H_{\mathrm{oi}}^q(t,s),H_{\mathrm{oj}}^q(t,s)]}^T=$

$[\frac{1}{q-1}\underset{i=0}{\overset{t}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}{i}^{q}p(i,j){{\mathrm{\μ}}_{\mathrm{oi}}}^{1-q}(t,s)+\frac{1}{q-1}\underset{i=0}{\overset{t}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}{i}^{1-q}p(i,j){{\mathrm{\μ}}_{\mathrm{oi}}}^q(t,s),$

$\frac{1}{q-1}\underset{i=0}{\overset{t}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}{j}^{q}p(i,j){{\mathrm{\μ}}_{\mathrm{oj}}}^{1-q}(t,s)+\frac{1}{q-1}\underset{i=0}{\overset{t}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}{j}^{1-q}p(i,j){{\mathrm{\μ}}_{\mathrm{oj}}}^q(t,s){]}^T$

The symmetrical Tsallis cross entropy of definition background classes:

$H_b^q(t,s)={[H_{\mathrm{bi}}^q(t,s),H_{\mathrm{bj}}^q(t,s)]}^T=$

$[\frac{1}{q-1}\underset{i=t+1}{\overset{H}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}{i}^{q}p(i,j){{\mathrm{\μ}}_{\mathrm{bi}}}^{1-q}(t,s)+\frac{1}{q-1}\underset{i=t+1}{\overset{H}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}{i}^{1-q}p(i,j){{\mathrm{\μ}}_{\mathrm{bi}}}^q(t,s),$

$\frac{1}{q-1}\underset{i=t+1}{\overset{H}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}{j}^{q}p(i,j){{\mathrm{\μ}}_{\mathrm{bj}}}^{1-q}(t,s)+\frac{1}{q-1}\underset{i=t+1}{\overset{H}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}{j}^{1-q}p(i,j){{\mathrm{\μ}}_{\mathrm{bj}}}^q(t,s){]}^T$

Order

$\left\{\begin{array}{c}{\mathrm{\α}}_{\mathrm{oi}}(t,s)=\underset{i=0}{\overset{t}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)i^q\\ {\mathrm{\α}}_{\mathrm{oj}}(t,s)=\underset{i=0}{\overset{t}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)j^q\end{array}\right.$ $\left\{\begin{array}{c}{\mathrm{\β}}_{\mathrm{oi}}(t,s)=\underset{i=0}{\overset{t}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)i^{1-q}\\ {\mathrm{\β}}_{\mathrm{oj}}(t,s)=\underset{i=0}{\overset{t}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)j^{1-q}\end{array}\right.$

$\left\{\begin{array}{c}{\mathrm{\α}}_{\mathrm{bi}}(t,s)=\underset{i=t+1}{\overset{H}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)i^q\\ {\mathrm{\α}}_{\mathrm{bj}}(t,s)=\underset{i=t+1}{\overset{H}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)j^q\end{array}\right.$ $\left\{\begin{array}{c}{\mathrm{\β}}_{\mathrm{bi}}(t,s)=\underset{i=t+1}{\overset{H}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)i^{1-q}\\ {\mathrm{\β}}_{\mathrm{bj}}(t,s)=\underset{i=t+1}{\overset{H}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)j^{1-q}\end{array}\right.$

(4.2) total two-dimensional symmetric Tsallis cross entropy is

$H^q(t,s)=H_o^q(t,s)+H_b^q(t,s)$

If Φ (t, s) is considered as the criterion function that two-dimensional symmetric Tsallis cross entropy threshold value is chosen, namely

$\mathrm{\Φ}(t,s)=\frac{1}{q-1}[{{\mathrm{\μ}}_{\mathrm{oi}}}^{1-q}(t,s){\mathrm{\α}}_{\mathrm{oi}}(t,s)+{{\mathrm{\μ}}_{\mathrm{oi}}}^q(t,s){\mathrm{\β}}_{\mathrm{oi}}(t,s)+{{\mathrm{\μ}}_{\mathrm{oj}}}^{1-q}(t,s){\mathrm{\α}}_{\mathrm{oj}}(t,s)+{{\mathrm{\μ}}_{\mathrm{oj}}}^q(t,s){\mathrm{\β}}_{\mathrm{oj}}(t,s)+$

${{\mathrm{\μ}}_{\mathrm{bi}}}^{1-q}(t,s){\mathrm{\α}}_{\mathrm{bi}}(t,s)+{{\mathrm{\μ}}_{\mathrm{bi}}}^q(t,s){\mathrm{\β}}_{\mathrm{bi}}(t,s)+{{\mathrm{\μ}}_{\mathrm{bj}}}^{1-q}(t,s){\mathrm{\α}}_{\mathrm{bj}}(t,s)+{{\mathrm{\μ}}_{\mathrm{bj}}}^q(t,s){\mathrm{\β}}_{\mathrm{bj}}(t,s)]=\frac{1}{q-1}{\mathrm{\Φ}}^{\′}(t,s)$

Parameter q usually get 0.8 o'clock best, this moment, q-1＜0, hour obtained optimal threshold when Φ (t, s) reaches, obtains optimal threshold in the time of should making Φ ' (t, s) reach maximum, namely

$(t^{*},s^{*})=\mathrm{Arg}\underset{0\≤t,s\≤L-1}{\max }\left\{{\mathrm{\Φ}}^{\′}(t,s)\right\}$

The 5th step: adopt novel quick recurrence method to calculate target class p _o(t, s), α _oi(t, s), α _oj(t, s), β _oi(t, s), β _oj(t, s),

With Have 7 correlatives altogether.

(5.1) existing with p _o(t, s) and α _oi(t, s) two amount recursion are calculated as example:

If note $p_s\left(t\right)=\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(t,j),{\mathrm{\α}}_s\left(t\right)=\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(t,j)t^q,$ There is following recursion formula:

$p_s\left(t\right)=\underset{j=0}{\overset{s-1}{\mathrm{\Σ}}}p(t,j)+p(t,s)=p_{s-1}\left(t\right)+p(t,s)$

${\mathrm{\α}}_s\left(t\right)=\underset{j=0}{\overset{s-1}{\mathrm{\Σ}}}p(t,j)t^q+p(t,s)t^q={\mathrm{\α}}_{s-1}\left(t\right)+p(t,s)t^q$

$p_o(t,s)=\underset{i=0}{\overset{t}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)=\underset{i=0}{\overset{t-1}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)+\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(t,j)=p_o(t-1,s)+p_s\left(t\right)$

${\mathrm{\α}}_{\mathrm{oi}}(t,s)=\underset{i=0}{\overset{t}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)i^q=\underset{i=0}{\overset{t-1}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)i^q+\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(t,j)t^q={\mathrm{\α}}_{\mathrm{oi}}(t-1,s)+{\mathrm{\α}}_s\left(t\right)$

For each calculating p _o(t, s) and α _oi(t, s) is as long as two are measured the p that utilizes front to obtain _o(t-1, s) and α _oi(t-1, s) and current p _s(t) and α _sAnd p (t), _s(t) and α _s(t) be that each train value is cumulative calculates by calculating, H+1 row altogether, need not be at every turn node-by-node algorithm again.In like manner can recursion calculate α _oj(t, s), β _oj(t, s), β _oj(t, s),

With

(5.2) calculate background classes p _b(t, s), α _bi(t, s), α _bj(t, s), β _bi(t, s), β _bj(t, s),

With

Have 7 correlatives altogether.

Existingly according to the histogrammic method of gray level-average gray level, introduced approximate hypothesis, ignored part background dot and the impact point of paying attention in other two zones, therefore to existing wrong minute cutting apart of gray level image.The present invention does not take approximate hypothesis:

Now with p _b(t, s), α _bi(t, s) and

Three amounts are example:

p _b(t，s)＝p _o(H，s)-p _o(t，s)

α _bi(t，s)＝α _oi(H，s)-α _oi(t，s)

$\stackrel{\‾}{{\mathrm{\μ}}_{\mathrm{bi}}}(t,s)=\stackrel{\‾}{{\mathrm{\μ}}_{\mathrm{oi}}}(H,s)-\stackrel{\‾}{{\mathrm{\μ}}_{\mathrm{oi}}}(t,s)$

For each calculating p _b(t, s), α _bi(t, s) and

As long as measure the value of utilizing last row in the look-up table of front and deduct current p for three _o(t, s), namely the correlative of target class and background classes and deduct the target class correlative and just can obtain the background classes correlative.In like manner can calculate α _bj(t, s), β _bi(t, s), β _bj(t, s) and

Therefore (5.3), due to the distribution character of Gray Level-Gradient two-dimensional histogram, exist neutral element in area 0 and 1, during with the relevant amount of two-dimensional histogram, certainly existing repetition values in recursion.To this,, as p (i, j)=0, do not carry out double counting in calculating, reduced so invalid computing, accelerated arithmetic speed.

The 6th step: adopt the value of the more symmetrical Tsallis cross entropy of the mode formula of tabling look-up, corresponding best threshold vector (t when obtaining Φ ' (t, s) maximal value ^*, s ^*).

Claims (5)

1. the Fast Threshold dividing method of intensity-based-gradient two-dimensional symmetric Tsallis cross entropy, it is characterized in that: it can realize the industrial flow-line image is cut apart accurately and rapidly, makes that image-region after cutting apart is inner evenly, profile boundary accurate, grain details be clear and legible; The method is based on the Threshold sementation of two-dimensional symmetric Tsallis cross entropy; Adopt new Gray Level-Gradient two-dimensional histogram, first use intermediate value 4 neighborhood templates to carry out filtering and noise reduction to gray level image, then ask for its neighborhood gradient, set up two-dimensional histogram; The two-dimensional symmetric Tsallis cross entropy formula that employing is derived, as criterion function, is realized the Threshold segmentation to image; Adopt the correlative in novel FAST RECURSIVE ALGORITHM calculation criterion function, reduce redundant computation, improve the real-time of algorithm; Whole algorithm comprises following step:

(1) Real-time Obtaining industrial flow-line gray level image p (x, y), process by adopting the stronger intermediate value 4 angular domain templates of adaptability to carry out filtering to gray level image, obtains filtered image g (x, y), and the maximum gray scale H of image after calculation of filtered;

(2) ask for the absolute difference of gray level after pixel grayscale and its filtering, thereby obtain the neighborhood gradient, and calculate maximum neighborhood gradient W;

(3) set up the Gray Level-Gradient two-dimensional histogram, the two-dimensional histogram horizontal ordinate is that mean value, the ordinate of gray level after pixel grayscale and its filtering is the neighborhood gradient of this pixel, note h (i, j) represent the frequency that this two tuple occurs, try to achieve the joint probability p (i, j) of its generation;

(4) passing threshold vector (t, s) is divided into lower-left area 0, lower right area 1, right regions 2,3 four parts of top left region to two-dimensional histogram, and area 0 is corresponding with impact point, and zone 1 is corresponding with background dot; Marginal point between zone 2 and zone 3 corresponding target and backgrounds and the noise spot in image;

(5) the total two-dimensional symmetric Tsallis cross entropy of target and background two classes, i.e. criterion function:

$\mathrm{\Φ}(t,s)=\frac{1}{q-1}\left\{\underset{i=0}{\overset{t}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)\right[{{\mathrm{\μ}}_{\mathrm{oi}}}^{1-q}(t,s)i^q+{{\mathrm{\μ}}_{\mathrm{oi}}}^q(t,s)i^{1-q}+{{\mathrm{\μ}}_{\mathrm{oj}}}^{1-q}(t,s)j^q+{{\mathrm{\μ}}_{\mathrm{oj}}}^q(t,s)j^{q-1}]+$

$\underset{i=t+1}{\overset{H}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)[{{\mathrm{\μ}}_{\mathrm{bi}}}^{1-q}(t,s)i^q+{{\mathrm{\μ}}_{\mathrm{bi}}}^q(t,s)i^{1-q}+{{\mathrm{\μ}}_{\mathrm{bj}}}^{1-q}(t,s)j^q+{{\mathrm{\μ}}_{\mathrm{bj}}}^q(t,s)j^{1-q}]\}$

Relevant definition amount is respectively:

$\left\{\begin{array}{c}{\mathrm{\α}}_{\mathrm{oi}}(t,s)=\underset{i=0}{\overset{t}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)i^q\\ {\mathrm{\α}}_{\mathrm{oj}}(t,s)=\underset{i=0}{\overset{t}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)j^q\end{array}\right.$ $\left\{\begin{array}{c}{\mathrm{\β}}_{\mathrm{oi}}(t,s)=\underset{i=0}{\overset{t}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)i^{1-q}\\ {\mathrm{\β}}_{\mathrm{oj}}(t,s)=\underset{i=0}{\overset{t}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)j^{1-q}\end{array}\right.$

$\left\{\begin{array}{c}{\mathrm{\α}}_{\mathrm{bi}}(t,s)=\underset{i=t+1}{\overset{H}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)i^q\\ {\mathrm{\α}}_{\mathrm{bj}}(t,s)=\underset{i=t+1}{\overset{H}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)j^q\end{array}\right.$ $\left\{\begin{array}{c}{\mathrm{\β}}_{\mathrm{bi}}(t,s)=\underset{i=t+1}{\overset{H}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)i^{1-q}\\ {\mathrm{\β}}_{\mathrm{bj}}(t,s)=\underset{i=t+1}{\overset{H}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)j^{1-q}\end{array}\right.$

(6) probability of statistics target class and background classes generation is respectively p _o(t, s) and p _b(t, s), the mean vector of target class and background classes is respectively And μ _b(t, s)=[μ _bi(t, s), μ _bj(t, s)] ^T, adopt novel quick recurrence method to calculate target class p _o(t, s), α _oi(t, s), α _oj(t, s), β _oi(t, s), β _oj(t, s),

With

Have 7 correlatives altogether, with p _o(t, s) is example:

If note

There is following recursion formula:

$P_s\left(t\right)=\underset{j=0}{\overset{s-1}{\mathrm{\Σ}}}p(t,j)+p(t,s)=p_{s-1}\left(t\right)+p(t,s)$

$p_o(t,s)=\underset{i=0}{\overset{t}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)=\underset{i=0}{\overset{t-1}{\mathrm{\Σ}}}\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(i,j)+\underset{j=0}{\overset{s}{\mathrm{\Σ}}}p(t,j)=p_o(t-1,s)+p_s\left(t\right)$

(7) the approximate hypothesis of abandoning tradition two-dimensional histogram, 7 of background classes correlatives, with p _b(t, s) is example: p _b(t, s)=p _o(H, s)-p _o(t, s);

(8) calculate in as p (i, j)=0, do not carry out double counting, reduced so invalid computing, accelerated arithmetic speed;

(9) adopt the value of the more symmetrical Tsallis cross entropy of the mode formula of tabling look-up, corresponding best threshold vector (t when obtaining Φ ' (t, s) maximal value ^*, s ^*).

2. the Fast Threshold dividing method of intensity-based-gradient two-dimensional symmetric Tsallis cross entropy according to claim 1, it is characterized in that: described new Gray Level-Gradient two-dimensional histogram, horizontal ordinate is the mean value of gray level after pixel grayscale and its filtering, the neighborhood gray level is that ordinate is the neighborhood gradient of this pixel through the intermediate value 4 filtered gray levels of angular domain template.

3. the Fast Threshold dividing method of intensity-based-gradient two-dimensional symmetric Tsallis cross entropy according to claim 1 is characterized in that: described two-dimensional symmetric Tsallis cross entropy combines and derives criterion function with new Gray Level-Gradient two-dimensional histogram.

4. the Fast Threshold dividing method of intensity-based-gradient two-dimensional symmetric Tsallis cross entropy according to claim 1 is characterized in that: described novel FAST RECURSIVE ALGORITHM, reduced the redundant computation of algorithm, and improved real-time.

5. the Fast Threshold dividing method of intensity-based-gradient two-dimensional symmetric Tsallis cross entropy according to claim 1, it is characterized in that: described accurate Threshold segmentation, abandon the approximate hypothesis in traditional gray level-other two zones of neighborhood averaging gray level, improved the accuracy that gray level image is cut apart.

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