CN101604395B - Method for classifying invariant moment of similar objects by multi-scale mathematical morphology - Google Patents

Abstract

The invention provides a method for classifying an invariant moment of similar objects by multi-scale mathematical morphology. The method comprises the following basic flow: firstly, extracting detailed characteristics of an object training image by the multi-scale mathematical morphology; performing various combinations on multi-scale detailed characteristics of an object to form real different parts of similar objects in different types on multiple scales; secondly, calculating values of invariant moments of the real different parts by selecting an arbitrary invariant moment method; thirdly, evaluating the values of the invariant moments of the real different parts through one measurement, and automatically selecting the real different parts which can effectively differentiate the similar objects and the corresponding invariant moment thereof; and finally, classifying the similar objects by the selected real different parts and the corresponding invariant moment thereof. The method can realize effective classification on the similar objects, can be widely applied to various target identification and classification systems, and has wide market prospect and application value in the field of digital image processing and pattern recognition.

Description

A kind of morphologic method for classifying invariant moment of similar objects of multi-scale mathematical that utilizes

(1) technical field

The present invention relates to a kind of morphologic method for classifying invariant moment of similar objects of multi-scale mathematical that utilizes, belong to Digital Image Processing and mode identification technology.It relates generally to mathematical morphology, invariant moments and target identification technology, can be widely used in Target Recognition and target classification.

(2) background technology

Invariant moments is the important mathematical tool of Target Recognition and classification, and good invariant moments classification capacity can effectively improve the validity of Target Recognition and classification.In order to reach better recognition and classifying quality, various invariant moments are suggested, and comprising: Hu square, Z square, small echo square etc.Though these Invariant Moment Method effect when distinguishing the inhomogeneity object is better, the effect of these Invariant Moment Method is relatively poor when the profile of inhomogeneity object is closely similar.

Hu at first proposed to have seven invariant moments of translation, rotation, convergent-divergent unchangeability in 1961, low order square wherein is mainly used in the global feature of describing object, and High Order Moment is mainly used in the minutia of describing object.Subsequently, the Hu square is widely used in the various application, but the Hu square also shows various shortcomings in various application, as can not effectively discerning the very similar inhomogeneity object of profile.The Z square not only has good orthogonality as a kind of effective orthogonal moment, and can be effectively applied in image reconstruction.The orthogonal property of Z square makes its object identification ability be better than Hu square and other some orthogonal moments commonly used, can describe the invariant features of image better.But because the Z square also is the global shape calculating invariant moment features by object, so the Z square can not divide profile very similar inhomogeneity object by active zone equally.Wavelet transformation can be on different scale the exploded view picture, can extract the details of image on different scale.Sheng etc. are that instrument passes through the Z square and constructed a series of small echo invariant moments with the wavelet transformation.The small echo invariant moments can be constructed any rank invariant moments that can reflect object different scale feature, because wavelet transformation can extract the feature on the object different scale, so the small echo invariant moments can more efficiently be distinguished similar object.But the effect of small echo invariant moments is subjected to certain inhibition when distinguishing the very similar inhomogeneity object of profile.

In fact, even two type objects are closely similar, two type objects also have than big-difference on some details.Therefore, if invariant moments can effectively be extracted and be used to calculate to these details differences, the classification capacity of these Invariant Moment Method will be improved greatly.This shows, the key of active zone branch profile homologue body is to find the method that can effectively extract minutias real different in the similar object, utilize these features to carry out invariant moments then and calculate,, reach the purpose of distinguishing similar object with this classification capacity that improves invariant moments.Mathematical morphology has obtained widespread use in Flame Image Process, the effective details of smoothed image, and mathematical morphology can extract the details in the image in other words.What is more important, multi-scale mathematical morphology can extract the details on the image different scale, and this can help the utilization of image detail more.

(3) summary of the invention

1, purpose: for active zone divides similar object and remedies the deficiency of classic method, the invention provides a kind of morphologic method for classifying invariant moment of similar objects of multi-scale mathematical that utilizes, this method is extracted the minutia of similar object on different scale by multi-scale mathematical morphology, and define a kind of selection and estimate minutia and the corresponding invariant moments that automatic selection can improve the invariant moments classifying quality, solve effective classification problem of similar object, for various practical applications provide effective tool.

2, technical scheme: in order to achieve this end, in the technical scheme of the present invention, its flow process is at first to utilize the minutia of multi-scale mathematical morphology extraction object training image, and the multiple dimensioned minutia of object is carried out the real different parts of the various merging formation similar objects of inhomogeneity on a plurality of yardsticks.Then, the Invariant Moment Method of choosing any one kind of them is calculated the value of the invariant moments of these real different parts.Subsequently, by a kind of estimate the value of the invariant moments of real different parts is evaluated and tested selection real different parts and the corresponding invariant moments thereof that can active zone divide similar object automatically.At last, the invariant moments of the real different parts of utilization selection and correspondence thereof is to similar sorting objects.Realize effective classification of similar object.

A kind of morphologic method for classifying invariant moment of similar objects of multi-scale mathematical that utilizes of the present invention, its concrete steps are as follows:

Be provided with the invariant moments of individual certain type of n and the morphology operations that needs calculate a yardstick;

Step 1: get the two type objects f that need differentiation ₁And f ₂Training image;

Step 2: establish i=1, i represents the sequence number of invariant moments, and its scope is 1≤i≤n;

Step 3: establish q=0, q represents the sequence number of calculative yardstick;

Step 4: establish p=q+1, p represents the sequence number of calculative another yardstick relevant with q;

Step 5: at object f ₁, calculate f ₁The multiple dimensioned morphology minutia of merging from yardstick p to yardstick q:

P＞q, 1≤p≤a, 1≤q≤a; f ₁ ^PqThe f that expression calculates ₁The multiple dimensioned morphology minutia of merging from yardstick p to yardstick q;

Calculate f ₁ ^PqI invariant moments: ${\mathrm{MM}}_i^{\mathrm{pq}}=\mathrm{IM}\left({\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="H2009100893373E00021.png,H2009100893373E00031.png"\; state="\{\{state\}\}">f</figure-callout>}}_1^{\mathrm{pq}}\right);$ Calculate f ₁The MM of all corresponding training images _i ^Pq, and with all MM _i ^PqForm a vectorial VM _i ^Pq, at another kind of object f ₂With form another vectorial VM with quadrat method _i ^Pq

Step 6: the Q that estimates that is calculated as follows two vectors _i ^Pq:

$Q_i^{\mathrm{pq}}({\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="H2009100893373E00021.png,H2009100893373E00031.png"\; state="\{\{state\}\}">f</figure-callout>}}_1,f_2)=\left|\frac{\mathrm{\&sigma;}({\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="H2009100893373E00021.png,H2009100893373E00031.png"\; state="\{\{state\}\}">f</figure-callout>}}_1,{\mathrm{MM}}_i^{\mathrm{pq}})+\mathrm{\&sigma;}({\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="H2009100893373E00041.png"\; state="\{\{state\}\}">f</figure-callout>}}_2,{\mathrm{MM}}_i^{\mathrm{pq}})}{m({\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="H2009100893373E00021.png,H2009100893373E00031.png"\; state="\{\{state\}\}">f</figure-callout>}}_1,{\mathrm{MM}}_i^{\mathrm{pq}})-m({\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="H2009100893373E00041.png"\; state="\{\{state\}\}">f</figure-callout>}}_2,{\mathrm{MM}}_i^{\mathrm{pq}})}\right|,$

And with Q _i ^PqPut into measure vector Q.Wherein: σ and m are f ₁And f ₂The variance and the average of all invariant moments values of different training image correspondences;

Step 7: p=p+1 is if p＞a enters step 8; Otherwise enter step 5;

Step 8: q=q+1 is if q＞a enters step 9; Otherwise enter step 4;

Step 9: i=i+1 is if i＞n enters step 10; Otherwise enter step 3;

Step 10: r minimum value and corresponding invariant moments MM thereof before finding among the Q _i ^Pq

Step 11: utilize r MM _i ^PqWith the real different parts of correspondence by near neighbor method to the similar sorting objects of two classes.

The present invention utilizes multi-scale mathematical morphology to extract the minutia of object training image, and the multiple dimensioned minutia of object merged form a plurality of real different parts of the similar object of inhomogeneity on a plurality of yardsticks, the difference that makes these real different parts is greater than the difference on the original objects global shape; At this moment, available any Invariant Moment Method is calculated the value of the invariant moments of these real different parts, because the value of invariant moments calculates on real different parts, so the value of invariant moments has notable difference between the inhomogeneity object; By a kind of estimate the value of the invariant moments of these real different parts is evaluated and tested the selection active zone real different parts and the corresponding invariant moments thereof of dividing similar object more automatically; The invariant moments of real different parts that utilization is selected and correspondence thereof realizes effective classification of similar object to similar sorting objects.

3, advantage and effect: the present invention makes full use of the similar object possible different piece on the shape details outside, can select the real different parts of similar object automatically, the value of the invariant moments that calculates by the local real different parts of utilizing similar object replaces utilizing the value of the invariant moments that the overall calculation of similar object obtains, reach the purpose of the similar object of effective classification, can be widely used in all kinds of Target Recognition and categorizing system, have vast market prospect and using value.

(4) description of drawings

Fig. 1 utilizes the theory diagram of the morphologic method for classifying invariant moment of similar objects of multi-scale mathematical for the present invention.

Fig. 2 is for showing example image " 1 " and " I " of the similar object classifying quality of the present invention.

" 1 " and a kind of real different parts in " I " that Fig. 3 extracts for multi-scale mathematical morphology.

Fig. 4 is the contrast of the classifying quality of classifying quality of the present invention and Hu square.Wherein (a) figure is the classifying quality of two invariant moments selecting of the present invention, and (b) figure is the classifying quality of Hu square.

Fig. 5 is the contrast of the classifying quality of classifying quality of the present invention and small echo invariant moments.Wherein (a) figure is the classifying quality of two invariant moments selecting of the present invention, and (b) figure is the classifying quality of small echo invariant moments.

Symbol description is as follows among the figure: M1 among Fig. 4 (a) and M2 represent the first and second rank squares of Hu square respectively; MIM among Fig. 4 (b) ₁ ⁵¹And MIM ₂ ⁵¹Be better two invariant moments of performance of utilizing the present invention on the square basis, first and second rank of Hu square, to obtain, be illustrated respectively in the first and second rank squares on the 5th to first yardstick; ‖ F among Fig. 5 (a) _2,6,0 ^Wavelet‖ and ‖ F _2,4,0 ^Wavelet‖ is two small echo squares that can active zone divide similar object; MIM among Fig. 5 (b) ₃ ⁴¹And MIM ₄ ⁴¹Be better two invariant moments of performance of utilizing the present invention on first, second, third and Fourth-order moment basis of Hu square, to obtain, be illustrated respectively in the third and fourth rank square on the 4th to first yardstick.

(5) embodiment

Implementing condition precedent of the present invention is: the training image for the treatment of class object must be provided.

The condition of utilizing the present invention to classify is: needs obtain to treat the image of class object.

In order to understand technical scheme of the present invention better, embodiments of the present invention are further described below in conjunction with accompanying drawing.

A kind of morphologic method for classifying invariant moment of similar objects of multi-scale mathematical that utilizes of the present invention, the flow process of its work as shown in Figure 1, the concrete implementation detail step of each several part is as follows:

Step 1: get the two type objects f that need differentiation ₁And f ₂Training image;

Step 2: establish i=1 (1≤i≤n), get i invariant moments.To similar sorting objects the time, the effect of Hu square is relatively poor, and in order to show validity of the present invention, the present invention selects for use the Hu square as the invariant moments of using in the method.Certainly also can select Z square, small echo square etc. for use.The basic definition of 7 Hu squares commonly used is as follows:

M1＝η ₂₀+η ₀₂，

$\mathrm{<figure-callout\; id="2"\; label="M"\; filenames="H2009100893373E00041.png"\; state="\{\{state\}\}">M</figure-callout>}2={({\mathrm{\&eta;}}_{20}+{\mathrm{\&eta;}}_{02})}^2-4{\mathrm{\&eta;}}_{11}^2,$

$\mathrm{<figure-callout\; id="3"\; label="M"\; filenames="H2009100893373E00031.png,H2009100893373E00041.png"\; state="\{\{state\}\}">M</figure-callout>}3={({\mathrm{\&eta;}}_{30}+3{\mathrm{\&eta;}}_{12}\mathrm{})}^2-{(3{\mathrm{\&eta;}}_{11}^2-{\mathrm{\&eta;}}_{03})}^2,$

$\mathrm{<figure-callout\; id="4"\; label="M"\; filenames="H2009100893373E00031.png,H2009100893373E00041.png"\; state="\{\{state\}\}">M</figure-callout>}4={({\mathrm{\&eta;}}_{30}+{\mathrm{\&eta;}}_{12})}^2-{({\mathrm{\&eta;}}_{21}^2-{\mathrm{\&eta;}}_{03})}^2,$

M5＝(η ₃₀-3η ₁₂)(η ₃₀+η ₁₂)[(η ₃₀+η ₁₂) ²-3(η ₂₁+η ₀₃) ²]+(3η ₂₁-η ₀₃)(η ₂₁+η ₀₃)[3(η ₃₀+η ₁₂) ²-(η ₂₁+η ₀₃) ²]，

M6＝(η ₂₀-η ₀₂)[(η ₃₀+η ₁₂) ²-(η ₂₁+η ₀₃) ²]+4η ₁₁(η ₃₀+η ₁₂)(η ₂₁+η ₀₃)，

M7＝(3η ₂₁-η ₃₀)(η ₃₀+η ₁₂)[(η ₃₀+η ₁₂) ²-3(η ₂₁+η ₀₃) ²]+(3η ₁₂-η ₃₀)(η ₂₁+η ₀₃)[3(η ₀₃+η ₁₂) ²-(η ₂₁+η ₀₃) ²]。

Wherein, ${\mathrm{\&eta;}}_{\mathrm{pq}}=\frac{{\mathrm{\&mu;}}_{\mathrm{pq}}}{{\mathrm{\&mu;}}_{00}},$

${\mathrm{\&mu;}}_{\mathrm{pq}}=\underset{i=0}{\overset{u-1}{\mathrm{\&Sigma;}}}\underset{j=0}{\overset{v-1}{\mathrm{\&Sigma;}}}{(x_i-\stackrel{\&OverBar;}{x})}^p{(y_i-\stackrel{\&OverBar;}{y})}^{q}f(x,y),$

$\stackrel{\&OverBar;}{x}=\frac{s_{10}}{s_{00}},$ $\stackrel{\&OverBar;}{y}=\frac{s_{01}}{s_{00}},$

$s_{\mathrm{pq}}=\underset{i=0}{\overset{u-1}{\mathrm{\&Sigma;}}}\underset{j=0}{\overset{v-1}{\mathrm{\&Sigma;}}}{x}_i^p{y}_j^{q}f(x,y),$

U, v are the length and width of image.

Because the present invention can effectively extract the real different parts of similar object by the details of similar object, so n is optional with the less low order invariant moments of calculated amount, as the preceding two rank invariant moments (M1 of Hu square, M2, n=2 at this moment) or preceding quadravalence invariant moments (M1, M2, M3, M4, n=4 at this moment).

Step 3: establish q=0, start circulation at q.

Step 4: establish p=q+1, start circulation at p.

Step 5: at object f ₁, be calculated as follows f ₁Multiple dimensioned morphological feature.

Multiple dimensioned be characterized as of image on the p yardstick

The minutia of image from yardstick p to yardstick q that merges is as follows:

Wherein,

${\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="H2009100893373E00021.png,H2009100893373E00031.png"\; state="\{\{state\}\}">f</figure-callout>}}_1\&CirclePlus;B=\underset{u,v}{\max }\left(f_1(x-u,y-v)\right)$

Zero, ●,

With

Be respectively mathematical morphology open and close, expansion and erosion operation symbol. $\mathrm{qB}=B\&CirclePlus;B\&CirclePlus;...\&CirclePlus;B,$ Altogether to B expansion q time.

Calculate the multiple dimensioned feature f that merges ₁ ^PqI invariant moments: ${\mathrm{MM}}_i^{\mathrm{pq}}=\mathrm{IM}\left({\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="H2009100893373E00021.png,H2009100893373E00031.png"\; state="\{\{state\}\}">f</figure-callout>}}_1^{\mathrm{pq}}\right).$ Calculate the value MM of i invariant moments of all training image correspondences of this object _i ^Pq, and with all MM _i ^PqForm a vectorial VM _i ^Pq

At another kind of object f ₂Form another vectorial VM _i ^Pq

Step 6: the Q that estimates that is calculated as follows two vectors _i ^Pq:

$Q_i^{\mathrm{pq}}({\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="H2009100893373E00021.png,H2009100893373E00031.png"\; state="\{\{state\}\}">f</figure-callout>}}_1,f_2)=\left|\frac{\mathrm{\&sigma;}({\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="H2009100893373E00021.png,H2009100893373E00031.png"\; state="\{\{state\}\}">f</figure-callout>}}_1,{\mathrm{MM}}_i^{\mathrm{pq}})+\mathrm{\&sigma;}({\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="H2009100893373E00041.png"\; state="\{\{state\}\}">f</figure-callout>}}_2,{\mathrm{MM}}_i^{\mathrm{pq}})}{m({\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="H2009100893373E00021.png,H2009100893373E00031.png"\; state="\{\{state\}\}">f</figure-callout>}}_1,{\mathrm{MM}}_i^{\mathrm{pq}})-m({\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="H2009100893373E00041.png"\; state="\{\{state\}\}">f</figure-callout>}}_2,{\mathrm{MM}}_i^{\mathrm{pq}})}\right|,$

Wherein, σ is the variance and the average of the invariant moments value of different training image correspondences with m; And with Q _i ^PqPut into measure vector Q.From Q _i ^PqDefinition as can be seen, Q _i ^PqGet over the bright invariant moments MM of novel _i ^PqClassification capacity stronger, corresponding real different parts more can embody the difference between the two class different objects.

Step 7: circulation p, establish p=p+1, if p＞a enters step 8; Otherwise enter step 5.A is the scale parameter of multiple dimensioned morphology operations, can choose according to practical application, general desirable a＜10.

Step 8: circulation q, establish q=q+1, if q＞a enters step 9; Otherwise enter step 4.

Step 9: circulation i, establish i=i+1, if i＞n enters step 10; Otherwise enter step 3.

Step 10: select the good invariant moments of classification capacity

From Q _i ^PqDefinition as can be known, Q _i ^PqBeing worth more little, corresponding invariant moments, to distinguish the ability of current inhomogeneity object good more, therefore only need find among the Q before the invariant moments MM of value correspondence of r minimum _i ^PqAnd corresponding real different parts f ^Pq, be used to distinguish the similar object of two classes.R can choose according to concrete application, in order to take into account validity and robustness, common desirable r=2.

Step 11: to similar sorting objects

At first utilize f ^PqCalculate the real different parts of two class homologue volume images, utilize r corresponding MM then _i ^PqOn real different parts, calculate the invariant moments of the similar object of two classes, and the nearest neighbour method that utilization is at last used always (referring to: Bian Zhaoqi, Zhang Xuegong etc. pattern-recognition. publishing house of Tsing-Hua University, Beijing, 1999, chapter 6 .) invariant moments of classification two type objects, reach the purpose of distinguishing two type objects.

In order to show effect of the present invention, " 1 " and " I " of adopting appearance similar as experimental image, parts of images as shown in Figure 2.As can be seen from Figure 2, " 1 " is extremely similar with " I ", only has less difference at the top.Utilize multi-scale mathematical morphology to extract the real different parts of " 1 " and " I ", Fig. 3 is a kind of real different parts wherein.As can be seen from Figure 3, compare with Fig. 2, the part that extracts among Fig. 3 exists more different really.In order to show effect of the present invention better, selected for use the relatively poor relatively Hu square of classification capacity as the invariant moments MM that needs among the present invention to use, it is labeled as MIM, and to the Hu square with can divide the small echo invariant moments of similar object to compare by active zone.With stability preferably two the low order invariant moments in first rank and second rank be used for the method (n=2) that the present invention proposes, Fig. 4 is the classifying quality of the present invention and Hu square, though the first and second rank squares of Hu square can not be distinguished " 1 " and " I " (figure (a)), and have utilized the morphologic the present invention of multi-scale mathematical can effectively distinguish " 1 " and " I " (figure (b)).In order to show effect of the present invention better, the present invention and small echo invariant moments are compared, Fig. 5 is a classifying quality.Fig. 5 (a) though in the small echo invariant moments can distinguish " 1 " and " I ", also just just can distinguish.But utilized the present invention (n=4) (Fig. 5 (b)) of 4 low order Hu squares can distinguish " 1 " and " I " well.This explanation the present invention can divide similar object by active zone, and more effective than the classic method.In addition, any Invariant Moment Method can replace the Hu square and be used for the invariant moments MM that wants required for the present invention, and the classification capacity of invariant moments MM is good more, and the ability that the present invention distinguishes similar object is good more.Therefore, the present invention not only can be used for similar object classification, also can be widely used in the raising of invariant moments invariant moments classification capacity when distinguishing similar object, has wide practical use in types of applications.

Claims (1)

1. one kind is utilized the morphologic method for classifying invariant moment of similar objects of multi-scale mathematical, is provided with the invariant moments of n selected type and the morphology operations that needs calculate a yardstick, and it is characterized in that: these method concrete steps are as follows:

Step 1: get the two type objects f that need differentiation ₁And f ₂Training image;

Step 2: establish i=1, i represents the sequence number of invariant moments, and its scope is 1≤i≤n;

Step 3: establish q=0, q represents the sequence number of calculative yardstick;

Step 4: establish p=q+1, p represents the sequence number of calculative another yardstick relevant with q;

Step 5: at object f ₁, calculate f ₁The multiple dimensioned morphology minutia of merging from yardstick p to yardstick q:

P＞q, 1≤p≤a, 1≤q≤a;

The f that expression calculates ₁The multiple dimensioned morphology minutia of merging from yardstick p to yardstick q;

Wherein,

$f_1\&CirclePlus;B=\underset{u,v}{\max }\left(f_1(x-u,y-v)\right)$

Zero, ●, With

Be respectively mathematical morphology open and close, expansion and erosion operation symbol; Altogether to B expansion q time;

Calculate

I invariant moments:

Expression utilizes invariant moments to calculate

The invariant moments value, IM represents invariant moments,

Expression is calculated

Invariant moments and its result be

Calculate f ₁All corresponding training images

And with all Form a vector Remember that this vector is V ₁At another kind of object f ₂With form another vector with quadrat method Remember that this vector is V ₂

Step 6: be calculated as follows estimating of two vectors

$Q_i^{\mathrm{pq}}(f_1,f_2)=\left|\frac{{\mathrm{\&sigma;}}_1+{\mathrm{\&sigma;}}_2}{m_1-m_2}\right|,$

And will Put into measure vector Q, wherein: σ ₁And m ₁Be vectorial V ₁Variance and average; σ ₂And m ₂Be vectorial V ₂Variance and average;

Step 7: p=p+1 is if p＞a enters step 8; Otherwise enter step 5;

Step 8: q=q+1 is if q＞a enters step 9; Otherwise enter step 4;

Step 9: i=i+1 is if i＞n enters step 10; Otherwise enter step 3;

Step 10: r minimum value and corresponding invariant moments thereof before finding among the Q

Step 11: utilize r With the real different parts of correspondence by near neighbor method to the similar sorting objects of two classes.

Images