CN101604395A - A Moment-Invariant Classification Method for Similar Objects Using Multiscale Mathematical Morphology - Google Patents

Abstract

A method of invariant moment classification of similar objects using multi-scale mathematical morphology. The basic process is to firstly use multi-scale mathematical morphology to extract the detailed features of the object training image, and combine the multi-scale detailed features of the object to form different Truly distinct parts of similar objects at multiple scales. Then, choose one of the invariant moment methods to calculate the values of the invariant moments for these truly different parts. Subsequently, the value of the invariant moments of the truly different parts is evaluated by a measure, and the truly different parts and their corresponding invariant moments that can effectively distinguish similar objects are automatically selected. Finally, similar objects are classified using the selected truly distinct parts and their corresponding invariant moments. Achieving efficient classification of similar objects. The invention can be widely used in various object recognition and classification systems, and has broad market prospects and application value in the fields of digital image processing and pattern recognition.

Description

A Moment-Invariant Classification Method for Similar Objects Using Multiscale Mathematical Morphology

(1) Technical field

The invention relates to a method for classifying invariant moments of similar objects using multi-scale mathematical morphology, and belongs to the technical fields of digital image processing and pattern recognition. It mainly involves mathematical morphology, invariant moments and target recognition technology, and can be widely used in target recognition and target classification.

(2) Background technology

Invariant moment is an important mathematical tool for target recognition and classification, and good invariant moment classification ability can effectively improve the effectiveness of target recognition and classification. In order to achieve better recognition and classification results, various invariant moments are proposed, including: Hu moment, Z moment, wavelet moment, etc. Although these moment invariant methods are good at distinguishing objects of different classes, they are less effective when the shapes of objects of different classes are very similar.

Hu first proposed seven invariant moments with translation, rotation, and scaling invariance in 1961. The low-order moments are mainly used to describe the overall characteristics of the object, and the high-order moments are mainly used to describe the detailed characteristics of the object. Subsequently, the Hu moment is widely used in various applications, but the Hu moment also shows various shortcomings in various applications, such as not being able to effectively identify different types of objects with very similar shapes. As an effective orthogonal moment, Z moment not only has good orthogonality, but also can be effectively applied to image reconstruction. The orthogonality of the Z moment makes its object recognition ability better than the Hu moment and some other commonly used orthogonal moments, and can better describe the invariant characteristics of the image. However, since the Z moment is also calculated through the overall shape of the object, the Z moment cannot effectively distinguish different types of objects with very similar shapes. Wavelet transform can decompose images on different scales, and can extract the details of images on different scales. Sheng et al. used wavelet transform as a tool to construct a series of wavelet invariant moments through Z moments. Wavelet invariant moments can construct arbitrary order invariant moments that can reflect the characteristics of different scales of objects. Since wavelet transform can extract the characteristics of objects at different scales, wavelet invariant moments can effectively distinguish similar objects. However, the effect of wavelet invariant moments is restrained to a certain extent when distinguishing different types of objects with very similar shapes.

In fact, even if the two types of objects are very similar, there will be large differences in some details between the two types of objects. Therefore, if these detailed differences can be effectively extracted and used to calculate invariant moments, the classification ability of these invariant moment methods will be greatly improved. It can be seen that the key to effectively distinguishing similar objects is to find a method that can effectively extract the truly different detailed features of similar objects, and then use these features to calculate invariant moments, so as to improve the classification ability of invariant moments and achieve the goal of distinguishing similar objects. object's purpose. Mathematical morphology has been widely used in image processing, which can effectively smooth the details of the image, which means that mathematical morphology can extract the details in the image. More importantly, multi-scale mathematical morphology can extract the details of images at different scales, which will be more conducive to the utilization of image details.

(3) Contents of the invention

1. Purpose: In order to effectively distinguish similar objects and make up for the shortcomings of traditional methods, the present invention provides a similar object invariant moment classification method using multi-scale mathematical morphology. This method extracts similar objects in different The detailed features on the scale, and define a selection measure to automatically select the detailed features and corresponding invariant moments that can improve the classification effect of invariant moments, solve the problem of effective classification of similar objects, and provide effective tools for various practical applications.

2. Technical solution: In order to achieve this goal, in the technical solution of the present invention, the process is to firstly use multi-scale mathematical morphology to extract the detailed features of the object training image, and variously combine the multi-scale detailed features of the object to form different types Truly distinct parts of similar objects at multiple scales. Then, choose one of the invariant moment methods to calculate the values of the invariant moments for these truly different parts. Subsequently, the value of the invariant moments of the truly different parts is evaluated by a measure, and the truly different parts and their corresponding invariant moments that can effectively distinguish similar objects are automatically selected. Finally, similar objects are classified using the selected truly distinct parts and their corresponding invariant moments. Achieving efficient classification of similar objects.

The present invention utilizes the similar object invariant moment classification method of multi-scale mathematical morphology, and its specific steps are as follows:

There are n invariant moments of a certain type and morphological operations that need to calculate a scale;

Step 1: Take the training images of the two types of objects f ₁ and f ₂ that need to be distinguished;

Step 2: Set i=1, i represents the serial number of the invariant moment, and its range is 1≤i≤n;

Step 3: Set q=0, where q represents the serial number of the scale to be calculated;

Step 4: Let p=q+1, p represents the serial number of another scale related to q that needs to be calculated;

Step 5: For object f ₁ , calculate the merged multi-scale morphological detail features of f ₁ from scale p to scale q:

p＞q，1≤p≤a，1≤q≤a；f₁ ^pq表示计算得到的f₁从尺度p到尺度q的合并的多尺度形态学细节特征；

p>q, 1≤p≤a, 1≤q≤a; f ₁ ^pq represents the merged multi-scale morphological detail features of calculated f ₁ from scale p to scale q;

Compute the ith invariant moment of f ₁ ^pq : ${\mathrm{MM}}_i^{\mathrm{pq}}=\mathrm{IM}\left({\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="A2009100893370010H1.png,A2009100893370011H1.png"\; state="\{\{state\}\}">f</figure-callout>}}_1^{\mathrm{pq}}\right);$ Calculate MM _i ^pq of all training images corresponding to f ₁ , and form all MM _i ^pq into a vector VM _i ^pq , and form another vector VM _i ^pq in the same way for another type of object f ₂ ;

Step 6: Calculate the measure Q _i ^pq of the two vectors according to the following formula:

${\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; pq</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="f"\; filenames="A2009100893370010H1.png,A2009100893370011H1.png"\; state="\{\{state\}\}">f</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; |</span>\frac{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="f"\; filenames="A2009100893370010H1.png,A2009100893370011H1.png"\; state="\{\{state\}\}">f</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; MM</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; pq</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="f"\; filenames="A2009100893370013H1.png"\; state="\{\{state\}\}">f</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; MM</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; pq</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="f"\; filenames="A2009100893370010H1.png,A2009100893370011H1.png"\; state="\{\{state\}\}">f</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; MM</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; pq</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="f"\; filenames="A2009100893370013H1.png"\; state="\{\{state\}\}">f</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; MM</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; pq</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; ,</span>$

And put Q _i ^pq into the measure vector Q. where: σ and m are the variance and mean of all invariant moment values corresponding to different training images of _f1 and _f2 ;

Step seven: p=p+1, if p>a, go to step eight; otherwise go to step five;

Step 8: q=q+1, if q>a, go to step 9; otherwise go to step 4;

Step nine: i=i+1, if i>n, go to step ten; otherwise go to step three;

Step 10: Find the first r smallest values in Q and their corresponding invariant moments MM _i ^pq ;

Step 11: Use the r MM _i ^pq and the corresponding real different parts to classify two types of similar objects through the nearest neighbor method.

The present invention uses multi-scale mathematical morphology to extract the detailed features of object training images, and combines the multi-scale detailed features of objects to form multiple real different parts of different types of similar objects on multiple scales, so that the difference between these real different parts is greater than the difference in the overall shape of the original object; at this time, any method of invariant moments can be used to calculate the values of invariant moments of these really different parts, because the values of invariant moments are calculated on really different parts, so they are different The values of the invariant moments between similar objects are significantly different; by evaluating the values of the invariant moments of these truly different parts through a measure, automatic selection can more effectively distinguish the real different parts of similar objects and their corresponding invariant moments ; classify similar objects using the selected truly distinct parts and their corresponding invariant moments, enabling efficient classification of similar objects.

3. Advantages and effects: the present invention makes full use of the possible different parts of similar objects in the shape details, can automatically select the real different parts of similar objects, and replace them with the value of invariant moments calculated by using the local real different parts of similar objects The value of invariant moments obtained by the overall calculation of similar objects is used to achieve the purpose of effectively classifying similar objects, which can be widely used in various target recognition and classification systems, and has broad market prospects and application value.

(4) Description of drawings

Fig. 1 is a schematic block diagram of the method for classifying invariant moments of similar objects using multi-scale mathematical morphology in the present invention.

Fig. 2 is example images "1" and "I" showing the effect of the present invention on similar object classification.

Figure 3 is a truly different part of "1" and "I" extracted by multi-scale mathematical morphology.

Fig. 4 is a comparison between the classification effect of the present invention and the classification effect of Hu moment. Wherein (a) figure is the classification effect of two invariant moments selected by the present invention, (b) figure is the classification effect of Hu moment.

Fig. 5 is a comparison between the classification effect of the present invention and the classification effect of wavelet invariant moments. Wherein (a) figure is the classification effect of two invariant moments selected by the present invention, and (b) figure is the classification effect of wavelet invariant moments.

The symbols in the figure are explained as follows: M1 and M2 in Fig. 4(a) represent the first and second order moments of Hu moment respectively; MIM ₁ ⁵¹ and MIM ₂ ⁵¹ in Fig. 4(b) are the Hu moment The two invariant moments with better performance obtained on the basis of the first and second order moments of , denote the first and second order moments on the fifth to first scale respectively; _2,6,0 ^wavelet ‖ and ‖F _2,4,0 ^wavelet ‖ are two wavelet moments that can effectively distinguish similar objects; MIM ₃ ⁴¹ and MIM ₄ ⁴¹ in Fig. Two invariant moments with better performance obtained on the basis of the first, second, third and fourth order moments of , represent the third and fourth order moments on the fourth to first scale, respectively.

(5) Specific implementation methods

The prerequisite for implementing the present invention is: training images of objects to be classified must be provided.

The condition for classifying by using the present invention is: the image of the object to be classified needs to be obtained.

In order to better understand the technical solutions of the present invention, the implementation manners of the present invention will be further described below in conjunction with the accompanying drawings.

A method for classifying similar objects using multi-scale mathematical morphology invariant moments of the present invention, its working process is shown in Figure 1, and the specific implementation details of each part are as follows:

Step 1: Take the training images of the two types of objects f ₁ and f ₂ that need to be distinguished;

Step 2: Set i=1 (1≤i≤n), and take the i-th invariant moment. When classifying similar objects, the effect of Hu moment is poor. In order to demonstrate the effectiveness of the present invention, the present invention selects Hu moment as the invariant moment used in the method. Of course, Z moment, wavelet moment, etc. can also be used. The basic definitions of the seven commonly used Hu moments are as follows:

M1=η ₂₀ +η ₀₂ ,

$\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="m"\; filenames="A2009100893370013H1.png"\; state="\{\{state\}\}">m</figure-callout></span>}\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; 20</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; 02</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 4</span>}{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>$

$\mathrm{<span\; class="notranslate">\; <figure-callout\; id="3"\; label="m"\; filenames="A2009100893370013H1.png"\; state="\{\{state\}\}">m</figure-callout></span>}\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; 30</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 3</span>}{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}\mathrm{}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; 03</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>$

$\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; 30</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; 03</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>$

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 ].

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

${\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; pq</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; p</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; q</span>}}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$

$\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="10"\; label="s"\; filenames="A2009100893370013H1.png"\; state="\{\{state\}\}">s</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 10</span>}}}{{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 00</span>}}}<span\; class="notranslate">\; ,</span>$ $\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 01</span>}}}{{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 00</span>}}}<span\; class="notranslate">\; ,</span>$

${\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; pq</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; p</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; q</span>}}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$

u, v are the length and width of the image.

Since the present invention can effectively extract the real different parts of similar objects through the details of similar objects, n can choose low-order invariant moments with a small amount of calculation, such as the first two order invariant moments of Hu moments (M1, M2, at this time n=2) or the first four order invariant moments (M1, M2, M3, M4, n=4 at this time).

Step 3: Set q=0, start the loop for q.

Step 4: Set p=q+1, start the cycle for p.

Step 5: For the object f ₁ , calculate the multi-scale morphological features of f ₁ according to the following formula.

The multi-scale features of the image on the p-th scale are

The detailed features of the merged image from scale p to scale q are as follows:

in,

${\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="f"\; filenames="A2009100893370010H1.png,A2009100893370011H1.png"\; state="\{\{state\}\}">f</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&CirclePlus;</span>\mathrm{<span\; class="notranslate">\; B</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; v</span>}}{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>$

和

分别为数学形态学开、闭、膨胀和腐蚀运算符号。 $\mathrm{qB}=B\&CirclePlus;B\&CirclePlus;...\&CirclePlus;B,$ 共对B膨胀q次。○, ●,

and

They are the opening, closing, dilating and eroding operation symbols of mathematical morphology, respectively. $\mathrm{wxya}=B\&CirclePlus;B\&CirclePlus;...\&CirclePlus;B,$ B is expanded q times in total.

Compute the i-th invariant moment of the merged multiscale feature f ₁ ^pq : ${\mathrm{MM}}_i^{\mathrm{pq}}=\mathrm{IM}\left({\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="A2009100893370010H1.png,A2009100893370011H1.png"\; state="\{\{state\}\}">f</figure-callout>}}_1^{\mathrm{pq}}\right).$ Calculate the value MM _i ^pq of the i-th invariant moment corresponding to all training images of the object, and form all MM _i ^pq into a vector VM _i ^pq .

Another vector VM _i ^pq is formed for another type of object f ₂ .

Step 6: Calculate the measure Q _i ^pq of the two vectors according to the following formula:

${\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; pq</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="f"\; filenames="A2009100893370010H1.png,A2009100893370011H1.png"\; state="\{\{state\}\}">f</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; |</span>\frac{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="f"\; filenames="A2009100893370010H1.png,A2009100893370011H1.png"\; state="\{\{state\}\}">f</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; MM</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; pq</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="f"\; filenames="A2009100893370013H1.png"\; state="\{\{state\}\}">f</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; MM</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; pq</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="f"\; filenames="A2009100893370010H1.png,A2009100893370011H1.png"\; state="\{\{state\}\}">f</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; MM</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; pq</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="f"\; filenames="A2009100893370013H1.png"\; state="\{\{state\}\}">f</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; MM</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; pq</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; ,</span>$

Among them, σ and m are the variance and mean of the invariant moment values corresponding to different training images; and Q _i ^pq is put into the measure vector Q. From the definition of Q _i ^pq , it can be seen that the smaller the Q _i ^pq is, the stronger the classification ability of the invariant moment MM _i ^{pq is} , and the corresponding truly different parts can better reflect the difference between two different objects.

Step 7: loop p, set p=p+1, if p>a, go to step 8; otherwise go to step 5. a is the number of scales for multi-scale morphological operations, which can be selected according to practical applications, generally a < 10.

Step 8: Cycle q, set q=q+1, if q>a, go to step 9; otherwise go to step 4.

Step nine: loop i, set i=i+1, if i>n, go to step ten; otherwise go to step three.

Step 10: Select invariant moments with good classification ability

From the definition of Q _i ^pq , we can see that the smaller the value of Q _i ^pq , the better the ability of the corresponding invariant moment to distinguish different types of objects, so it is only necessary to find the invariant moment MM _i ^pq corresponding to the first r smallest values in Q and its corresponding truly different part f ^pq , which are used to distinguish two types of similar objects. r can be selected according to specific applications, in order to take into account the effectiveness and robustness, usually r = 2 is desirable.

Step Eleven: Classify Similar Objects

First use f ^pq to calculate the real different parts of the images of two similar objects, then use the corresponding r MM _i ^pq to calculate the invariant moments of the two similar objects on the real different parts, and finally use the commonly used nearest neighbor method (see: Bian Zhao Qi, Zhang Xuegong, etc. Pattern Recognition. Tsinghua University Press, Beijing, 1999, Chapter 6.) Classify the invariant moments of two types of objects to achieve the purpose of distinguishing between two types of objects.

In order to demonstrate the effect of the present invention, "1" and "I" with similar shapes are used as experimental images, some of which are shown in FIG. 2 . As can be seen from Figure 2, "1" and "I" are very similar, with only a small difference at the top. Using multi-scale mathematical morphology to extract the real different parts of "1" and "I", one of which is shown in Figure 3. It can be seen from Figure 3 that compared with Figure 2, the extracted part in Figure 3 is indeed quite different. In order to better demonstrate the effect of the present invention, the Hu moment with relatively poor classification ability is selected as the invariant moment MM that needs to be used in the present invention, and it is marked as MIM, and compared with the Hu moment and the MM that can effectively distinguish similar objects Wavelet invariant moments for comparison. The better first order and second order two low-order invariant moments of stability are used in the method (n=2) that the present invention proposes, and Fig. 4 is the classification effect of the present invention and Hu moment, although the Hu moment's first order The first and second moments cannot distinguish between "1" and "I" (figure (a)), but the invention using multi-scale mathematical morphology can effectively distinguish "1" and "I" (figure (b)) . In order to better demonstrate the effect of the present invention, the present invention is compared with the wavelet invariant moment, and Fig. 5 is the classification effect. In Fig. 5(a), although the wavelet invariant moment can distinguish "1" and "I", it is only just able to distinguish. But the present invention (n=4) (FIG. 5(b)) utilizing 4 low-order Hu moments can distinguish "1" and "I" very well. This shows that the present invention can effectively distinguish similar objects, and the effect is better than the traditional method. In addition, any invariant moment method can replace the Hu moment for the invariant moment MM required by the present invention, and the better the classification ability of the invariant moment MM, the better the ability of the present invention to distinguish similar objects. Therefore, the present invention can not only be used for classifying similar objects, but also can be widely used for improving moment-invariant classification ability when distinguishing similar objects with invariant moments, and has broad application prospects in various applications.

Claims (1)

1. A method for classifying invariant moments of similar objects using multi-scale mathematical morphology, which is provided with n selected types of invariant moments and needs to calculate a scale of morphological operations, characterized in that: the specific steps of the method as follows: Step 1: Take the training images of the two types of objects f ₁ and f ₂ that need to be distinguished; Step 2: set i=1, i represents the serial number of the invariant moment, and its range is 1≤i≤n; Step 3: Set q=0, where q represents the serial number of the scale to be calculated; Step 4: Set p=q+1, where p represents the serial number of another scale related to q that needs to be calculated; Step 5: For object f ₁ , calculate the merged multi-scale morphological detail features of f ₁ from scale p to scale q:

p>q, 1≤p≤a, 1≤q≤a; f ₁ ^pq represents the merged multi-scale morphological detail features of calculated f ₁ from scale p to scale q; Compute the ith invariant moment of f ₁ ^pq : ${\mathrm{MM}}_i^{\mathrm{pq}}=\mathrm{IM}\left(f_1^{\mathrm{pq}}\right);$ Calculate MM _i ^pq of all training images corresponding to f ₁ , and form all MM _i ^pq into a vector VM _i ^pq , and form another vector VM _i ^pq in the same way for another type of object f ₂ ; Step 6: Calculate the measure Q _i ^pq of the two vectors according to the following formula: ${\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; pq</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; |</span>\frac{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; MM</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; pq</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; MM</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; pq</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; MM</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; pq</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; MM</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; pq</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; ,</span>$ And put Q _i ^pq into the measure vector Q, where: σ and m are the variance and mean of all invariant moment values corresponding to different training images of f ₁ and f ₂ ; Step seven: p=p+1, if p>a, go to step eight; otherwise go to step five; Step 8: q=q+1, if q>a, go to step 9; otherwise go to step 4; Step nine: i=i+1, if i>n, go to step ten; otherwise go to step three; Step 10: Find the first r smallest values in Q and their corresponding invariant moments MM _i ^pq ; Step 11: Use the r MM _i ^pq and the corresponding real different parts to classify two types of similar objects through the nearest neighbor method.

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