CN115575405B - Fruit appearance quality detection method based on multispectral image feature quantity - Google Patents

Abstract

The invention discloses a fruit appearance quality detection method based on multispectral image feature quantity, which considers that optimal wave bands and feature wavelengths can be optimized in multispectral imaging technology to reduce data processing time and improve the effectiveness of spectrum data, so that the difference degree of the spectrum image feature quantity and normal fruit feature quantity under different wave bands is analyzed through a fruit defective fruit sample set with surface defects to optimize the spectrum wave bands and the multispectral image feature quantity, and whether the fruit has the surface defects in appearance quality detection is judged.

Description

A method for detecting fruit appearance quality based on multispectral image features

Technical Field

The present invention belongs to the technical field of fruit quality detection, and in particular relates to a method for detecting the appearance quality of fruits by analyzing characteristic quantities of multispectral images to thereby select spectral bands corresponding to different types of surface defects and characteristic quantities of multispectral images.

Background technique

Multispectral imaging is an emerging nondestructive testing technology. As an important improvement on hyperspectral imaging technology, it can collect and analyze data within a discrete spectral range, thereby greatly simplifying the data and reducing redundant information to improve processing speed. At the same time, different chemometric models and preprocessing methods are used for spectral data to select the best band and characteristic wavelength, which can greatly reduce data processing time and improve the validity of spectral data. Multispectral imaging technology has received extensive attention in recent years. Due to its advantages of being non-destructive, fast, simple, green, and not requiring sample pretreatment, it is widely used in qualitative and quantitative detection of food ingredients and content, as well as identification of different varieties and adulteration. It is suitable for monitoring and quality control of food production, processing, storage, transportation and other processes, laying a technical foundation for the next step of developing fast, non-destructive, accurate and efficient real-time detection tools.

In the fruit quality inspection and automatic grading system, color cameras are usually used to collect fruit images, and then the collected images are subjected to pattern recognition, and finally the corresponding grading processing is performed according to the recognition results. The quality of fruit image acquisition will directly affect the accuracy of the final determination of fruit quality and grade, so the information contained in the collected fruit images should reflect the various external characteristics of the fruit as detailed as possible. When using computer vision technology to inspect and grade fruit quality, surface defects such as rot/rotten spots/moldy, bruises/punctures, dry scars/skin spots, abrasions and oxidation, deformities, and cracks/cracks are important indicators of fruit appearance quality. Considering that in practical applications, the fruit images collected by color cameras cannot reflect the subtle features of the fruit surface well, in order to improve the reliability of detection and grading, images of fruits under different spectral conditions can be used to extract more surface features. In practical applications, according to the RGB (Red Green Blue) color model theory, the image areas collected in different bands can be represented by monochrome colors such as R, G and B, and then superimposed as the components in the RGB color model to obtain multispectral images such as RGB, RGI (Red Green Ratio Index), GBI (Green Blue Ratio Index), etc.

Summary of the invention

The purpose of the present invention is to analyze the difference between the spectral image feature quantities in different bands and the feature quantities of normal fruits through a sample set of defective fruits with surface defects, so as to optimize the spectral bands and multi-spectral image feature quantities, in order to improve the effectiveness of spectral data for application in fruit appearance quality detection.

In order to achieve the above object, the present invention includes the following steps shown in Figure 1:

Step 1: Assume that for a sample k with surface defects in a certain fruit defect sample set, when the spectral image is collected for the surface defect j under the spectral band i, the corresponding value x(i,j,l,k) can be obtained for the image feature l, where k∈[1,K], K is the total number of defective fruit samples of this kind of fruit, j∈[1,J], J is the total number of surface defect types, i∈[1,I], I is the total number of spectral bands, l∈[1,L], L is the total number of image feature types; let θ _j be the weight coefficient of surface defect j, and Let μ _i,j be the weight coefficient of the corresponding surface defect j in spectral band i, and Let _wi,j,l be the weight coefficient of the image feature l corresponding to the surface defect j in the spectral band i, and Taking into account that the optimal spectral bands and their image feature quantities corresponding to the appearance quality inspection of different types of surface defects are also different, it is proposed to take the difference degree of the image feature quantities corresponding to the spectral bands of defective fruits and normal fruits as the target and introduce Lagrange multipliers such as λ ₁ , λ ₂ and λ ₃ to establish the objective function F( _wi,j,l ,μ _i,j ,θ _j ,λ ₁ ,λ ₂ ,λ ₃ ) and maximize the objective function F(wi,j,l ,μ _i, j ,θ _j ,λ ₁ ,λ ₂ ,λ ₃ ) by selecting parameters wi _{,j ,l} ,μ _i,j ,θ _j :

Among them, y(i,j,l) is the average value corresponding to the absence of surface defect j when the normal fruit sample set of this kind of fruit is collected for the image feature l under spectral band i;

Step 2: Take the first-order and second-order derivatives of F( _wi,j,l ,μi _,j , _θj , _λ1 , _λ2 , _λ3 ) with respect to _θj , and we get:

The first-order derivative of F( _wi,j,l ,μi _,j , _θj , _λ1 , _λ2 , _λ3 ) with respect to _θj is It can be seen that the second-order derivative of F( _wi,j,l ,μi _,j , _θj , _λ1 , _λ2 , _λ3 ) with respect to _θj is It can be seen that there exists θ _j that maximizes F(w _i,j,l ,μ _i,j ,θ _j ,λ ₁ ,λ ₂ ,λ ₃ );

The first-order derivative of F( _wi,j,l ,μi _,j , _θj , _λ1 , _λ2 , _λ3 ) with respect to _θj is The expression of λ ₃ with respect to θ _j can be obtained:

Depend on The expression of θ _j with respect to λ ₃ can be obtained:

It can be seen that the theoretical value expression of λ ₃ can be expressed as:

Then the theoretical value expression of θ _j can be obtained:

Among them, m is the intermediate variable;

Step 3: Take the first-order and second-order derivatives of F( _wi,j,l ,μi _,j , _θj , _λ1 , _λ2 , _λ3 ) with respect to wi _,j,l , and we get:

The first derivative of F(w _i,j,l ,μ _i,j ,θ _j ,λ ₁ ,λ ₂ ,λ ₃ ) with respect to w _i,j,l It can be seen that the second-order derivative of F( _wi,j,l ,μi _,j , _θj , _λ1 , _λ2 , _λ3 ) with respect to w _{i,j,l is} It can be seen that there exists w _i,j,l that maximizes F(w _i,j,l ,μ _i,j ,θ _j ,λ ₁ ,λ ₂ ,λ ₃ );

The first derivative of F(w _i,j,l ,μ _i,j ,θ _j ,λ ₁ ,λ ₂ ,λ ₃ ) with respect to w _i,j,l We can get the expression of λ ₁ with respect to w _i,j,l :

Depend on We can get the expression of w _i,j,l with respect to λ ₁ :

It can be seen that the theoretical value expression of λ ₁ can be expressed as:

Then we can get the theoretical value expression of _wi,j,l :

Among them, n is the intermediate variable;

Step 4: Take the first-order and second-order derivatives of F( _wi,j,l ,μi _,j , _θj , _λ1 , _λ2 , _λ3 ) with respect to μi _,j, and we get:

The first-order derivative of F( _wi,j,l ,μi _,j , _θj , _λ1 , _λ2 , _λ3 ) with respect to μi _{,j is} It can be seen that the second-order derivative of F( _wi,j,l ,μi _,j , _θj , _λ1 , _λ2 , _λ3 ) with respect to μi _{,j is} It can be seen that there exists μ _i,j that maximizes F(w _i,j,l ,μ _i,j ,θ _j ,λ ₁ ,λ ₂ ,λ ₃ );

The first-order derivative of F( _wi,j,l ,μi _,j , _θj , _λ1 , _λ2 , _λ3 ) with respect to μi _{,j is} The expression of λ ₂ with respect to μ _i,j can be obtained:

Depend on The expression of μ _i,j with respect to λ ₂ can be obtained:

It can be seen that the theoretical value expression of λ ₂ can be expressed as:

Then the theoretical value expression of μ _i,j can be obtained:

Among them, d is the intermediate variable;

Step 5: The actual weight coefficient of the surface defect can be generated by substituting the theoretical value expressions of θ _j , μ _i, j and wi,j,l into the iterative process of the weight coefficient when the objective function F(wi _{, j,l,μ i,j , θ} j,λ ₁ ,λ ₂ ,λ ₃ ) satisfies the maximization condition. Actual weight coefficients of spectral bands and the actual weight coefficient of the image feature The iterative process is specifically expressed as follows:

① In the initialization process, the spectral image feature values x(i,j,l,k) of samples with surface defects in the defective fruit sample set of the fruit in different spectral bands for different surface defects and the corresponding spectral image feature values of the normal fruit sample set are collected, and the statistical average is calculated to obtain the average value y(i,j,l) of the image feature value corresponding to the normal fruit sample set, and _θj (t＝0) is set to 1/J, μi _,j (t＝0) is set to 1/I, and _θj (t＝0) and μi _,j (t＝0) as well as x(i,j,l,k) and y(i,j,l) are substituted into the theoretical value expression of w _i,j,l to obtain w _i,j,l (t＝0);

② Add 1 to t, substitute w _i,j,l (t-1) and θ _j (t-1) into the theoretical value expression of μ _i,j to give μ _i,j (t);

③Substitute w _i,j,l (t-1) and μ _i,j (t) into the theoretical value expression of θ _j to give θ _j (t);

④Substitute θ _j (t) and μ _i,j (t) into the theoretical value expression of wi _,j,l to give wi _,j,l (t);

⑤ Compare |[ _wi,j,l (t)-wi _,j,l (t-1)]/wi _,j,l (t)|, |[μi _,j (t)-μi _,j (t-1)]/μi _,j (t)| and |[ _θj (t) _-θj (t-1)]/ _θj (t)|. If all of them are less than or equal to δ, enter the iterative process ⑥; otherwise, enter the iterative process ⑤, where δ is the error threshold of the iterative process.

⑥ Establish a set Ψ _i,j,l ＝{wi,j, _{l (t)} with w i, j,l} (t) as an element, establish a set Φ _i,j ＝{μ _i,j (t)} with μ _i,j (t) as an element, and establish a set Θ _j ＝{θ _j (t)} with θ _j (t) as an element, where i∈[1,I], j∈[1,J], l∈[1,L]; if w _i,j,l (t)＜ε _w , it means that the corresponding spectral image feature contributes little to the detection of surface defect j in spectral band i, then w _i,j,l (t) is removed from Ψ _i,j,l , so as to achieve the optimization of multi-spectral image feature in this spectral band, and add the corresponding i,j,l combination to the set Where ε _w is the weight threshold of the spectral image feature; if μ _i,j (t) < ε _μ , it means that the corresponding spectral band contributes less to the detection of surface defect j, then μ _i,j (t) is removed from Φ _i,j to achieve the optimization of spectral bands, and the corresponding i,j combination is added to the set Where ε _μ is the spectral band weight threshold; if θ _j (t) < ε _θ , it means that the corresponding spectral band contributes less to the overall detection of fruit appearance quality, then θ _j (t) is removed from Θ _j , and the corresponding j is added to the set Where ε _θ is the surface defect weight threshold;

⑦ Given by the set Ψ _i,j,l = { _wi,j,l (t)} Given by the set Φ _i,j = {μ _i,j (t)} Given by the set Θ _j ={θ _j (t)} Where i∈[1,I], j∈[1,J], l∈[1,L];

⑧ Order and Then we can get:

The actual weight coefficient of surface defects can be obtained from this Actual weight coefficients of spectral bands and the actual weight coefficient of the image feature Output.

Step 6: Measure the surface defects of the fruit to be inspected. Spectral bands within the range For surface defect j, if the deviation of the image feature quantity of fruit r with respect to surface defect j satisfies If the fruit has no surface defect j in the appearance quality inspection, it can be considered that the fruit has surface defect j, otherwise, the fruit is considered to have surface defect j, where θ _j is the deviation threshold of the image feature quantity of the fruit with respect to surface defect j.

BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1: Steps for detecting fruit appearance quality based on multispectral image features

Detailed ways

The technical solution provided by the present invention is described in detail below using a specific embodiment of detecting the appearance quality of fragrant pears in the spectral band range of 930 to 2548 nm, which specifically includes the following steps shown in FIG1 :

Step 1: Assume that for sample k with surface defects in the sample set of defective pear fruits, when collecting spectral images for surface defect j under spectral band i, the corresponding value x(i,j,l,k) can be obtained for the image feature l of monochrome such as R, G and B, where k∈[1,K], the total number of defective pear fruits K is set to 1000, j∈[1,J], including the total number of surface defects such as rot, bruise, flower skin, abrasion, deformity or crack. The number J is 6, i∈[1,I], the total number of spectral bands I such as 1000, 1025, 1076, 1152, 1203, 1279, 1300, 1406, 1431, 1533, 1609, 1634, 1888, 2092, 2142, 2320, 2473, 2500 is 18, l∈[1,L], the total number of image feature types such as R, G and B monochrome is 3; let θ _j be the weight coefficient of surface defect j, and Let μ _i,j be the weight coefficient of the corresponding surface defect j in spectral band i, and Let _wi,j,l be the weight coefficient of the image feature l corresponding to the surface defect j in the spectral band i, and Taking into account that the optimal spectral bands and their image feature quantities corresponding to the appearance quality detection of different types of surface defects are also different, it is proposed to take the difference degree of image feature quantities corresponding to the spectral bands of defective pear fruits with surface defects and normal fruits as the target and introduce Lagrange multipliers λ ₁ , λ ₂ and λ ₃ to establish the objective function F( _wi,j,l ,μ _i,j ,θ _j ,λ ₁ ,λ ₂ ,λ ₃ ) and maximize the objective function F(wi,j,l ,μ _i, j ,θ _j ,λ ₁ ,λ ₂ ,λ ₃ ) by selecting parameters wi _{,j ,l} ,μ _i,j ,θ _j :

Among them, y(i,j,l) is the average value corresponding to the absence of surface defect j when the spectral image of the normal fruit sample set of fragrant pear is collected under spectral band i for the image feature l;

Step 2: Take the first-order and second-order derivatives of F( _wi,j,l ,μi _,j , _θj , _λ1 , _λ2 , _λ3 ) with respect to _θj , and we get:

The first-order derivative of F( _wi,j,l ,μi _,j , _θj , _λ1 , _λ2 , _λ3 ) with respect to _θj is It can be seen that the second-order derivative of F( _wi,j,l ,μi _,j , _θj , _λ1 , _λ2 , _λ3 ) with respect to _θj is It can be seen that there exists θ _j that maximizes F( _wi,j,l ,μi _,j ,θ _j , _λ1 , _λ2 , _λ3 ), and the theoretical value expression of θ _j can be expressed as:

Among them, m is the intermediate variable;

Step 3: Take the first-order and second-order derivatives of F( _wi,j,l ,μi _,j , _θj , _λ1 , _λ2 , _λ3 ) with respect to wi _,j,l , and we get:

The first derivative of F(w _i,j,l ,μ _i,j ,θ _j ,λ ₁ ,λ ₂ ,λ ₃ ) with respect to w _i,j,l It can be seen that the second-order derivative of F( _wi,j,l ,μi _,j , _θj , _λ1 , _λ2 , _λ3 ) with respect to w _{i,j,l is} It can be seen that there exists wi _,j,l that maximizes F(wi _,j,l ,μi _,j , _θj , _λ1 , _λ2 , _λ3 ). At this time, the theoretical value of _wi,j,l is expressed as The formula can be expressed as:

Among them, n is the intermediate variable;

Step 4: By calculating the first-order derivative and the second-order derivative of μ i, _j from F( _wi,j,l ,μ _i,j ,θ _j ,λ ₁ ,λ ₂ ,λ ₃ ), the theoretical value expression of μ _i,j can be obtained:

The first-order derivative of F( _wi,j,l ,μi _,j , _θj , _λ1 , _λ2 , _λ3 ) with respect to μi _{,j is} It can be seen that the second-order derivative of F( _wi,j,l ,μi _,j , _θj , _λ1 , _λ2 , _λ3 ) with respect to μi _{,j is} It can be seen that there exists μ _i,j that maximizes F( _wi,j,l ,μ _i,j , _θj , _λ1 , _λ2 , _λ3 ), and the theoretical value expression of μ _i,j can be expressed as:

Among them, d is the intermediate variable;

Step 5: The actual weight coefficient of the surface defect can be generated by substituting the theoretical value expressions of θ _j , μ _i, j and wi,j,l into the iterative process of the weight coefficient when the objective function F(wi _{, j,l,μ i,j , θ} j,λ ₁ ,λ ₂ ,λ ₃ ) satisfies the maximization condition. Actual weight coefficients of spectral bands and the actual weight coefficient of the image feature The iterative process is specifically expressed as follows:

① In the initialization process, the spectral image feature values x(i,j,l,k) of 1000 defective pear fruit samples in different spectral bands for different surface defects and the corresponding spectral image feature values of the sample set established by 50 normal fruits are collected, and the statistical average is calculated to obtain the average value y(i,j,l) of the image feature value corresponding to the normal fruit sample set, and _θj (t＝0) is set to 0.167, μi _,j (t＝0) is set to 0.056, and _θj (t＝0) and μi _,j (t＝0) as well as x(i,j,l,k) and y(i,j,l) are substituted into the theoretical value expression of w _i,j,l to obtain w _i,j,l (t＝0);

② Add 1 to t, substitute w _i,j,l (t-1) and θ _j (t-1) into the theoretical value expression of μ _i,j to give μ _i,j (t);

③Substitute w _i,j,l (t-1) and μ _i,j (t) into the theoretical value expression of θ _j to give θ _j (t);

④Substitute θ _j (t) and μ _i,j (t) into the theoretical value expression of wi _,j,l to give wi _,j,l (t);

⑤ Compare |[ _wi,j,l (t)-wi _,j,l (t-1)]/ _wi,j,l (t)|, |[μi _,j (t)-μi _,j (t-1)]/μi _,j (t)| and |[ _θj (t) _-θj (t-1)]/ _θj (t|. If all of them are less than or equal to the iterative process error threshold δ, then enter iterative process ⑥; otherwise, enter iterative process ⑤, where δ is set to 2%;

⑥ Establish a set Ψ _i,j,l ＝{wi,j, _{l (t)} with w i, j,l} (t) as an element, establish a set Φ _i,j ＝{μ _i,j (t)} with μ _i,j (t) as an element, and establish a set Θ _j ＝{θ _j (t)} with θ _j (t) as an element, where i∈[1,I], j∈[1,J], l∈[1,L]; if w _i,j,l (t)＜ε _w , it means that the corresponding spectral image feature contributes little to the detection of surface defect j in spectral band i, then w _i,j,l (t) is removed from Ψ _i,j,l , so as to achieve the optimization of multi-spectral image feature in this spectral band, and add the corresponding i,j,l combination to the set If μ _i,j (t) < ε _μ , it means that the corresponding spectral band contributes less to the detection of surface defect j. Then μ _i,j (t) is removed from Φ _i,j to achieve the optimization of spectral bands, and the corresponding i,j combination is added to the set If θ _j (t) < ε _θ , it means that the corresponding spectral band contributes less to the overall detection of fruit appearance quality. Then θ _j (t) is removed from Θ _j and the corresponding j is added to the set Among them, ε _w is set to 0.01, ε _μ is set to 0.02, and ε _θ is set to 0.05;

⑦ Given by the set Ψ _i,j,l = { _wi,j,l (t)} Given by the set Φ _i,j = {μ _i,j (t)} Given by the set Θ _j ={θ _j (t)} Where i∈[1,I], j∈[1,J], l∈[1,L];

⑧ Order and Then we can get:

The actual weight coefficient of surface defects can be obtained from this Actual weight coefficients of spectral bands and the actual weight coefficient of the image feature Output.

Step 6: Measure the surface defects of the pear to be tested. Spectral bands within the range For surface defect j, if the deviation of the image feature quantity of pear r with respect to surface defect j satisfies If the pear has no surface defects in the appearance quality inspection, it can be considered that the fruit has surface defects. The deviation threshold θ _j of the image feature quantity of the fragrant pear with respect to the surface defect j is set to 5%.

In this specific implementation, after obtaining the required image area after removing the background, the image areas collected under different spectral bands such as 1000, 1025, 1076, 1152, 1203, 1279, 1300, 1406, 1431, 1533, 1609, 1634, 1888, 2092, 2142, 2320, 2473, 2500 can be synthesized into multispectral images by using image feature quantities such as R, G and B. The recognition rate is significantly better than that of monochrome images, and it is also very effective for rot, bruises, flower skin and abrasions. The recognition error of surface defects such as shape, deformity or crack is reduced by 4% on average, indicating that the method has good practical effect. The actual weight coefficient of the image feature quantity can also be used to understand the contribution of the image feature quantity to the multispectral image recognition rate, which is conducive to recommending the synthesis method of the multispectral image. At the same time, different surface defects have different grayscale distributions for different surface features. It can be seen that the actual weight coefficient of the spectral band can be used to find the spectral band that reacts more obviously to surface defects, so as to select the spectral band that is more suitable for surface defects to realize the appearance quality detection of fruit.

Claims (4)

1. The fruit appearance quality detection method based on the multispectral image feature quantity is characterized by comprising the following steps of:

Step 1: providing a sample K with surface defects in a certain fruit residual fruit sample set, and acquiring corresponding values x (I, J, L, K) aiming at the surface defects J when spectrum image acquisition is carried out under a spectrum band I and aiming at image feature quantity L, wherein K epsilon [1, K ] is the total number of residual fruit samples of the fruit, J epsilon [1, J ] is the total number of surface defect types, I epsilon [1, I ] is the total number of spectrum bands, L epsilon [1, L ] is the total number of R, G, B monochromies; let θ _j be the weight coefficient of the surface defect j, and Let mu _i,j be the weight coefficient of the corresponding surface defect j on the spectrum band i, andLet w _i,j,l be the weight coefficient of the image feature quantity l corresponding to the surface defect j in the spectral band i, andIt is proposed to build the objective function F (w _i,j,l,μ_i,j,θ_j,λ₁,λ₂,λ₃) with the objective of the degree of difference in the image characteristics corresponding to the spectral bands of the residual and normal fruits and introduce lambda ₁、λ₂ and lambda ₃ lagrangian multipliers, and to maximize the objective function F (w _i,j,l,μ_i,j,θ_j,λ₁,λ₂,λ₃) by selecting the parameter w _i,j,l,μ_i,j,θ_j:

Wherein y (i, j, l) is an average value corresponding to the condition that no surface defect j exists when the image characteristic quantity l is aimed at when the spectrum image acquisition is carried out on the normal fruit sample set of the fruit in a spectrum band i;

Step 2: from F (w _i,j,l,μ_i,j,θ_j,λ₁,λ₂,λ₃) to θ _j, the first and second derivatives are obtained:

First derivative of θ _j by F (w _i,j,l,μ_i,j,θ_j,λ₁,λ₂,λ₃) It can be seen that the second derivative of F (w _i,j,l,μ_i,j,θ_j,λ₁,λ₂,λ₃) with respect to θ _j It can be seen that the presence of θ _j maximizes F (w _i,j,l,μ_i,j,θ_j,λ₁,λ₂,λ₃);

First derivative of θ _j by F (w _i,j,l,μ_i,j,θ_j,λ₁,λ₂,λ₃) The expression of lambda ₃ for theta _j is obtained byAn expression of θ _j with respect to λ ₃, and hence a theoretical expression of λ ₃, can be obtained, and then a theoretical expression of θ _j can be obtained:

wherein m is an intermediate variable;

Step 3: from the first and second derivatives of F (w _i,j,l,μ_i,j,θ_j,λ₁,λ₂,λ₃) to w _i,j,l, we can obtain:

The first derivative of w _i,j,l by F (w _i,j,l,μ_i,j,θ_j,λ₁,λ₂,λ₃) It can be seen that the second derivative of F (w _i,j,l,μ_i,j,θ_j,λ₁,λ₂,λ₃) with respect to w _i,j,l It can be seen that the presence of w _i,j,l maximizes F (w _i,j,l,μ_i,j,θ_j,λ₁,λ₂,λ₃);

The first derivative of w _i,j,l by F (w _i,j,l,μ_i,j,θ_j,λ₁,λ₂,λ₃) The expression of lambda ₁ for w _i,j,l is obtained byThe expression of w _i,j,l for lambda ₁, and hence the theoretical expression of lambda ₁, can be obtained, the theoretical expression of w _i,j,l:

Wherein n is an intermediate variable;

step 4: from F (w _i,j,l,μ_i,j,θ_j,λ₁,λ₂,λ₃) to μ _i,j, the first and second derivatives are obtained:

First derivative of μ _i,j by F (w _i,j,l,μ_i,j,θ_j,λ₁,λ₂,λ₃) It can be seen that the second derivative of F (w _i,j,l,μ_i,j,θ_j,λ₁,λ₂,λ₃) with respect to μ _i,j It can be seen that the presence of μ _i,j maximizes F (w _i,j,l,μ_i,j,θ_j,λ₁,λ₂,λ₃);

First derivative of μ _i,j by F (w _i,j,l,μ_i,j,θ_j,λ₁,λ₂,λ₃) The expression of lambda ₂ for mu _i,j can be obtained byThe expression of μ _i,j for λ ₂, and hence the theoretical expression of λ ₂, can be obtained, and then the theoretical expression of μ _i,j:

wherein d is an intermediate variable;

Step 5: the theoretical value expressions of theta _j、μ_i,j and w _i,j,l when the objective function F (w _i,j,l,μ_i,j,θ_j,λ₁,λ₂,λ₃) meets the maximization condition can be substituted into the iterative process of the weight coefficients to generate the actual weight coefficients of the surface defects Actual weighting coefficients of spectral bandsAnd the actual weight coefficient of the image feature quantity

Step 6: measuring the defects of different surfaces of fruit r to be detectedOver a spectral band of rangeIn-range image feature quantity, for surface defect j, if the deviation of the image feature quantity of fruit r with respect to surface defect j satisfiesIf the fruit is not found to have the surface defect j in the appearance quality detection, otherwise, the fruit is found to have the surface defect j, wherein, The image characteristic quantity of the fruit with respect to the surface defect j deviates from a threshold;

in step 5, the iterative process of the weight coefficient may be described as:

① In the initialization process, collecting spectral image characteristic quantities x (I, J, l, k) of samples with surface defects in the fruit residual fruit sample set and corresponding spectral image characteristic quantities of the fruit normal fruit sample set aiming at different spectral bands of different surface defects, obtaining an image characteristic quantity average value y (I, J, l) corresponding to the normal fruit sample set by calculating a statistical average value, setting θ _j (t=0) as 1/J, setting μ _i,j (t=0) as 1/I, substituting θ _j (t=0) and μ _i,j (t=0) and x (I, J, l, k) and y (I, J, l) into theoretical value expressions of w _i,j,l to give w _i,j,l (t=0);

② Substituting w _i,j,l (t-1) and θ _j (t-1) into the theoretical value expression of μ _i,j gives μ _i,j (t) with t plus 1;

③ Substituting w _i,j,l (t-1) and μ _i,j (t) into the theoretical value expression of θ _j gives θ _j (t);

④ Substituting θ _j (t) and μ _i,j (t) into the theoretical value expression of w _i,j,l gives w _i,j,l (t);

⑤ Comparing the I [ w _i,j,l(t)-w_i,j,l(t-1)]/w_i,j,l(t)|、|[μ_i,j(t)-μ_i,j(t-1)]/μ_i,j (t) | with the I [ theta _j(t)-θ_j(t-1)]/θ_j (t) |, entering an iteration process ⑥ if both are smaller than or equal to delta, otherwise entering an iteration process ⑤, wherein delta is an iteration process error threshold;

⑥ The set ψ _i,j,l＝{w_i,j,l (t) is established by w _i,j,l (t) as an element, the set Φ _i,j＝{μ_i,j (t) is established by mu _i,j (t) as an element, and the set Θ _j＝{θ_j (t) is established by θ _j (t) as an element, wherein i is [1, I ], j is [1, J ], l is [1, L ]; if w _i,j,l(t)<ε_w shows that the detection contribution degree of the corresponding spectral image feature quantity to the surface defect j in the spectral band i is smaller, w _i,j,l (t) is removed from ψ _i,j,l, so that the optimization of the multispectral image feature quantity in the spectral band is realized, and the corresponding i, j and l combination is added into the set Wherein epsilon _w is a spectral image feature quantity weight threshold; if mu _i,j(t)<ε_μ indicates that the corresponding spectrum band has smaller detection contribution degree to the surface defect j, mu _i,j (t) is removed from phi _i,j, so that the spectrum band is optimized, and the corresponding i, j combination is added into the collectionWherein epsilon _μ is a spectral band weight threshold; if theta _j(t)<ε_θ shows that the corresponding spectrum band has smaller overall detection contribution degree to the appearance quality of the fruits, then theta _j (t) is removed from theta _j, and the corresponding j is added into the collectionWherein ε _θ is the surface defect weight threshold;

⑦ Given by the set ψ _i,j,l＝{w_i,j,l (t) } Given by the set Φ _i,j＝{μ_i,j (t)Given by the set Θ _j＝{θ_j (t)Wherein i epsilon [1, I ], j epsilon [1, J ], l epsilon [1, L ];

⑧ Order the AndThen it is possible to obtain:

thereby obtaining the actual weight coefficient of the surface defect Actual weighting coefficients of spectral bandsAnd the actual weight coefficient of the image feature quantityAnd outputting.

2. The method for detecting the appearance quality of fruits based on the characteristic quantity of multispectral images according to claim 1, wherein the method comprises the following steps of: in step 2, the expression of λ ₃ with respect to θ _j, the expression of θ _j with respect to λ ₃, and the theoretical value expression of λ ₃ can respectively represent:

。

3. The method for detecting the appearance quality of fruits based on the characteristic quantity of multispectral images according to claim 1, wherein the method comprises the following steps of: in step3, the expression of λ ₁ with respect to w _i,j,l, the expression of w _i,j,l with respect to λ ₁, and the theoretical value expression of λ ₁, respectively, can be expressed as:

。

4. The method for detecting the appearance quality of fruits based on the characteristic quantity of multispectral images according to claim 1, wherein the method comprises the following steps of: in step 4, the expression of λ ₂ with respect to μ _i,j, the expression of μ _i,j with respect to λ ₂, and the theoretical value expression of λ ₂ are expressed as:

。