CN113129397B - Decoding method of parallelogram coding mark based on graphic geometric relation - Google Patents

Abstract

The invention discloses a decoding method of a parallelogram coding mark based on a graphic geometric relationship. The parallelogram coding mark is composed of a parallelogram background pattern and a coding pattern, and the coding pattern is inside the parallelogram background pattern, including a positioning pattern and an orientation pattern. And the coding combination pattern, the orientation pattern and the positioning pattern are used for the judgment of the direction of the parallelogram coding mark; the coding combination pattern is used for coding the four vertices of the coding mark. The coding pattern in the parallelogram coding mark proposed by the present invention can automatically determine the relative rotation direction of the measured target and the camera in the process of camera calibration, three-dimensional data splicing, etc., thereby improving flexibility; the position of each component pattern is determined by graphic geometry. The method of relation and vector product is distinguished, and has strong robustness; this decoding method greatly improves the accuracy of decoding; it has the advantages of high efficiency and fast decoding speed, and can realize real-time decoding.

Description

A Decoding Method of Parallelogram Coding Marks Based on Graphic Geometric Relationships

technical field

The invention relates to the field of visual measurement in computer vision, in particular to a method for decoding parallelogram coding marks based on graphic geometric relationships, which is suitable for the fields of camera calibration, target feature extraction, stereo matching and three-dimensional data splicing.

Background technique

In visual measurement, feature recognition and matching of measured objects is one of the research hotspots in this field. However, in the case of a high-resolution large field of view or other complex backgrounds, the accuracy of feature extraction and matching cannot meet the accuracy requirements, and by setting coding marks on the surface of the measured object, the current feature extraction and matching can be greatly improved. Speed and accuracy, and can also solve the matching problem of multiple images. Therefore, the design and identification of coding marks is a key link in visual measurement.

In 1972, Russo and Knockeart achieved compilation and recognition by exploiting the unique properties of markers, and coding marker technology has developed rapidly since then. In order to meet the requirements of industrial measurement, there are many types of coding marks, but most of them are annular, circular or fan-shaped, etc. These coding marks have the following defects: when the shooting angle changes, part of the coding is deformed, which affects the Accuracy; the encoding capacity is small, and it is powerless to face the target of large size.

SUMMARY OF THE INVENTION

The invention aims to overcome the defects of the existing coding marks, and proposes a decoding method of a parallelogram coding mark based on the geometric relationship of the figures, which is suitable for multi-eye stereo vision calibration under a large field of view, and has a great effect on affine transformed images. Good stability, large coding capacity, and high coding precision and accuracy for targets with larger sizes.

In order to realize the above-mentioned effect, the technical scheme adopted in the present invention is:

A method for decoding a parallelogram coding mark based on a graphic geometric relationship, the coding mark is a square coding square, the surface of the coding square is provided with a parallelogram background pattern and a coding pattern, and the coding pattern is located in the parallelogram background pattern Inside, the coding pattern includes a positioning pattern, a directional pattern and a coding combination pattern, the directional pattern and the positioning pattern are used for the judgment of the direction of the parallelogram coding mark, and the coding combination pattern is used for each corner of the parallelogram coding mark. coding, each coding combination pattern consists of one coding combination orientation pattern and three coding combination coding patterns. Utilize the method of digital image processing to obtain the coding sequence number and sub-pixel coordinates of each feature corner in the image containing N parallelogram coding marks captured by the camera, and then complete the steps of decoding the parallelogram coding marks as follows:

Step 1.1, utilize the N parallelogram coding marks placed in the camera shooting space to obtain a coding mark image, which contains N parallelogram coding marks in the middle of the coding mark image;

Step 1.2, establish the pixel coordinate system of the corner points:

In the above-mentioned image containing N parallelogram coding marks, the upper left corner of the image is taken as the origin o of the corner pixel coordinate system, the x-axis direction of the corner pixel coordinate system is from left to right, and the corner is taken from top to bottom. The y-axis direction of the point pixel coordinate system, thereby establishing the corner pixel coordinate system o-xy;

Step 2.1, performing 8-bit grayscale processing on the encoded mark image to obtain the encoded mark grayscale image P ₁ ; wherein, the encoded mark grayscale image P ₁ is an 8-bit grayscale image;

Step 2.2, duplicating and backing up the grayscale image P1 _of the coding mark to obtain a grayscale backup image P1 _' of the coding mark;

Step 2.3. Binarize the grayscale backup image P ₁ ′ of the coding mark, so that the background color of each parallelogram coding mark is black (that is, the gray value is 0), and the orientation in each parallelogram coding mark is The pattern and the positioning pattern are both white (that is, the gray value is 255), and the color of the coding unit pattern can be white or black according to the coding rule of the parallelogram coding mark, and then obtain the coding mark binarization image P ₂ ;

Step 3. Set the black connected domain circularity threshold λ′ and the pixel number threshold λ″;

Step 4.1. Calculate the circularity value λ _n and the number of pixels c _n of all black connected domains in the coded mark binarized image P ₂ , wherein the circularity value of each black connected domain can be obtained from formula (1),

Among them, l _n represents the perimeter of the corresponding black connected domain outline, s _n represents the area of the corresponding black connected domain, n=1, 2, 3, 4...;

Step 4.2, select the appropriate black connected domain circularity threshold λ′ and pixel number threshold λ″ to obtain N directional rings corresponding to each of the N parallelogram coding marks in the coding mark binarization image P ₂ The black connected domain in the center; the black connected domain at the center of the N directional rings are respectively recorded as the black connected domain M ₁ of the ring, the black connected domain M ₂ of the ring, and the black connected domain of the ring in the binarized image P ₂ of the coding mark. The domain M ₃ , ..., the ring black connected domain M _N , and the ring black connected domain M ₁ , the torus black connected domain M ₂ , the torus black connected domain M ₃ , ... , the ring black connected domain M _N in turn Put it into the set of black connected domains A', namely the black connected domain M ₁ , the black connected domain M ₂ , the black connected domain M ₃ , ... and the black connected domain M _N are respectively torus The first element, the _second element, . The black connected domain of ; wherein, the circular black connected domain M ₁ , the circular black connected domain M ₂ , the circular black connected domain M ₃ , ..., the circular black connected domain M _N in the binarized image P ₂ of the coding mark The circularity values of , are all less than the circularity threshold λ′, and the black connected domain M ₁ , the black connected domain M ₂ , the black connected domain _{M 3} , ..., the black connected domain MN of the circular ring are pixel points The number is greater than the threshold λ″ of the number of pixels;

Step 4.3, take the integer variable i and assign i=1;

Step 4.4. Calculate the pixel coordinates of the centroid of the _i -th ring black connected domain Mi in the black connected domain set A′ and denote it as o″ _d,i (x″ _d,i ,y″ _d,i ), Take the obtained centroid pixel coordinate o″ _d,i (x″ _d,i ,y″ _d,i ) of the i-th annular black connected domain Mi as the _i -th element of the centroid set A of the annular black connected domain;

Step 4.5, judge whether i is less than N, if i<N, assign i+ ₁ to i, and return to step 4.4 to execute in sequence; Centroid pixel coordinates o″ _d,1 (x″ _d,1 ,y″ _d,1 ), o″ _d,2 (x″ _d,2 ,y″ _d,2 ), …, o″ _d,N (x ″ _{d, N} , y″ _{d, N} ), and put them into the set A of centroids of the black connected domain of the ring in turn;

Step 5, take integer variable ζ and assign ζ=1;

Step 6.1. Make two copies of the coding mark binarized image P ₂ to obtain the first backup binarized image P′ _ζ,1 of the ζ group and the second backup binarized image P′ of the ζ group respectively. _ζ,2 ;

Step 6.2. Use the complex background removal algorithm to perform digital image processing on the first backup binarized image P′ _ζ,1 of the ζth group to obtain the ζth parallelogram binarized image without complex background P″ _ζ,1 ;

In the ζth non-complex background parallelogram binarized image P″ _ζ,1 , all the pixels inside the parallelogram coding mark containing the centroid pixel coordinate values (x″ _d,ζ ,y″ _d,ζ ) is set to 255 (that is, white), and the gray value of all pixels outside the parallelogram coding mark containing the centroid pixel coordinate value (x″ _{d, ζ} , y″ _{d, ζ} ) are set to 0. (i.e. black);

Step 7.1, copy and backup the coding mark grayscale image P1 again to obtain the _ζth backup grayscale image _Pζ ″′;

Step 7.2. Use the corner detection algorithm to extract the sub-pixel coordinates of the 4 corner points in the ζth non-complex background parallelogram binarized image P″ _ζ,1 , and record them as the ζth non-complex background parallelogram binary image Four candidate corner points C″ _ζ,1 (x″ _ζ,1 ,y″ _ζ,1 ), C″ _ζ,2 (x″ _ζ,2 ,y″ ζ _{,1 on the transformed image P″ ζ,1 , 2} ), C″ _ζ,3 (x″ _ζ,3 ,y″ _ζ,3 ), C″ _ζ,4 (x″ _ζ,4 ,y″ _ζ,4 );

Step 7.3. Perform black connected domain erosion in the ζth non-complex background parallelogram binarized image P″ _{ζ,1 ,} so that the white connected in the ζth non-complex background parallelogram binarized image P″ ζ,1 Domain expansion, in the subsequent image multiplication operation, it can ensure that the complete grayscale pattern of the parallelogram coding mark including the centroid pixel coordinate values (x″ _{d, ζ} , y″ _{d, ζ} ) is extracted from the result image and its The 4 characteristic corners are preserved completely; and the ζth binarized image P″ _ζ,1 of a parallelogram without a complex background is recorded as the ζth arithmetic binarized image P″ _ζ,2 through the image processed in this step;

Step 7.4. Set the value of the part with the gray value of 255 in the ζth operation binarized image P″ ζ, ₂ to 1, and set the gray value in the ζth operation binarized image P″ _ζ,2 to 1. The value of the 0 part is set to 0, and then the binarized image P″ _ζ,2 and the ζth backup grayscale image P _ζ ″′ are used for multiplication, and the resulting image is recorded as the ζth The overlay result image T _ζ ; the ζth overlay result image T _ζ only contains the image information of the parallelogram coded mark including the centroid pixel coordinate values (x″ _{d, ζ} , y″ _{d, ζ} ), and other parallelograms are removed. The image information of the quadrilateral coding logo;

Step 7.5, using the corner detection algorithm to extract the sub-pixel coordinates of all corners in the ζ-th coverage result image T _ζ and store them in the ζ-th preliminary corner sub-pixel coordinate set B _ζ ; The sub-pixel coordinate set B _ζ of the corner selection point stores the four characteristic corner points of the parallelogram coding mark containing the centroid pixel coordinate values (x″ _{d, ζ} , y″ _{d, ζ} ) on the ζth overlay result image T _ζ . sub-pixel coordinate values and sub-pixel coordinate values of interference corners, where the interference corners are interference corners other than characteristic corners;

Step 7.6, take the integer variable i and assign i=1;

Step 7.7, find the corner sub-pixel coordinate closest to the sub-pixel coordinate value (x″ _{ζ, i} , y″ _{ζ, i} ) in the ζ-th primary corner sub-pixel coordinate set B _ζ and denote it as C ′ _ζ,i (x′ _ζ,i ,y′ _ζ,i );

Step 7.8, judge whether i is less than 4, if i<4, then assign i+1 to i and return to step 7.7; otherwise, the ζth coverage result image T _ζ has been obtained at this time. The sub-pixel coordinates C′ _ζ,1 (x′ _ζ,1 , _y ′ _{ζ ,1} ), C′ _{ζ, 2} (x′ _ζ,2 ,y′ _ζ,2 ), C′ _ζ,3 (x′ _ζ,3 ,y′ _ζ,3 ), C′ _ζ,4 (x′ _ζ,4 ,y′ _{ζ, 4} ), and perform step 8.1;

Step 8.1. On the second backup binarized image _P′ζ,2 of the ζth group, mark the parallelogram encoding mark containing the centroid pixel coordinate values (x″ _d,ζ , y″ _d,ζ ) as the ζth a parallelogram coding mark;

Step 8.2. On the second backup binarized image P' _ζ,2 of the ζ group, select the sub-pixel coordinate values as (x' _ζ,1 ,y' _ζ,1 ), (x' _ζ,2 , y′ _ζ,2 ), (x′ _ζ,3 ,y′ _ζ,3 ), (x′ _ζ,4 ,y′ _ζ,4 ) 4 pixels as the corners of the ζth parallelogram coding mark 4 vertices of quadrilateral S _ζ , connect 4 vertices and then obtain the corner quadrilateral S _ζ of the ζth parallelogram coding mark;

Step 9. On the second backup binarized image P′ _ζ,2 of the ζ group, find the white connected domain closest to the centroid pixel coordinate value (x″ _{d, ζ} , y″ _{d, ζ} ), and use this The gray value of the white connected domain is assigned as 0;

Step 10: On the second backup binarized image P′ _ζ,2 of the ζth group, the gray values of all the pixels inside the corner quadrilateral S _ζ of the ζth parallelogram coding mark remain unchanged, and the The gray value assignment of all pixel points other than the corner quadrilateral S _ζ of the ζ parallelogram coding marks is 255;

Step 11.1. On the second backup binarized image _P'ζ,2 of the ζth group, extract all the inner and outer contours in the corner quadrilateral S _ζ of the ζth parallelogram coding mark, and denote it as the ζth parallelogram. A set of contours D _ζ within the quadrilateral coded sign;

Step 11.2. Count the number of pixels contained in each contour in the contour set _Dζ in the ζth parallelogram coding mark, and record the contour containing the second largest number of pixels as the second backup binarized image P′ of the ζth group The positioning circle outline G _ζ in the ζ-th parallelogram coding mark on _ζ,2 is calculated and its centroid pixel coordinates are calculated and recorded as the ζ-th group of the second backup binarized image P′ _{ζ,2 on} the ζ-th parallelogram coding Pixel coordinates of the centroid of the positioning circle in the sign o′ _l,ζ (x′ _l,ζ ,y′ _l,ζ );

Step 12, the 4 contours containing the least number of pixels in the contour set D _ζ in the ζ-th parallelogram coding mark are marked as the coding combination directional pattern outline Z _ζ,1 , the coding combination directional pattern outline Z _ζ,2 , the coding combination The directional pattern profile Z _ζ,3 and the encoded combined directional pattern profile Z _ζ,4 and their centroids are calculated respectively

Step 13.1, according to the contour set D _ζ in the ζth parallelogram coding mark, remove the two contours that contain the largest number of pixels and the 4 contours that contain the least number of pixels, and the size of the remaining contours κ _ζ is divided into the following situations: :

(1) If κ _ζ == 0, execute step 14.1;

编码组合图案

…、编码组合图案

(2) If κ _ζ ≠ 0, then these κ _ζ contours are the contours of the coded combination coding pattern in the ζth parallelogram coding mark, which are respectively denoted as coding combination patterns

Coded Combination Patterns

..., coding combination pattern

Step 14.1, give integer variable i and initial value i=1;

的质心

将i+1重新赋值给i后继续执行此步骤，直到i＞κ_ζ结束；由此可以得到对应编码组合图案

编码组合图案

…、编码组合图案

的质心像素坐标

Step 14.2, on the second backup binarized image P′ _ζ,2 of the ζ group, calculate the coding combination pattern

centroid of

Continue to perform this step after reassigning i+1 to i, until i> _κζ ends; thus the corresponding coding combination pattern can be obtained

Coded Combination Patterns

..., coding combination pattern

The centroid pixel coordinates of

Step 15.1. On the second backup binarized image _P'ζ,2 of the ζth group, record the ζth parallelogram coding marks in the 1st coding area, the 2nd coding area, the 3rd coding area and the 4th coding area. The sub-pixel coordinates of the feature corners of the coding region are C _ζ,1 (x _ζ,1 ,y _ζ,1 ), C _ζ,2 (x _ζ,2 ,y _ζ,2 ), C _ζ,3 (x ζ,2 ), respectively. _ζ,3 ,y _ζ,3 ), C _ζ,4 (x _ζ,4 ,y _ζ,4 ); and on the second backup binarized image P′ _ζ,2 of the ζth group, the pixel coordinate value The pixel point of (x′ _{d,ζ ,} y′ _d,ζ ) is denoted as the centroid o ′ _d,ζ (x′ _d,ζ ,y′ _d,ζ ), and set the sub-pixel coordinate values as (x′ _ζ,1 ,y′ _ζ,1 ), (x′ _ζ,2 ,y′ _{ζ, 2} ), (x′ _ζ,3 ,y′ _ζ,3 ), (x′ _ζ,4 ,y′ _ζ,4 ) 4 pixels are denoted as C″′ _ζ,1 (x″′ _{ζ, 1} ,y″′ _ζ,1 ), C″′ _ζ,2 (x″′ _ζ,2 ,y″′ _ζ,2 ), C″′ _ζ,3 (x″′ _ζ,3 ,y″′ _{ζ ,3} ), C″′ _ζ,4 (x″′ _ζ,4 ,y″′ _ζ,4 );

由公式(2)得出，Step 15.2 On the second backup binarized image _P'ζ,2 of the ζth group, the direction vector in the ζth parallelogram coding mark

According to formula (2),

Step 16. On the second backup binarized image P′ _ζ,2 of the ζ group, find 4 pixel points C″′ _ζ,1 (x″′ _ζ,1 ,y″′ _ζ,1 ), C″′ _ζ,2 (x″′ _ζ,2 ,y″′ _ζ,2 ), C″′ _ζ,3 (x″′ _ζ,3 ,y″′ _ζ,3 ), C″′ _ζ,4 (x″′ _ζ,4 ,y″′ _ζ,4 ) are the two nearest pixels to the pixel coordinates o′ _l,ζ (x′ _l,ζ ,y′ _l,ζ ) of the centroid of the positioning circle, respectively record are C _ζ,1min (x _ζ,1min ,y _ζ,1min ) and C _ζ,2min (x _ζ,2min ,y _ζ,2min );

Find the sub-pixel coordinate values of the characteristic corners of the second coding area and the third coding area in the ζth parallelogram coding mark in the 4 pixel points and assign them to C _ζ,2 (x _ζ,2 ,y _{ζ, 2} ) and C _ζ,3 (x _ζ,3 ,y _ζ,3 );

和第2判断向量

并通过式(5)和式(6)计算出第1区域划分正弦值sinα_ζ和第2区域划分正弦值sinβ_ζ；Calculate the first judgment vector in the ζth parallelogram coding mark by formulas (3) and (4)

and the second judgment vector

And by formula (5) and formula (6), calculate the 1st area division sine value sinα _ζ and the 2nd area division sine value sinβ _ζ ;

Execute in the following two cases:

(1) If sinα _ζ <0, sinβ _ζ >0, then C _ζ,1min (x _ζ,1min ,y _ζ,1min ) is the characteristic corner point of the third coding region in the ζth parallelogram coding mark. The sub-pixel coordinate value of _ζ,1min (x _ζ,1min ,y _ζ,1min ) is assigned to C _ζ,3 (x _ζ,3 ,y _ζ,3 ); C _ζ,2min (x _ζ,2min ,y _{ζ, 2min} ) is the characteristic corner point of the second coding region in the ζth parallelogram coding mark, and assign the sub-pixel coordinate value of C _ζ,2min (x _ζ,2min ,y _ζ,2min ) to C _ζ,2 (x _ζ ) _,2 ,y _ζ,2 );

(2) If sinα _ζ >0, sinβ _ζ <0, then C _ζ,2min (x _ζ,2min ,y _ζ,2min ) is the characteristic corner point of the third coding region in the ζth parallelogram coding mark. The sub-pixel coordinate value of _ζ,2min (x _ζ,2min ,y _ζ,2min ) is assigned to C _ζ,3 (x _ζ,3 ,y _ζ,3 ); C _ζ,1min (x _ζ,1min ,y _{ζ, 1min} ) is the characteristic corner point of the second coding region in the ζth parallelogram coding mark, assign the sub-pixel coordinate value of C _ζ,1min (x _ζ,1min ,y _ζ,1min ) to C _ζ,2 (x _ζ ) _,2 ,y _ζ,2 );

Step 17: On the second backup binarized image P′ _ζ,2 of the ζ group, through the above step 16, the 4 pixel points C″′ _ζ,1 (x″ _ζ,1 ,y″′ _{ζ, 1} ), C″′ _ζ,2 (x″′ _ζ,2 ,y″′ _ζ,2 ), C″′ _ζ,3 (x″′ _ζ,3 ,y″′ _ζ,3 ), C″′ _ζ,4 (x″′ _ζ,4 ,y″′ _ζ,4 ) find the sub-pixel coordinate values of the characteristic corners of the second coding region and the third coding region in the ζth parallelogram coding mark and assign them to C _ζ,2 (x _ζ,2 ,y _ζ,2 ) and C _ζ,3 (x _ζ,3 ,y _ζ,3 ), assign the sub-pixel coordinate values of the remaining two pixels to the ζth The temporary coordinate value 1 of a parallelogram coding mark is denoted as C′ _ζ,5 (x′ _ζ,5 ,y′ _ζ,5 ), and the temporary coordinate value 2 is denoted as C′ _ζ,6 (x′ _{ζ, 6} ,y′ _ζ,6 );

和第4判断向量

According to formulas (7) and (8), the third judgment vector in the ζth parallelogram coding mark is obtained

and the fourth judgment vector

和第4判断向量

通过式(9)和式(10)得出第3区域划分正弦值sinω_ζ和第4区域划分正弦值sinξ_ζ；Step 18: On the second backup binarized image P′ _ζ,2 of the ζ group, according to the third judgment vector

and the fourth judgment vector

By formula (9) and formula (10), the 3rd area division sine value sinω _ζ and the 4th area division sine value sinξ _ζ are obtained;

According to the value of sinω _ζ and sinξ _ζ , the C′ _ζ,5 (x′ _ζ,5 ,y′ _ζ,5 ) or C′ _ζ,6 (x′ _ζ,6 ,y′ _ζ,6 ) The sub-pixel coordinate value is assigned to C _ζ,4 (x _ζ,4 ,y _ζ,4 ) or C _ζ,1 (x _ζ,1 ,y _ζ,1 );

Execute in the following two cases:

(1) If sinω _ζ ==0, sinξ _ζ ≠0, then C' _ζ,5 (x' _ζ,5 ,y' _ζ,5 ) is the feature of the fourth coding region in the ζ-th parallelogram coding mark Corner point, assign the sub-pixel coordinate value of C′ _ζ,5 (x′ _ζ,5 ,y′ _ζ,5 ) to C _ζ,4 (x _ζ,4 ,y _ζ,4 ); C′ _ζ,6 (x' _ζ,6 ,y' _ζ,6 ) is the characteristic corner point of the first coding region in the ζth parallelogram coding mark, set C' _ζ,6 (x' _ζ,6 ,y' _ζ,6 ) The sub-pixel coordinate value of is assigned to C _ζ,1 (x _ζ,1 ,y _ζ,1 );

(2) If sinω _ζ ≠0, sinξ _ζ ==0, then C' _ζ,6 (x' _ζ,6 ,y' _ζ,6 ) is the feature of the fourth coding region in the ζ-th parallelogram coding mark Corner point, assign the sub-pixel coordinate value of C′ _ζ,6 (x′ _ζ,6 ,y′ _ζ,6 ) to C _ζ,4 (x _ζ,4 ,y _ζ,4 ); C′ _ζ,5 (x′ _ζ,5 ,y′ _ζ,5 ) is the characteristic corner point of the first coding region in the ζth parallelogram coding mark, set C′ _ζ,5 (x′ _ζ,5 ,y′ _ζ,5 ) The sub-pixel coordinate value of is assigned to C _ζ,1 (x _ζ,1 ,y _ζ,1 );

So far, the sub-pixel coordinates C ζ _{, 1} (x _{ζ, 1} , y _ζ,1 ), the sub-pixel coordinates C _ζ,2 (x _ζ,2 ,y _ζ,2 ) of the feature corners of the second coding region, and the sub-pixel coordinates C _ζ of the feature corners of the third coding region _,3 (x _ζ,3 ,y _ζ,3 ) and the sub-pixel coordinates C _ζ,4 (x _ζ,4 ,y _ζ,4 ) of the feature corners of the fourth coding region;

且由公式(11)得出：Step 19. On the second backup binarized image P′ _ζ,2 of the ζ group, the feature corner point C _ζ,1 (x _ζ,1 ,y _ζ,1 ) will point to the feature corner point C _ζ,4 (x ζ,4 (x ζ,1 ) _ζ,4 ,y _ζ,4 ) vector is denoted as vector

And from formula (11) we get:

Take integer variable i and assign i=1;

向量

和方向向量

通过公式(12)、(13)和(14)计算出第i编码组合判断向量

编码组合判断余弦值

和

Step 20. On the second backup binarized image _P'ζ,2 of the ζth group, combine the directional pattern centroids according to the code

vector

and the direction vector

The ith code combination judgment vector is calculated by formulas (12), (13) and (14)

Code Combination Judgment Cosine

and

Divided into the following four cases:

且

则

为第3编码区域的编码组合定向图案质心，将

赋值给o′_z ^ζ,3(x′_z ^ζ,3,y′_z ^ζ,3)；(1) If

and

but

To orient the pattern centroids for the encoded combination of the 3rd encoded region, set the

Assign to o′ _z ^ζ,3 (x′ _z ^ζ,3 ,y′ _z ^ζ,3 );

且

则

为第2编码区域的编码组合定向图案质心，将

赋值给o′_z ^ζ,2(x′_z ^ζ,2,y′_z ^ζ,2)；(2) If

and

but

To orient the pattern centroids for the coded combination of the 2nd coded region, set the

Assign to o′ _z ^ζ,2 (x′ _z ^ζ,2 ,y′ _z ^ζ,2 );

且

则

为第1编码区域的编码组合定向图案质心，将

赋值给o′_z ^ζ,1(x′_z ^ζ,1,y′_z ^ζ,1)；(3) If

and

but

To orient the pattern centroids for the encoded combination of the 1st encoded region, set the

Assign to o′ _z ^ζ,1 (x′ _z ^ζ,1 ,y′ _z ^ζ,1 );

且

则

为第4编码区域的编码组合定向图案质心，将

赋值给o′_z ^ζ,4(x′_z ^ζ,4,y′_z ^ζ,4)；(4) If

and

but

To orient the pattern centroids for the coded combination of the 4th coded region, set the

Assign to o′ _z ^ζ,4 (x′ _z ^ζ,4 ,y′ _z ^ζ,4 );

Judging whether i satisfies i<4, if i<4, then assign i+1 to i, and return to execute step 20; otherwise, obtain the coding combination orientation pattern centroid of the first coding region in the ζth parallelogram coding mark o′ _z ^ζ,1 (x′ _z ^ζ,1 ,y′ _z ^ζ,1 ), the centroid of the encoding combined orientation pattern of the second encoding region o′ _z ^ζ,2 (x′ _z ^ζ,2 ,y′ _z ^{ζ , 2} ), the encoded combined orientation pattern centroid o″ _z ^ζ,3 (x′ _z ^ζ,3 ,y′ _z ^ζ,3 ) of the third encoding region and the encoded combined orientation pattern centroid o′ _z ^ζ of the fourth encoding region ^,4 (x′ _z ^ζ,4 ,y′ _z ^ζ,4 ), and proceed to step 21;

Step 21, re-assign i=1 to the integer variable i;

并初始化这4个二维数组中的所有元素，且赋值为-1；另外取4个整数变量

初始化

Step 22. Define 4 two-dimensional floating point arrays

And initialize all elements in these 4 two-dimensional arrays, and assign the value to -1; additionally take 4 integer variables

initialization

的质心像素坐标

与定位圆中心o′_l,ζ所形成的第ζ组第i区别向量

Step 23, on the 2nd backup binarized image P′ _ζ,2 of the ζth group, calculate the circular outline of the code combination code pattern mark in the ζth parallelogram code mark

The centroid pixel coordinates of

The ζth group i-th difference vector formed by the center o′ _l,ζ of the positioning circle

Calculated by formula (16) and formula (17)

Divided into the following four cases:

且

则令

将

赋值给

若i＞κ_ζ-1，则执行步骤24，否则将i+1赋值给i，返回执行步骤23；(1) If

and

order

Will

assign to

If i>κ _ζ -1, then execute step 24, otherwise assign i+1 to i, and return to execute step 23;

且

则令

将

赋值给

若i＞κ_ζ-1，则执行步骤24，否则将i+1赋值给i，返回执行步骤23；(2) If

and

order

Will

assign to

If i>κ _ζ -1, then execute step 24, otherwise assign i+1 to i, and return to execute step 23;

且

则令

将

赋值给

若i＞κ_ζ-1，则执行步骤24，否则将i+1赋值给i，返回执行步骤23；(3) If

and

order

Will

assign to

If i>κ _ζ -1, then execute step 24, otherwise assign i+1 to i, and return to execute step 23;

且

则令

将

赋值给

若i＞κ_ζ-1，则执行步骤24，否则将i+1赋值给i，返回执行步骤23；(4) If

and

order

Will

assign to

If i>κ _ζ -1, then execute step 24, otherwise assign i+1 to i, and return to execute step 23;

Step 24.1, re-assign i=1 to the integer variable i;

的取值情况，取整数变量

和

并赋值；Step 24.2, according to

The value of the case, take the integer variable

and

and assign;

Execute in the following cases:

则取整数变量

和

并赋值

(1) If

take an integer variable

and

and assign

将数组

中同一行元素均不为-1的元素分别记为

和

并分别赋值给o_ζ,1(x_ζ,1,y_ζ,1)的横坐标和纵坐标，并计算正弦值

(2) If

the array

The elements in the same row whose elements are not -1 are recorded as

and

And assign it to the abscissa and ordinate of o _ζ,1 (x _ζ,1 ,y _ζ,1 ) respectively, and calculate the sine value

To judge:

则取整数变量

和

并赋值

1) If

take an integer variable

and

and assign

则取整数变量

和

并赋值

2) If

take an integer variable

and

and assign

则取整数变量

和

并赋值

3) If

take an integer variable

and

and assign

将数组

中同一行元素均不为-1的元素分别记为

和

和

并分别赋值给o_ζ,1(x_ζ,1,y_ζ,1)的横坐标和纵坐标以及o_ζ,2(x_ζ,2,y_ζ,2)的横坐标和纵坐标，同时计算正弦值

和

(3) If

the array

The elements in the same row whose elements are not -1 are recorded as

and

and

and assign them to the abscissa and ordinate of o _ζ,1 (x _ζ,1 ,y _ζ,1 ) and the abscissa and ordinate of o _ζ,2 (x _ζ,2 ,y _ζ,2 ), and calculate at the same time Sine

and

and make a judgment:

或

则取整数变量

和

并赋值

1) If

or

take an integer variable

and

and assign

或

则取整数变量

和

并赋值

2) If

or

take an integer variable

and

and assign

或

则取整数变量

和

并赋值

3) If

or

take an integer variable

and

and assign

则取整数变量

和

并赋值

(4) If

take an integer variable

and

and assign

If i<4, assign i+1 to i and return to step 24.2; otherwise, continue to step 25;

Step 25, obtain the number W _ζ of the ζth parallelogram coding mark by formula (21):

W _ζ =V _ζ ^T ·U (21)

Among them, the column vector U=(2 ⁰ ,2 ¹ ,2 ² ,...2 ¹¹ ) ^T , the column vector

其中W_ζ为标定角点

所属编码方格的编号，σ的取值代表标定角点

所属的第σ编码区域；Step 26, mark the code number of the characteristic corner point that belongs to the σth coding region (wherein σ=1,2,3,4) in the ζth parallelogram coding mark as

where W _ζ is the calibration corner

The number of the coding square to which it belongs, and the value of σ represents the calibration corner

the σth coding region to which it belongs;

So far, the respective code numbers of the 4 characteristic corner points in the zth parallelogram coding mark and their corresponding sub-pixel coordinate values have been obtained:

的特征角点的亚像素坐标值为(x_ζ,1,y_ζ,1)；Code number is

The sub-pixel coordinate value of the feature corner of is (x _ζ,1 ,y _ζ,1 );

的特征角点的亚像素坐标值为(x_ζ,2,y_ζ,2)；Code number is

The sub-pixel coordinate value of the feature corner of is (x _ζ,2 ,y _ζ,2 );

的特征角点的亚像素坐标值为(x_ζ,3,y_ζ,3)；Code number is

The sub-pixel coordinate value of the feature corner of is (x _ζ,3 ,y _ζ,3 );

的特征角点的亚像素坐标值为(x_ζ,4,y_ζ,4)；Code number is

The sub-pixel coordinate value of the feature corner of is (x _ζ,4 ,y _ζ,4 );

Step 27, judge whether ζ is less than N, if satisfied, then ζ+1 is reassigned to ζ, and returns to step 6.1 to execute sequentially; If not satisfied, have found the sub of 4 characteristic corners on each parallelogram coding mark. Pixel coordinate value and corresponding code number.

Further, in step 6.1, the obtained first backup binarized image P′ _ζ,1 of the ζth group and the pixel coordinate value (x " _{d, ζ} , y" _{d, ζ} ) as the input condition, the complex background of the first backup binarized image P′ _ζ,1 of the ζ group is removed by using the complex background removal algorithm of coding marks, and finally the ζ-th non-complex background is obtained. The steps of binarizing the image P″ _ζ of a parallelogram with a complex background are as follows:

Step 6.1.1, take integer variable i and assign i=1;

Step 6.1.2. Find the white connected domain closest to the pixel coordinate value (x″ _{d, ζ} , y″ _{d, ζ} ) on the first backup binarized image P′ _ζ,1 of the ζ group and record it as the first The ith ring white connected domain M' _i on the first backup binarized image P' _ζ,1 of the ζ group, and the gray value of the ith ring white connected domain M' _i is assigned to 0 ;

Step 6.1.3, judge whether i is less than N, if i<N, assign i+1 to i, and return to step 6.1.2 to execute in sequence; otherwise, set the first backup binarized image P′ _ζ of the ζ group _{, The orientation circles in all parallelogram coding marks in 1} are set to black, and the first backup binarized image P' _ζ,1 of the ζ group is recorded as the ζ-th black background extraction image after this step is processed. image P' _ζ,b , and perform step 6.1.4;

Step 6.1.4. In all the black connected domains on the ζth black background extraction image P′ _ζ,b , find the black connected domain mark that is closest to the pixel coordinate value (x″ _{d, ζ} , y″ _{d, ζ} ). Extract the black connected domain Ω _ζ of the ζth parallelogram background on the image P′ _ζ,b for the ζth black background;

Step 6.1.5. Extract all the inner and outer contours of the ζth parallelogram background black connected domain Ω _ζ on the ζth black background extraction image P′ _ζ,b to obtain the ζth parallelogram background black connected domain Ω _ζ The inner and outer contour set V _ζ of ;

Step 6.1.6, compare the perimeters of all contours in the contour set V _ζ , and record the contour with the longest perimeter as the outer contour E _{ζ of the ζth parallelogram background black connected domain Ω ζ ;}

Step 6.1.7. On the ζth black background extraction image P′ _ζ,b , assign the gray value of all pixels within the outer contour E _ζ to 255, and the gray value of all pixels outside the outer contour E _ζ . The value is assigned as 0, so as to obtain the ζth non-complex background parallelogram binarized image P″ _ζ ; so that in the ζth non-complex background parallelogram binarized image P″ _ζ , the centroid pixel coordinate value (x″ ζ is included _d,ζ ,y″ _d,ζ ) The gray value of all pixels inside the parallelogram coding mark is set to 255 (that is, white), including the centroid pixel coordinate value (x″ _d,ζ ,y″ _d,ζ ) of the parallelogram coding mark outside the gray value of all pixels are set to 0 (ie black).

Also provided is a computer-readable storage medium comprising a computer program for use in conjunction with an electronic device having an image processing function, the computer program being executable by a processor to perform the decoding method.

Compared with the prior art, the beneficial effects of the present invention are as follows:

1. The coding pattern in the parallelogram coding mark proposed by the present invention is composed of a positioning pattern, an orientation pattern and a coding combination pattern, wherein the positioning pattern and the orientation pattern can be realized in the process of camera calibration, three-dimensional data splicing, etc. The relative rotation direction of the measuring target and the camera improves the flexibility;

2, in the parallelogram coding mark proposed by the present invention, comprise four coding combination patterns, comprise three coding combination coding patterns in each coding combination pattern, the parallelogram coding mark proposed by the present invention can produce 4096 kinds of different codes altogether, The capacity can be expanded, so 3D data stitching can also be completed for targets with larger sizes;

3. In the parallelogram coding mark proposed by the present invention, the position of orientation pattern, positioning pattern and each coding combination pattern, and the position of each coding combination coding pattern are distinguished by the method of graphic geometric relationship and vector product. Strong robustness, high accuracy for affine transformed images;

4. A decoding method for a parallelogram coding mark based on a graphic geometric relationship proposed by the present invention can effectively remove the interference of noise, and the proposed method for removing complex background greatly improves the accuracy of decoding;

5. The decoding method of the parallelogram coding mark based on the graphic geometric relationship proposed by the present invention has high efficiency, fast decoding speed, and can realize real-time decoding.

Description of drawings

Fig. 1 is the schematic diagram of the parallelogram coding mark of the present invention;

Fig. 2 is in the parallelogram coding mark of the present invention, the arrangement schematic diagram of coding pattern in each vertex, corner point and each coding combination;

FIG. 3 is a display diagram of the grayscale image P ₁ of the coding mark;

FIG. 4 is a display diagram of the binarized image P ₂ at the coding mark;

Fig. 5 is a display diagram of extracting the set _A of centroids of annular black connected domains on the coded mark binarization image P2;

FIG. 6 is a display diagram of the first parallelogram binarized image P″ _1,1 without complex background;

7 is a graph showing the result of extracting the sub-pixel coordinates of the corners of the first parallelogram binarized image P″ _1,1 without complex background using the Harris point detection algorithm;

FIG. 8 is the first overlay result image T ₁ obtained after performing image multiplication between the first parallelogram binarized image P ₁ ″ without complex background and the first backup grayscale image P ₁ ″′;

9 is a graph showing the result of extracting the sub-pixel coordinates of the corner points in the first coverage result image T ₁ by utilizing the Harris point detection algorithm;

FIG. 10 is a display diagram of the first binarized image P ₁ ″ without a complex background coding mark;

FIG. 11 is a schematic flowchart of the decoding method according to the present invention.

Detailed ways

The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, so that the advantages and features of the present invention can be more easily understood by those skilled in the art, and the protection scope of the present invention can be more clearly defined.

Please refer to Fig. 1, a kind of decoding method of the parallelogram coding mark based on the graphic geometrical relationship, the coding mark is a square coding square, and the surface of the coding square is provided with a parallelogram background pattern and a coding pattern, and the coding pattern Located inside the parallelogram background pattern, the encoding pattern includes a positioning pattern, an orientation pattern and a combined encoding pattern, the orientation pattern and the positioning pattern are used for the judgment of the direction of the parallelogram encoding mark, and the encoding combined pattern is used for the parallelogram encoding Codes that mark four corners, each code combination pattern is composed of one code combination orientation pattern and three code combination code patterns.

The positioning patterns, the orientation patterns, all the encoding combination orientation patterns and all the encoding combination encoding patterns in the parallelogram coding mark are non-overlapping and non-connected.

为规定向量

则平行四边形编码标志内的定位图案和定向图案的位置关系如下：平行四边形编码标志内由定向图案质心指向定位图案质心的方向与规定向量

的方向相同。Take any characteristic corner of the parallelogram coding mark and mark it as a vector to determine the first vertex o" ₁ , and on the parallelogram coding mark, any side that intersects to form a vector to determine the first vertex o" ₁ is marked as a vector to determine the first side N _v1 , take the vertex of the parallelogram coding mark on the first side N _v1 of the vector determination and record it as the vector determination second point o″ ₂ , wherein the vector determination second point o″ ₂ and the vector determination first vertex o″ ₁ are mutually 2 points that do not coincide, denote a vector

is the specified vector

Then the positional relationship between the positioning pattern and the orientation pattern in the parallelogram coding mark is as follows: the direction from the centroid of the orientation pattern to the centroid of the positioning pattern in the parallelogram encoding mark is the same as the specified vector.

in the same direction.

同向的单位向量记为第1个规定单位向量

当人正视看向平行四边形编码标志时，以向量确定第一顶点o″₁为旋转中心，在标志平面P_t内将第1个规定单位向量

逆时针旋转β′角度(0°＜β′＜90°)得到第2个规定单位向量

在空间中以向量确定第一顶点o″₁为起点做一个与

所得向量的方向相同的单位向量，并记为正向向量

将距离平行四边形编码标志中定向图案最近的两个特征角点分别记为第1临时顶点o″₃和第2临时顶点o″₄；若向量

叉乘规定向量

所得向量的方向与正向向量

的方向相同，则将记为向量

辅助向量

若向量

叉乘规定向量

所得向量的方向与正向向量

的方向相同，则将向量

记为辅助向量

Denote the plane on which the parallelogram coding mark is located as the mark plane P _t , and take the first vertex o″ ₁ determined by the vector as the starting point to make a vector with the specified vector

The unit vector in the same direction is recorded as the first specified unit vector

When a person looks directly at the parallelogram coding mark, the first vertex o″ ₁ determined by the vector is used as the rotation center, and the first specified unit vector is set in the mark plane P _t

Rotate the angle β′ counterclockwise (0°<β′<90°) to obtain the second specified unit vector

Make _an and

The resulting vector is a unit vector with the same direction as the forward vector

The two characteristic corner points closest to the orientation pattern in the parallelogram coding mark are recorded as the first temporary vertex o″ ₃ and the second temporary vertex o″ ₄ ; if the vector

cross product specified vector

The direction and forward vector of the resulting vector

in the same direction, it will be recorded as a vector

auxiliary vector

if vector

cross product specified vector

The direction and forward vector of the resulting vector

in the same direction, the vector

denoted as auxiliary vector

Note that the color of the parallelogram background pattern in the parallelogram coding sign is color 1, and the colors of the orientation pattern, positioning pattern, all coding combination orientation patterns and all coding combination coding patterns in the parallelogram coding sign are color 2, wherein , Color 1 is significantly different from Color 2. In this embodiment, the color of the parallelogram background pattern in the parallelogram coding sign is black (color 1), and the orientation pattern, positioning pattern, all coding combination orientation patterns and all coding combination coding patterns in the parallelogram coding sign All colors are white (color 2).

Inside the parallelogram coding mark, the smallest area among the areas of all coding combined coding patterns is recorded as the minimum area of the coding combined coding pattern, the area of the directional pattern, all coding combined directional patterns and all coding combined coding patterns inside the parallelogram coding mark The size satisfies the following relationship: the area of all the coding combination coding patterns inside the parallelogram coding mark is smaller than the area of the directional pattern inside the parallelogram coding mark, and the area of all coding combination directional patterns inside the parallelogram coding mark is smaller than the coding combination coding Pattern minimum area. In this embodiment, the directional pattern is a circular connected domain with a diameter of 12 mm, the coding combined directional pattern is a circular connected domain with a diameter of 3 mm, the coding combined coding pattern is a circular connected domain with a diameter of 6 mm, and the positioning pattern is an outer circle A circular connected domain with a diameter of 12 mm and an inner circle of 5 mm in diameter is shown in Figure 1.

The position of the orientation pattern and the positioning pattern must meet the following requirements: the line segment formed by the geometric center of the orientation pattern and the geometric center of the positioning pattern is l ₁ , then the line segment l ₁ must be parallel to any side of the parallelogram, and the line segment l ₁ The midpoint p ₁ of is near the geometric center point of the parallelogram lattice. The positions of the four code combinations need to meet the following requirements: connect the midpoint p ₁ of the line segment l ₁ to the midpoint of the four sides of the parallelogram lattice to form four line segments, and the obtained four line segments divide the entire parallelogram lattice into four regions . Then, the four encoded combined orientation patterns are located inside the four regions, respectively, and the geometric center of each encoded combined orientation pattern is near the geometric center point of the respective region. And, among the four vertices of the parallelogram lattice, each vertex has and only one coding combination orientation pattern with the closest distance to it, that is, in the straight-line distance between each vertex and the geometric center of the four coding combination orientation patterns, there are and only There is a coded combination directional pattern with the shortest straight-line distance.

At the same time, among the four coded combined directional patterns, two of the coded combined directional patterns were significantly closer to the directional patterns than to the positioning patterns. Likewise, the other two encoded combined orientation patterns are significantly closer to the orientation pattern than to the orientation pattern. As shown in Figure 2, in each coding combination, the positions of the coding patterns of the three coding combinations must meet the following requirements: the orientation pattern is A ₁ , and its geometric center is a ₁ , and the positioning pattern is A ₂ , and its geometric center is a ₂ , the directed line segment from a ₁ to a ₂ is called the standard vector α. In the four coding combinations, the directional pattern of the Y-th coding combination is denoted as C _Y , and its geometric center is c _Y . In the Y-th coding combination, the first coding pattern of the Y-th coding combination is D _Y1 , and its geometric center is d _Y1 , the second encoding pattern of the Y-th encoding combination is D _Y2 , and its geometric center is d _Y2 , and the third encoding pattern of the Y-th encoding combination is D _Y3 , and its geometric center is d _Y3 . Starting from the geometric center c _Y of the Y-th encoding combination directional pattern C _Y , leading to the geometric center d _Y1 of the Y-th encoding combination first encoding pattern D _Y1 and the Y-th encoding combination The geometric center d _Y2 of the second encoding pattern D _Y2 The directional line segment of the geometric center d _Y3 of the third coding pattern D _Y3 of the Y-th coding combination is called a vector γ _Y1 , a vector γ _Y2 , and a vector γ _Y3 , respectively. At the same time, the vector products γ _Y1 ×α, γ _Y2 ×α, and γ _Y3 ×α of the vector γ _Y1 , the vector γ _Y2 , and the vector γ _Y3 respectively and the standard vector α are η _Y1 , η _Y2 , η _Y3 , respectively, as shown in the following equations Show:

Then η _Y1 , η _Y2 , η _Y3 need to have obvious differences in the length or direction of the module; among them, Y=1, 2, 3, 4.

As shown in Figure 11, the method of digital image processing is used to obtain the coding sequence number and sub-pixel coordinates of each feature corner point in the image containing N (N is taken as 10 in this embodiment) parallelogram coding marks captured by the camera, and then complete the parallelogram The steps for decoding the encoding flag are as follows:

Step 1.1, utilize 10 parallelogram coding marks placed in the camera shooting space to obtain a coding mark image, which includes 10 parallelogram coding marks in the said coding mark image;

Step 1.2, establish the pixel coordinate system of the corner point: in the above-mentioned image containing 10 parallelogram coding marks, take the upper left corner of the image as the origin o of the corner pixel coordinate system, and from left to right as the corner pixel coordinate system The x-axis direction of , is taken as the y-axis direction of the corner pixel coordinate system from top to bottom, thereby establishing the corner pixel coordinate system o-xy;

Step 2.1, performing grayscale processing on the encoded logo image to obtain the encoded logo grayscale image P ₁ ; wherein, the encoded logo grayscale image P ₁ is an 8-bit grayscale image, as shown in Figure 3;

Step 2.2, duplicating and backing up the grayscale image P1 _of the coding mark to obtain a grayscale backup image P1 _' of the coding mark;

Step 2.3. Binarize the grayscale backup image P ₁ ′ of the coding mark, so that the background color of each parallelogram coding mark is black (that is, the gray value is 0), and the orientation in each parallelogram coding mark is The pattern and the positioning pattern are both white (that is, the grayscale value is 255), and the color of the coding unit pattern can be white or black according to the coding rule of the parallelogram coding mark, and then obtain the coding mark binarization image P ₂ , as shown in the figure 3 shown;

Step 3. Set the black connected domain circularity threshold λ′=1, and the pixel number threshold λ″=30;

Step 4.1. Calculate the circularity value λ _n and the number of pixels c _n of all black connected domains in the coded mark binarized image P ₂ , wherein the circularity value of each black connected domain can be obtained from formula (1),

Among them, l _n represents the perimeter of the corresponding black connected domain outline, s _n represents the area of the corresponding black connected domain, n=1, 2, ..., 10;

Step 4.2. The black connected domain circularity threshold λ′=1 and the pixel number threshold λ″=30 selected in this embodiment can obtain the corresponding corresponding ₁₀ parallelogram coding marks in the coding mark binarization image P2. The black connected domains at the centers of the 10 directional rings; the black connected domains at the centers of the 10 directional rings are respectively recorded as the black connected domains M ₁ of the rings and the black connected domains M of the rings in the binarized image P ₂ of the coding mark _2. The torus black connected domain M ₃ , ..., the torus black connected domain M ₁₀ , and the torus black connected domain M ₁ , the torus black connected domain M ₂ , the torus black connected domain M ₃ , ... , the torus The black connected domains M ₁₀ are sequentially placed in the set A' of circular black connected domains, namely the circular black connected domain M ₁ , the circular black connected domain M ₂ , the circular black connected domain M ₃ , . . . , the circular black connected domain M ₁₀ are the 1st element, the _2nd element, . The black connected domain inside the oriented circular ring in the middle; wherein, the circular black connected domain M ₁ , the circular black connected domain M ₂ , the circular black connected domain M ₃ , ..., the circular ring in the binarized image P ₂ of the coding mark The circularity value of the black connected domain M ₁₀ is all less than 1, and the pixel points of the circular black connected domain M ₁ , the circular black connected domain M ₂ , the circular black connected domain M ₃ , ..., the circular black connected domain M ₁₀ The number is greater than 30;

Step 4.3, take the integer variable i and assign i=1;

Step 4.4. Calculate the pixel coordinates of the centroid of the _i -th ring black connected domain Mi in the black connected domain set A′ and denote it as o″ _d,i (x″ _d,i ,y″ _d,i ), Put the obtained centroid pixel coordinates o″ _d,i (x″ _d,i ,y″ _d,i ) of the black connected domain Mi of the _i -th ring into the centroid set A of the black connected domain of the ring, as a ring The ith element of the black connected domain centroid set A;

Step 4.5, judge whether i is less than N, if i < 10, assign i+1 to i, and return to step 4.4 to execute in sequence; otherwise, obtain the black connected domain M ₁ of the ring in the binarized image P ₂ of the coding mark , circular black connected domain M ₂ , circular black connected domain M ₃ , ..., the centroid pixel coordinates of circular black connected domain M ₁₀ o″ _d,1 (775,135), o″ _d,2 (x″ _d,2 , y″ _d,2 ), …, o″ _d,10 (x″ _d,10 ,y″ _d,10 ), and put them into the set A of the black connected domain centroids of the ring in turn, as shown in Figure 5;

Step 5, take integer variable ζ and assign ζ=1;

Step 6.1. Make two copies of the coding flag binarized image P ₂ to obtain the first backup binarized image P′ _1,1 of the first group and the second backup binarized image P′ of the first group _1,2 ;

Step 6.2, using the algorithm of removing the complex background of the coding mark to perform digital image processing on the first backup binarized image P′ _1,1 of the first group, and then obtain the first parallelogram binarized image P″ _{1 without complex background, 1} ; in the _first parallelogram binarized image P″ 1,1 without complex background, the grayscale values of all the pixels inside the parallelogram encoding mark including the centroid pixel coordinate value (775, 135) are set to 255 (ie white), the gray value of all pixels outside the parallelogram coding mark containing the centroid pixel coordinate value (775,135) are set to 0 (ie black);

Step 7.1, copy and backup the grayscale image P ₁ of the coding mark to obtain the first backup grayscale image P ₁ ″′;

Step 7.2. Use the Harris corner detection algorithm to extract the sub-pixel coordinates of the four corner points in the first parallelogram binarized image P″ _1,1 without complex background, and record it as the first parallelogram without complex background II Four candidate corner points C″ _1,1 (0.6904×10 ³ , 0.1910×10 ³ ), C″ _1,2 (0.6899×10 ³ , 0.0238×10 ³ ) on the valued image P″ _1,1 , C″ _1,3 (0.8575×10 ³ , 0.0237×10 ³ ), C″ _1,4 (0.8573×10 ³ , 0.1908×10 ³ );

Step 7.3. Perform black connected domain erosion in the first parallelogram binarized image P″ _1,1 without complex background to make the white connected domain in the first parallelogram binarized image P″ _1,1 without complex background Expansion, in the subsequent image multiplication operation, it can ensure that the complete grayscale pattern of the parallelogram coding mark containing the centroid pixel coordinate value (775,135) is extracted from the operation result image, and its 4 characteristic corners are kept intact; The image obtained through the processing in this step of the two parallelogram binarized images P″ _1,1 without a complex background is denoted as the first arithmetic binarized image P″ _1,2 ;

Step 7.4. Set the value of the part whose gray value is 255 in the first operation binarized image P″ _1,2 to 1, and set the gray value in the first operation binary image P″ _1,2 as 1 The value of the part of 0 is set to 0, and then the first operation binarized image P″ _{1, 2} and the first backup grayscale image P ₁ ″′ are used for multiplication, and the resultant image obtained is recorded as the first image The overlay result image T ₁ , as shown in FIG. 8 ; the first overlay result image T ₁ only contains the image information of the parallelogram encoding mark including the centroid pixel coordinate value (775, 135), and removes the image information of other parallelogram encoding marks. image information;

Step 7.5. Use the Harris corner detection algorithm to extract the sub-pixel coordinates of all corners in the first coverage result image T ₁ and store them in the first primary corner sub-pixel coordinate set B ₁ ; among them, the first The sub-pixel coordinate set B ₁ of the primary selected corner points stores the sub-pixel coordinate values of the four characteristic corner points and the sub-pixel coordinate values of the interference corner points on the first overlay result image T ₁ containing the pixel coordinate value of the centroid (775, 135) of the parallelogram coding mark. pixel coordinate value, the interference corners are interference corners other than characteristic corners;

Step 7.6, take the integer variable i and assign i=1;

Step 7.7. Find the corner sub-pixel coordinate closest to the sub-pixel coordinate value (x″ _{1, i} , y″ _{1, i} ) in the first primary corner sub-pixel coordinate set B ₁ and denote it as C ′ _1,i (x′ _1,i ,y′ _1,i );

Step 7.8, judge whether i is less than 4, if i < 4, assign i+1 to i and return to step 7.7; otherwise, the first coverage result image T ₁ contains the centroid pixel coordinate value (775,135 ), the sub-pixel coordinates C′ _1,1 (0.6927×10 ³ , 0.1889×10 ³ ), C′ _1,2 (0.6926×10 ³ , 0.0256×10 ³ ), C′ _1,3 (0.8559×10 ³ , 0.0257×10 ³ ), C′ _1,4 (0.8558×10 ³ , 0.1890×10 ³ ), as shown in FIG. 9 , and step 8.1 is performed;

Step 8.1, on the second backup binarized image P′ _1,2 of the first group, mark the parallelogram encoding mark containing the centroid pixel coordinate value (775,135) as the first parallelogram encoding mark;

Step 8.2. On the second backup binarized image P′ _1,2 of the first group, select sub-pixel coordinate values as (0.6904×10 ³ , 0.1910×10 ³ ), (0.6899×10 ³ , 0.0238×10 respectively) ³ ), (0.8575×10 ³ , 0.0237×10 ³ ), (0.8573×10 ³ , 0.1908×10 ³ ) 4 pixels as the 4 vertices of the corner quadrilateral S ₁ of the first parallelogram coding mark, Connect 4 vertices and then obtain the corner quadrilateral S ₁ of the first parallelogram coding mark;

Step 9. On the second backup binarized image P′ _1,2 of the first group, find the white color closest to the pixel coordinate value (775,135) of the centroid of the first directional ring in the black connected domain centroid set A of the above-mentioned ring. Connected domain, and assign the gray value of this white connected domain to 0;

Step 10: On the second backup binarized image P′ _1,2 of the first group, keep the grayscale values of all the pixels inside the corner quadrilateral S1 of the _first parallelogram coding mark unchanged, and set the first The gray value of all pixel points other than the corner point quadrilateral S ₁ of a parallelogram coding mark is assigned as 255;

Step 11.1. On the second backup binarized image P′ _1,2 of the first group, extract all the inner and outer contours in the parallelogram S ₁ at the corner point of the first parallelogram coding mark, and denote it as the first parallel a set of contours D ₁ of quadrilateral coding signs;

Step 11.2 Count the number of pixels contained in each contour in the contour set D ₁ in the first parallelogram coding mark, and mark the contour with the second largest number of pixels as the positioning circle contour G ₁ in the first parallelogram coding mark , calculate its centroid pixel coordinate and record it as the centroid pixel coordinate o′ _{l,1 (} 775,81) ;

Step 12: Count the number of pixels contained in each contour in the contour set D1 in the _first parallelogram coding mark, and record the four contours with the least number of pixels as the second backup binarized image P′ of the first group The coded combination directional pattern outline Z _1,1 , the coded combination directional pattern outline Z _1,2 , the coded combination directional pattern outline Z _1,3 , the coded combination directional pattern outline Z ₁ in the first parallelogram coding mark on _{1,2 ,4} , and calculate their centroid pixel coordinates respectively

Step 13.1. According to the contour set D ₁ in the first parallelogram coding mark, remove the two contours containing the largest number of pixels and the four contours containing the least number of pixels, and the remaining contours κ ₁ == 1; because κ ₁ ≠0, then this 1 outline is the outline of the coded combination coding pattern in the first parallelogram coding mark, which is denoted as the coding combination pattern

Step 14.1, give integer variable i and initial value i=1;

的质心像素坐标o′₁ ⁱ(x′₁ ⁱ,y′₁ ⁱ)，将i+1重新赋值给i后继续执行此步骤，直到i＞1结束；由此可以得到对应编码组合图案

编码组合图案

…、编码组合图案

的质心像素坐标

Step 14.2: Calculate the coding combination pattern on the second backup binarized image P' _1,2 of the first group

The centroid pixel coordinates o′ ₁ ⁱ (x′ ₁ ⁱ , y′ ₁ ⁱ ) of , reassign i+1 to i and continue to perform this step until i>1 ends; thus the corresponding coding combination pattern can be obtained

Coded Combination Patterns

..., coding combination pattern

The centroid pixel coordinates of

的质心像素坐标为o′₁ ¹(728,45)；In this embodiment, the coded combination pattern can be obtained

The centroid pixel coordinate of is o′ ₁ ¹ (728,45);

Step 15.1. On the second backup binarized image P′ _1,2 of the first group, record the location in the first encoding area, the second encoding area, the third encoding area and the fourth encoding area in the first parallelogram encoding mark The sub-pixel coordinates of the feature corners of the coding region are C _1,1 (x _1,1 ,y _1,1 ), C _1,2 (x _1,2 ,y _1,2 ), C _1,3 (x _1,3 ,y _1,3 ), C _1,4 (x _1,4 ,y _1,4 ); and on the second backup binarized image P′ _1,2 of the first group, the pixel coordinate value The pixel point of (775,135) is marked as the centroid o′ _d,1 (775,135) of the positioning ring of the first parallelogram coding mark on the second backup binarized image P′ _1,2 of the first group. The pixel coordinate values are (0.6927×10 ³ , 0.1889×10 ³ ), (0.6926×10 ³ ,0.0256×10 ³ ), (0.8559×10 ³ ,0.0257×10 ³ ), (0.8558×10 ³ ,0.1890×10 ^{3 )} ), the four pixels are respectively denoted as C″ _1,1 (0.6927×10 ³ , 0.1889×10 ³ ), C″′ _1,2 (0.6926×10 ³ , 0.0256×10 ³ ), C″′ _1,3 (0.8559×10 ³ , 0.0257×10 ³ ), C″′ _1,4 (0.8558×10 ³ , 0.1890×10 ³ );

由公式(2)得出，Step 15.2 On the second backup binarized image P′ _1,2 of the first group, the direction vector in the first parallelogram encoding flag

According to formula (2),

Step 16. On the second backup binarized image P' _1,2 of the first group, find 4 pixel points C"' _1,1 (0.6927×10 ³ , 0.1889×10 ³ ), C"′ _{1 , 2} (0.6926×10 ³ , 0.0256×10 ³ ), C″′ _1,3 (0.8559×10 ³ , 0.0257×10 ³ ), C″′ _1,4 (0.8558×10 ³ ,0.1890×10 ³ ) The two pixels closest to the pixel coordinates o′ _l,1 (775,81) of the centroid of the positioning circle are recorded as C _1,1min (x _1,1min ,y _1,1min ) and C _1,2min (x _1,2min , y _1,2min ), which are C _1,1min (0.6926×10 ³ , 0.0256×10 ³ ) and C _1,2min (0.8559×10 ³ , 0.0257×10 ³ ) in this embodiment.

和第2判断向量

并通过式(5)和式(6)计算出区域判断正弦值1sinα₁和区域判断正弦值2sinβ₁；Calculate the first judgment vector in the first parallelogram coding mark by formulas (3) and (4)

and the second judgment vector

And calculate the regional judgment sine value 1sinα ₁ and the regional judgment sine value 2sinβ ₁ by formula (5) and formula (6);

In this example:

sinα ₁ >0, sinβ ₁ <0, then C _1,2min (0.8559×10 ³ , 0.0257×10 ³ ) is the characteristic corner point of the third coding region in the first parallelogram coding mark, and C _1,2min ( The pixel coordinate value of 0.8559×10 ³ , 0.0257×10 ³ ) is assigned to C _1,3 (x _1,3 ,y _1,3 ); C _1,1min (0.6926×10 ³ ,0.0256×10 ³ ) is the first The characteristic corner points of the second coding region in the parallelogram coding mark, assign the pixel coordinate value of C _1,1min (0.6926×10 ³ ,0.0256×10 ³ ) to C _1,2 (x _1,2 ,y _{1, 2} );

和第4判断向量

Step 17, the second backup binarized image P' _1,2 of the first group, through the above step 16, at the 4 pixel points C"' _1,1 (0.6927×10 ³ , 0.1889×10 ³ ), C"' _1,2 (0.6926×10 ³ , 0.0256×10 ³ ), C″′ _1,3 (0.8559×10 ³ , 0.0257×10 ³ ), C″′ _1,4 (0.8558×10 ³ ,0.1890×10 ³ ) The sub-pixel coordinate values of the characteristic corners of the second coding area and the third coding area in the first parallelogram coding mark are found and assigned to C _1,2 (x _1,2 ,y _1,2 ) and C _1,3 (x _1,3 ,y _1,3 ); assign the sub-pixel coordinate values of the remaining two pixels to the first temporary coordinate value of the first parallelogram coding mark, and denote it as C′ _{1 , 5} (0.6927×10 ³ , 0.1889×10 ³ ), and the second temporary coordinate value, denoted as C′ _1,6 (0.8558×10 ³ , 0.1890×10 ³ ); calculate according to formulas (7) and (8) The third judgment vector in the first parallelogram coding flag

and the fourth judgment vector

和第4判断向量

通过式(9)和式(10)可得出第3区域判断正弦值sinω₁和第4区域判断正弦值sinξ₁；Step 18: On the second backup binarized image P′ _1,2 of the first group, according to the third judgment vector calculated in step 17

and the fourth judgment vector

Through formula (9) and formula (10), the judgment sine value sinω ₁ of the third region and the judgment sine value sinξ ₁ of the fourth region can be obtained;

和方向向量

平行：即sinω₁≠0,sinξ₁≈0，则C′_1,6(0.8558×10³,0.1890×10³)即为第1个平行四边形编码标志中第4编码区域的特征角点，把C′_1,6(0.8558×10³,0.1890×10³)的坐标值赋值给C_1,4(x_1,4,y_1,4)；C′_1,5(0.6927×10³,0.1889×10³)为第1个平行四边形编码标志中第1编码区域的特征角点，把C′_1,5(0.6927×10³,0.1889×10³)的坐标值赋值给C_1,1(x_1,1,y_1,1)；；In this embodiment, the parallel vector sine threshold g=0.01 is preset, and sinξ ₁ <g, then it is determined that the fourth determination vector

and the direction vector

Parallel: i.e. sinω ₁ ≠0, sinξ ₁ ≈0, then C′ _1,6 (0.8558×10 ³ , 0.1890×10 ³ ) is the characteristic corner of the fourth coding region in the first parallelogram coding mark. The coordinate value of C′ _1,6 (0.8558×10 ³ ,0.1890×10 ³ ) is assigned to C _1,4 (x _1,4 ,y _1,4 ); C′ _1,5 (0.6927×10 ³ ,0.1889× 10 ³ ) is the characteristic corner point of the first coding region in the first parallelogram coding mark, and assign the coordinate value of C′ _1,5 (0.6927×10 ³ ,0.1889×10 ³ ) to C _1,1 (x _{1 ,1} ,y _1,1 );

且由公式(11)得出：Step 19: On the second backup binarized image P′ _1,2 of the first group, point the feature corner C _1,1 (0.6927×10 ³ , 0.1889×10 ³ ) to the feature corner C _1,4 ( 0.8558×10 ³ , 0.1890×10 ³ ) vector is recorded as a vector

And from formula (11) we get:

Take integer variable i and assign i=1;

向量

和方向向量

通过公式(12)、(13)和(14)计算出第i编码组合判断向量

和编码组合判断余弦值

和

Step 20: On the second backup binarized image P′ _1,2 of the first group, orient the pattern centroid according to the code combination

vector

and the direction vector

The ith code combination judgment vector is calculated by formulas (12), (13) and (14)

Combined with encoding to determine cosine value

and

In the present embodiment, according to the above formula, the specific calculation result is:

且

则

为第1编由于码区域的编码组合定向图案质心，将

赋值给o′_z ^1,1(x′_z ^1,1,y′_z ^1,1)；because

and

but

For the 1st code, the code combination of the code region orients the pattern centroids, and sets the

Assign to o′ _z ^1,1 (x′ _z ^1,1 ,y′ _z ^1,1 );

且

则

为第2编码区域的编码组合定向图案质心，将

赋值给o′_z ^1,2(x′_z ^1,2,y′_z ^1,2)；because

and

but

To orient the pattern centroids for the coded combination of the 2nd coded region, set the

Assign to o′ _z ^1,2 (x′ _z ^1,2 ,y′ _z ^1,2 );

且

则

为第3编码区域的编码组合定向图案质心，将

赋值给o′_z ^1,3(x′_z ^1,3,y′_z ^1,3)；because

and

but

To orient the pattern centroids for the encoded combination of the 3rd encoded region, set the

Assign to o′ _z ^1,3 (x′ _z ^1,3 ,y′ _z ^1,3 );

且

则

为第4编码区域的编码组合定向图案质心，将

赋值给o′_z ^1,4(x′_z ^1,4,y′_z ^1,4)；because

and

but

To orient the pattern centroids for the coded combination of the 4th coded region, set the

Assign to o′ _z ^1,4 (x′ _z ^1,4 ,y′ _z ^1,4 );

Step 21, re-assign i=1 to the integer variable i;

Step 22. Define 4 two-dimensional floating point arrays Cr ₁ ¹ [3][2], Cr ₁ ² [3][2], Cr ₁ ³ [3][2], Cr ₁ ⁴ [3][2 ], and initialize all elements in these 4 two-dimensional arrays to -1; in addition, take 4 integer variables b ₁ ¹ , b ₁ ² , b ₁ ³ , b ₁ ⁴ , and initialize b ₁ ¹ = 0, b ₁ ² = 0, b ₁ ³ =0, b ₁ ⁴ =0;

Step 23: On the second backup binarized image P′ _1,2 of the first group, calculate the centroid pixel coordinate o _{′ 1} ^{1 (} 728,45) and the first group of the first difference vector formed by the positioning circle centroid o′ _l,1 respectively

Calculated by formula (16) and formula (17)

且

重新赋值给b₁ ²＝1，并且i＞0，直接执行步骤24.1；because

and

Reassign to b ₁ ² =1, and i>0, directly execute step 24.1;

Step 24.1, re-assign i=1 to the integer variable i;

Step 24.2, the results obtained in this example are as follows:

取整数变量

和

并赋值

(1)

take integer variable

and

and assign

取数组Cr₁ ²[3][2]中同一行元素均不为-1的元素Cr₁ ²[0][0]和Cr₁ ²[0][1]并分别赋值给o_1,1(x_1,1,y_1,1)的横坐标和纵坐标，并计算正弦值sinφ₁ ² (2)

Take the elements Cr ₁ ² [0][0] and Cr ₁ ² [0][1] in the same row of the array Cr ₁ ² [3][2] whose elements are not -1 and assign them to o _1,1 ( x _1,1 ,y _1,1 ) of the abscissa and ordinate, and calculate the sine value sinφ ₁ ²

和

并赋值

Since sinφ ₁ ² == 0, take the integer variable

and

and assign

取整数变量

和

并赋值

(3)

take integer variable

and

and assign

取整数变量

和

并赋值

(4)

take integer variable

and

and assign

Step 25, obtain the number W ₁ of the first parallelogram coding mark by formula (21):

W ₁ =V ₁ ^T ·U=8 (21)

Among them, column vector U=(2 ⁰ ,2 ¹ ,2 ² ,...2 ¹¹ ) ^T , column vector V ₁ =(0,0,0,1,0,0,0,0,0,0, 0,0) ^T .

Step 26, mark the code number of the calibration corner point belonging to the σth coding region (where σ=1, 2, 3, 4) in the first parallelogram coding mark as L ₈ ^σ , wherein the subscript 8 is the calibration corner point L The code number of the coding square to which ₈ ^σ belongs, and the value of the superscript σ represents the σ-th coding area to which the calibration corner L ₈ ^σ belongs;

In the present embodiment, the found code number is the subpixel coordinate value of 4 characteristic corner points on the parallelogram code mark of 8 and the corresponding corner point code number:

The sub-pixel coordinate value of the feature corner whose code number is L ₈ ¹ is C _1,1 (0.6927×10 ³ , 0.1889×10 ³ );

The sub-pixel coordinate value of the feature corner whose code number is L ₈ ² is C _1,2 (0.6926×10 ³ , 0.0256×10 ³ );

The sub-pixel coordinate value of the feature corner whose code number is L ₈ ³ is C _1,3 (0.8559×10 ³ , 0.0257×10 ³ );

The sub-pixel coordinate value of the feature corner whose code number is L ₈ ⁴ is C _1,4 (0.8558×10 ³ , 0.1890×10 ³ );

Step 27, judge whether ζ is less than 8, if satisfied, then ζ+1 is reassigned to ζ, and returns to step 6.1 and executes sequentially; Pixel coordinate value and corresponding code number.

Take the first group of the first backup binarized image P′ _1,1 obtained in step 6.1 and the pixel coordinate value (775,135) of the centroid of the first annular black connected domain centroid in the annular black connected domain centroid set A as input conditions, The steps of removing the complex background of the first backup binarized image P′ _1,1 of the first group by using the algorithm of removing the complex background of the coding mark, and finally obtaining the first parallelogram binarized image P ₁ ″ without complex background are as follows:

Step 6.1.1, take integer variable i and assign i=1;

Step 6.1.2. Find the white connected domain closest to the pixel coordinate value (775,135) on the first backup binarized image P' _1,1 of the first group and record it as the first backup binarized image of the first group The i-th circular white connected domain M' _i on P' _1,1 , and the pixel value of the i-th circular white connected domain M' _i is assigned as 0;

Step 6.1.3, judge whether i is less than 10, if i < 10, assign i+1 to i, and return to step 6.1.2 to execute sequentially; otherwise, the first backup binarized image P' of the first group has been The orientation circles in all parallelogram coding marks in _1,1 are set to black; and the first backup binarized image P′ _1,1 of the first group is processed in this step 6.1.3 The image obtained by the process is recorded as the first 1 black background extraction image P′ _1,b , and perform step 6.1.4;

Step 6.1.4. In all black connected domains on the first black background extraction image P' _1,b , find the black connected domain closest to the pixel coordinate value (775,135) and record it as the first black background extraction image P' The first parallelogram background black connected domain Ω ₁ on _1,b ;

Step 6.1.5. Extract all the inner and outer contours of the first parallelogram background black connected domain Ω ₁ in the first black background extraction image P′ _1,b to obtain the first parallelogram background black connected domain Ω ₁ The inner and outer contour set V ₁ of ;

Step 6.1.6. Compare the perimeters of all contours in the contour set V ₁ , and record the contour with the longest perimeter as the outer contour E ₁ of the black connected domain Ω ₁ of the first parallelogram background;

Step 6.1.7. Use the ray method on the first black background extraction image P′ _1,b to distinguish all pixels outside the outer contour E ₁ of the black connected domain Ω ₁ of the parallelogram background and all pixels within the outer contour E ₁ point, and assign the gray value of all pixels within the outer contour E ₁ to 255, and assign the gray value of all pixels outside the outer contour E ₁ to 0, and then obtain the first parallelogram binarized image without complex background. P ₁ ″; in the first parallelogram binarized image without complex background P ₁ ″, the pixel values of all the pixels inside the parallelogram coding mark including the centroid pixel coordinate value (775,135) are set to 255, including the centroid pixel The pixel values of all pixels outside the parallelogram encoding mark of the coordinate value (775, 135) are set to 0, as shown in Figure 10.

The decoding method of the parallelogram coding mark based on the graphic geometric relationship provided by the present invention needs to compile a corresponding computer program, and execute the program on the computer to realize the corresponding operation processing and logic control functions, so the present invention also provides a computer Reading a storage medium includes a computer program used in conjunction with an electronic device having an image processing function, the computer program being executable by a processor to perform the decoding method.

The above descriptions are only the embodiments of the present invention, and are not intended to limit the scope of the present invention. Any equivalent structure or equivalent process transformation made by using the contents of the description and drawings of the present invention, or directly or indirectly applied to other related technologies Fields are similarly included in the scope of patent protection of the present invention.

Claims (8)

1. A decoding method of a parallelogram coding mark based on a graph geometric relationship is characterized in that the coding mark is a square coding square, a parallelogram background pattern and a coding pattern are arranged on the surface of the coding square, the coding pattern is positioned inside the parallelogram background pattern, the coding pattern comprises a positioning pattern, an orientation pattern and a coding combination pattern, the orientation pattern and the positioning pattern are used for judging the direction of the parallelogram coding mark, the coding combination pattern is used for coding each corner point of the parallelogram coding mark, and each coding combination pattern is composed of one coding combination orientation pattern and three coding combination coding patterns, and the decoding method is characterized in that: the method for processing the digital image is used for obtaining the coding sequence number and the sub-pixel coordinates of each characteristic corner point in the image which is shot by the camera and contains N parallelogram coding marks, and further the steps for decoding the parallelogram coding marks are as follows:

step 1.1, acquiring a coding mark image by utilizing N parallelogram coding marks arranged in a camera shooting space, wherein the coding mark image comprises N parallelogram coding marks;

step 1.2, establishing a pixel coordinate system of an angular point;

step 2.1, carrying out gray level processing on the coding mark image to obtain a coding mark gray level image P ₁ ；

Step 2.2, 8 bits of gray level image P of coding mark ₁ Copying and backing up to obtain a grey level backup image P of the coding mark ₁ ′；

Step 2.3, the grey level backup image P of the coding mark ₁ ' carry on the binarization processing to get the binary image P of the coding mark ₂ ；

Step 3, setting a roundness threshold lambda 'of the black connected domain and a pixel number threshold lambda';

step 4.1, calculating a binary image P of the coding mark ₂ Circularity value λ of all black connected components in the image _n And the number of pixel points c _n Wherein the circularity value of each black connected domain is given by equation (1),

wherein l _n Perimeter, s, representing the contour of the corresponding black connected component _n Represents the area corresponding to the black connected domains, n =1,2,3,4;

step 4.2, selecting proper black connected domain roundness threshold lambda 'and pixel point number threshold lambda' to encode the mark binary image P ₂ Black connected domains of the centers of N directional circular rings corresponding to the N parallelogram coding marks are obtained and are placed into a circular ring black connected domain set A';

wherein, the coded mark binarizes the image P ₂ The circularity value of each circular ring black connected domain is smaller than the circularity threshold lambda', and the number of pixel points of each circular ring black connected domain is largeA threshold value lambda' of the number of pixels is set;

step 4.3, taking an integer variable i and assigning i =1;

step 4.4, calculating the ith ring black connected domain M in the ring black connected domain set A _i The coordinates of the centroid pixel are marked as o ″ _d,i (x″ _d,i ,y″ _d,i ) Obtaining the ith ring black connected domain M _i Centroid pixel coordinate o ″) _d,i (x″ _d,i ,y″ _d,i ) The ith element is taken as a circular black connected domain centroid set A;

step 4.5, judging whether i is smaller than N, if i is smaller than N, assigning i +1 to i, and returning to the step 4.4 to execute in sequence; otherwise, obtaining the binary image P of the coding mark ₂ The center of mass pixel coordinate o' of each ring black connected domain _d,1 (x″ _d,1 ,y″ _d,1 )、o″ _d,2 (x″ _d,2 ,y″ _d,2 )、…、o″ _d,N (x″ _d,N ,y″ _d,N ) Sequentially putting the circular black connected domain mass center sets into a circular black connected domain mass center set A;

step 5, taking an integer variable zeta and assigning zeta =1;

step 6.1, binarizing the image P with the coding mark ₂ Performing copy backup twice to respectively obtain a 1 st backup binary image P 'of the zeta group' _ζ,1 And the 2 nd backup binary image P 'of the zeta th group' _ζ,2 ；

Step 6.2, carrying out binarization on the 1 st backup binary image P 'of the zeta th group by using a complex background algorithm for removing coding marks' _ζ,1 Digital image processing is carried out to obtain the zeta th parallelogram binaryzation image P ″, without complex background _ζ,1 ；

Step 7.1, coding the mark gray level image P ₁ Copying and backing up again to obtain a zeta-th backup gray level image P' _ζ ；

Step 7.2, utilizing a corner detection algorithm to perform binarization on the zeta th parallelogram binary image P' without complex background _ζ,1 Extracting sub-pixel coordinates of 4 corner points, and marking as the zeta-th complex background-free parallelogram binaryzation image P ″ _ζ,1 Upper 4 alternative corner points C ″) _ζ,1 (x″ _ζ,1 ,y″ _ζ,1 )、C″ _ζ,2 (x″ _ζ,2 ,y″ _ζ,2 )、C″ _ζ,3 (x″ _ζ,3 ,y″ _ζ,3 )、C″ _ζ,4 (x″ _ζ,4 ,y″ _ζ,4 )；

Step 7.3, obtaining a parallelogram binaryzation image P ″' without a complex background at the zeta th _ζ,1 Black connected domain corrosion is performed in the process, so that the zeta-th parallelogram binaryzation image P' without complex background _ζ,1 White connected domain in (1) is enlarged; and recording the processed image as the zeta-th operation binary image P ″ _ζ,2 ；

Step 7.4, the zeta-th operation binaryzation image P ″ _ζ,2 Setting the value of the part with the middle gray scale value of 255 as 1, and calculating the zeta-th binary image P ″ _ζ,2 Setting the value of the part with the middle gray value of 0 as 0, and then utilizing the zeta-th operation to binarize the image P ″) _ζ,2 And the ζ th backup grayscale image P' _ζ Performing multiplication, and recording the obtained result image as the Zeta-th coverage result image T _ζ ；

Step 7.5, covering the result image T at the zeta th by utilizing a corner point detection algorithm _ζ Extracting sub-pixel coordinates of all corner points and storing the sub-pixel coordinates into a zeta-th primary corner point sub-pixel coordinate set B _ζ Performing the following steps;

step 7.6, taking an integer variable i and assigning value i =1;

step 7.7, in the zeta th primary corner point sub-pixel coordinate set B _ζ Finding the coordinate value (x ″) of the distance sub-pixel _ζ,i ,y″ _ζ,i ) Nearest corner sub-pixel coordinate is recorded as C' _ζ,i (x′ _ζ,i ,y′ _ζ,i )；

7.8, judging whether i is smaller than 4, if i is smaller than 4, assigning i +1 to i and returning to execute the step 7.7; otherwise, the ζ -th overlay result image T has been obtained at this time _ζ Contains the coordinate value (x ″) of centroid pixel _d,ζ ,y″ _d,ζ ) Of 4 characteristic corner points of the parallelogram-coded logo C' _ζ,1 (x′ _ζ,1 ,y′ _ζ,1 )、C′ _ζ,2 (x′ _ζ,2 ,y′ _ζ,2 )、C′ _ζ,3 (x′ _ζ,3 ,y′ _ζ,3 )、C′ _ζ,4 (x′ _ζ,4 ,y′ _ζ,4 ) And step 8.1 is executed;

step 8.1, backup binarization image P 'at the 2 nd of the zeta group' _ζ,2 Above, will contain the centroid pixel coordinate value (x ″) _d,ζ ,y″ _d,ζ ) The parallelogram coding mark is marked as the zeta th parallelogram coding mark;

step 8.2, backing up the binary image P 'at the 2 nd backup of the zeta group' _ζ,2 Wherein the sub-pixel coordinate values are (x' _ζ,1 ,y′ _ζ,1 )、(x′ _ζ,2 ,y′ _ζ,2 )、(x′ _ζ,3 ,y′ _ζ,3 )、(x′ _ζ,4 ,y′ _ζ,4 ) The 4 pixel points are used as the corner quadrangle S of the zeta-th parallelogram coding mark _ζ 4 vertices of (a), connecting the 4 vertices to obtain a corner quadrangle S of the zeta-th parallelogram coding mark _ζ ；

Step 9, backing up the binary image P 'at the 2 nd backup of the zeta group' _ζ,2 In the above, the pixel coordinate value (x ″) from the centroid is found _d,ζ ,y″ _d,ζ ) The nearest white connected domain, and the gray value of the white connected domain is assigned to be 0;

step 10, backing up a binary image P 'at the 2 nd backup of the zeta group' _ζ,2 Corner quadrilateral S of upper Zeta parallelogram coding sign _ζ Keeping the gray values of all internal pixel points unchanged, and making the corner quadrangle S of the zeta-th parallelogram coding mark _ζ The gray values of all other pixel points are assigned to be 255;

step 11.1, backup binarization image P 'at 2 nd of zeta group' _ζ,2 In the above, the corner quadrangle S of the ζ -th parallelogram coding mark is extracted _ζ The inner and outer contours in (1) are marked as a contour set D in the zeta-th parallelogram coding mark _ζ ；

Step 11.2, counting the outline set D in the zeta-th parallelogram coding mark _ζ The number of pixel points included in each contour is recorded as the zeta-th groupNo. 2 backup binary image P' _ζ,2 Positioning circle contour G in upper Zeth parallelogram coding mark _ζ Calculating the coordinates of the centroid pixel of the binary image and recording the coordinates as the 2 nd backup binary image P 'of the zeta group' _ζ,2 Locating circle centroid pixel coordinates o 'within the upper zeta parallelogram encoding logo' _l,ζ (x′ _l,ζ ,y′ _l,ζ )；

Step 12, collecting the outline D in the zeta-th parallelogram coding mark _ζ The 4 contours with the least number of pixel points are recorded as the contour Z of the coding combination orientation pattern _ζ,1 Coded composite directional pattern profile Z _ζ,2 Coded composite directional pattern profile Z _ζ,3 Coded combined orientation pattern profile Z _ζ,4 And respectively calculate the centroid thereof

Step 13.1, according to the outline set D in the zeta th parallelogram coding mark _ζ In the method, two contours with the largest number of pixel points and 4 contours with the smallest number of pixel points are removed, and the number of remaining contours kappa is determined _ζ Is divided into the following cases: if κ _ζ =0, then step 14.1 is executed; otherwise this κ _ζ The profiles are the profiles of the coded combined coding patterns in the zeta-th parallelogram coding mark and are respectively marked as the coded combined patterns

Coded composite pattern

823060A combined coding pattern

Step 14.1, giving an integer variable i and an initial value i =1;

step 14.2, backing up the binary image P 'at the 2 nd backup of the zeta group' _ζ,2 Calculating the code pattern

Center of mass of

This step continues after i +1 is reassigned to i until i > κ _ζ Ending; whereby a corresponding coded composite pattern can be obtained

Coded composite pattern

823060A combined coding pattern

Centroid pixel coordinates of

Step 15.1, backing up the binary image P 'at the 2 nd backup of the zeta group' _ζ,2 In the above, the sub-pixel coordinates of the characteristic corner points of the ζ -th parallelogram coding mark located in the 1 st coding region, the 2 nd coding region, the 3 rd coding region and the 4 th coding region are respectively C _ζ,1 (x _ζ,1 ,y _ζ,1 )、C _ζ,2 (x _ζ,2 ,y _ζ,2 )、C _ζ,3 (x _ζ,3 ,y _ζ,3 )、C _ζ,4 (x _ζ,4 ,y _ζ,4 ) (ii) a And backup binary image P 'at 2 nd of the zeta group' _ζ,2 The pixel coordinate value is (x ″) _d,ζ ,y″ _d,ζ ) The pixel point of (1) is recorded as a zeta-group 2 nd backup binary image P' _ζ,2 Directional ring centroid o 'of upper zeta-th parallelogram coding mark' _d,ζ (x′ _d,ζ ,y′ _d,ζ ) And seating the sub-pixelsThe standard value is (x' _ζ,1 ,y′ _ζ,1 )、(x′ _ζ,2 ,y′ _ζ,2 )、(x′ _ζ,3 ,y′ _ζ,3 )、(x′ _ζ,4 ,y′ _ζ,4 ) The 4 pixel points are respectively marked as C' _ζ,1 (x″′ _ζ,1 ,y″′ _ζ,1 )、C″′ _ζ,2 (x″′ _ζ,2 ,y″′ _ζ,2 )、C″′ _ζ,3 (x″′ _ζ,3 ,y″′ _ζ,3 )、C″′ _ζ,4 (x″′ _ζ,4 ,y″′ _ζ,4 )；

Step 15.2, backing up the binary image P 'at the 2 nd backup of the zeta group' _ζ,2 The direction vector in the above, ζ th parallelogram code flag

As is derived from the formula (2),

step 16, backing up the binary image P 'at the 2 nd backup of the zeta group' _ζ,2 On top, find 4 pixels C' _ζ,1 (x″′ _ζ,1 ,y″′ _ζ,1 )、C″′ _ζ,2 (x″′ _ζ,2 ,y″′ _ζ,2 )、C″′ _ζ,3 (x″′ _ζ,3 ,y″′ _ζ,3 )、C″′ _ζ,4 (x″′ _ζ,4 ,y″′ _ζ,4 ) Pixel coordinate o 'of middle-distance positioning circle centroid' _l,ζ (x′ _l,ζ ,y′ _l,ζ ) The nearest 2 pixels are respectively marked as C _ζ,1min (x _ζ,1min ,y _ζ,1min ) And C _ζ,2min (x _ζ,2min ,y _ζ,2min )；

Finding out the sub-pixel coordinate values of the characteristic corner points of the 2 nd coding region and the 3 rd coding region in the zeta-th parallelogram coding mark in 4 pixel points and respectively assigning the sub-pixel coordinate values to C _ζ,2 (x _ζ,2 ,y _ζ,2 ) And C _ζ,3 (x _ζ,3 ,y _ζ,3 )；

By the formula (3) And (4) calculating the 1 st judgment vector in the ζ th parallelogram coding mark

And 2 nd decision vector

And calculating the 1 st area dividing sine value sin alpha according to the formulas (5) and (6) _ζ And 2 nd area division sine value sin beta _ζ ；

Step 17, backing up the binary image P 'at the 2 nd backup of the zeta group' _ζ,2 And respectively assigning the sub-pixel coordinate values of the rest 2 pixel points to the temporary coordinate value 1 of the zeta-th parallelogram coding mark, and recording the temporary coordinate value as C' _ζ,5 (x′ _ζ,5 ,y′ _ζ,5 ) And temporary coordinate value 2, marked as C' _ζ,6 (x′ _ζ,6 ,y′ _ζ,6 )；

Determining the 3 rd judgment vector in the ζ th parallelogram coding flag according to equations (7) and (8)

And 4 th judgment vector

Step 18, backing up the binary image P 'at the 2 nd backup of the zeta group' _ζ,2 According to the 3 rd judgment vector

And 4 th judgment vector

The 3 rd region division sine value sin omega is obtained through the formula (9) and the formula (10) _ζ And 4 th area dividing sine value sin xi _ζ ；

According to sin ω _ζ And sin xi _ζ C is' _ζ,5 (x′ _ζ,5 ,y′ _ζ,5 ) Or C' _ζ,6 (x′ _ζ,6 ,y′ _ζ,6 ) Is assigned to C _ζ,4 (x _ζ,4 ,y _ζ,4 ) Or C _ζ,1 (x _ζ,1 ,y _ζ,1 )；

Step 19, backing up the binary image P 'at the 2 nd backup of the zeta group' _ζ,2 Will be composed of characteristic corner points C _ζ,1 (x _ζ,1 ,y _ζ,1 ) Directing deviceSymbolized corner point C _ζ,4 (x _ζ,4 ,y _ζ,4 ) Is recorded as a vector

And is derived from equation (11):

taking an integer variable i and assigning i =1;

step 20, backing up the binary image P 'at the 2 nd backup of the zeta group' _ζ,2 According to the coding combination, the pattern centroid is oriented

(Vector)

And direction vector

The i-th code combination decision vector is calculated by the equations (12), (13) and (14)

Coding combination judgment cosine value

And

the value taking condition of (1):

judging whether i meets the condition that i is less than 4, if i is less than 4, assigning i +1 to i, and returning to execute the step 20; otherwise, the center of mass of the coded combined orientation pattern of the 1 st coding region in the ζ th parallelogram coding mark is obtained

Coded combined orientation pattern centroid for coding region 2

Coded combined orientation pattern centroid for 3 rd coded region

And the coded combined orientation pattern centroid of the 4 th coded region

And proceeds to step 21;

step 21, assigning the integer variable i with i =1 again;

step 22, defining 4 two-dimensional floating-point type numerical groups

Initializing all elements in the 4 two-dimensional arrays, and assigning a value of-1; taking 4 integer variables

Initialization

Step 23, backup binarization image P 'at 2 nd of the zeta group' _ζ,2 In the above-mentioned manner,calculating the circular outline of the coded combined coded pattern mark in the Zeth parallelogram coded mark

Centroid pixel coordinates of

And the center o of the positioning circle' _l,ζ The ith difference vector of the formed ζ -th group

Calculated by the following equations (16) and (17)

Step 24.1, assigning the integer variable i with the value i =1 again;

step 24.2, according to

Taking integer variables

And

and assigning values;

if i is less than 4, assigning i +1 to i and returning to execute the step 24.2; otherwise, continuing to execute the step 25;

step 25, obtaining the serial number W of the zeta th parallelogram coding mark through the formula (21) _ζ ：

W _ζ ＝V _ζ ^T ·U (21)

Wherein, the column vector U = (2) ⁰ ,2 ¹ ,2 ² ,...2 ¹¹ ) ^T Column vector

Step 26, marking the code number of the characteristic corner point belonging to the sigma-th coding region in the zeta-th parallelogram coding mark as

Wherein W _ζ For calibrating angular points

The number of the coding square grid, the value of sigma represents the calibration angular point

(ii) a σ -encoding region to which σ =1,2,3,4;

thus, the coding numbers of the 4 feature corners in the ζ -th parallelogram coding mark and the corresponding sub-pixel coordinate values thereof are obtained:

coded number is

The sub-pixel coordinate value of the characteristic corner is (x) _ζ,1 ,y _ζ,1 )；

Coded number is

The sub-pixel coordinate value of the characteristic corner is (x) _ζ,2 ,y _ζ,2 )；

The code number is

The sub-pixel coordinate value of the characteristic corner is (x) _ζ,3 ,y _ζ,3 )；

Coded number is

The sub-pixel coordinate value of the characteristic corner is (x) _ζ,4 ,y _ζ,4 )；

Step 27, judging whether zeta is smaller than N, if yes, reassigning zeta +1 to zeta, and returning to step 6.1 to execute in sequence; if not, the sub-pixel coordinate values and the corresponding coding numbers of the 4 characteristic angular points on each parallelogram coding mark are found.

2. The decoding method according to claim 1, wherein: in step 6.1, obtaining a 1 st backup binary image P 'of the zeta th group' _ζ,1 And the Zeth circular ring black connected domain centroid pixel coordinate value (x ″) in the circular ring black connected domain centroid set A _d,ζ ,y″ _d,ζ ) Removing the 1 st backup binary image P 'of the zeta th group by using a complex background algorithm for removing a coding mark as an input condition' _ζ,1 And finally obtaining the zeta th parallelogram binaryzation image P' without complex background _ζ The steps are as follows:

step 6.1.1, taking an integer variable i and assigning i =1;

step 6.1.2, backup binary image P 'at the 1 st backup of the ζ th group' _ζ,1 Upper search distance pixel coordinate value (x ″) _d,ζ ,y″ _d,ζ ) The nearest white connected domain is recorded as the 1 st backup binary image P 'of the ζ th group' _ζ,1 The ith circular ring white connected domain M' _i And the ith circular ring white connected domain M' _i All the gray values are assigned to 0;

step 6.1.3, judging whether i is smaller than N, if i is smaller than N, assigning i +1 to i, and returning to the step 6.1.2 for sequential execution; if not, then,the zeta th group 1 st backup binary image P' _ζ,1 Setting the orientation circular rings in all the parallelogram coding marks to be black, and setting the 1 st backup binary image P 'of the zeta-th group' _ζ,1 The image processed in this step was recorded as the ζ -th black background extraction image P' _ζ,b And performing step 6.1.4;

step 6.1.4, extracting image P 'from the zeta-th black background' _ζ,b In all the black connected domains, find the coordinate value (x ″) of the distance pixel _d,ζ ,y″ _d,ζ ) The nearest black connected domain is denoted as the ζ -th black background extraction image P' _ζ,b The ζ th parallelogram background black connected domain Ω _ζ ；

Step 6.1.5, extracting image P 'from the ζ -th black background' _ζ,b Upper extraction of zeta-th parallelogram background black connected domain omega _ζ The zeta th parallelogram background black connected domain omega is obtained _ζ Inner and outer contour set V of _ζ ；

Step 6.1.6, compare contour set V _ζ The perimeter of the longest perimeter of all the contours in the drawing is recorded as the zeta-th parallelogram background black connected domain omega _ζ Outer contour E of _ζ ；

Step 6.1.7, extracting image P 'from the zeta-th black background' _ζ,b Upper, the outer contour E _ζ The gray value of all the pixels within is assigned to 255, and the outer contour E _ζ Except for the gray values of all the pixel points, the gray values are assigned to be 0, and therefore the zeta th parallelogram binaryzation image P' without the complex background is obtained _ζ (ii) a Leading the parallelogram to be a binary image P ″' without complex background at the zeta th _ζ In (1), the pixel coordinate value (x ″) of the centroid is included _d,ζ ,y″ _d,ζ ) The gray value of all pixel points in the parallelogram coding mark is set to be 255, and the gray value contains the coordinate value (x ″) of the centroid pixel _d,ζ ,y″ _d,ζ ) The gray values of all the pixel points outside the parallelogram coding mark are set to be 0.

3. The decoding method according to claim 1, wherein: in step 16, execution is performed in two cases:

(1) Sin alpha _ζ ＜0,sinβ _ζ If greater than 0, then C _ζ,1min (x _ζ,1min ,y _ζ,1min ) For the characteristic corner point of the 3 rd coding region in the ζ th parallelogram coding mark, C _ζ,1min (x _ζ,1min ,y _ζ,1min ) Is assigned to C _ζ,3 (x _ζ,3 ,y _ζ,3 )；C _ζ,2min (x _ζ,2min ,y _ζ,2min ) For the characteristic corner of the 2 nd coding region in the ζ th parallelogram coding index, C _ζ,2min (x _ζ,2min ,y _ζ,2min ) Is assigned to C _ζ,2 (x _ζ,2 ,y _ζ,2 )；

(2) If sin alpha _ζ ＞0,sinβ _ζ If < 0, then C _ζ,2min (x _ζ,2min ,y _ζ,2min ) For the characteristic corner of the 3 rd coding region in the ζ -th parallelogram coding index, C _ζ,2min (x _ζ,2min ,y _ζ,2min ) Is assigned to C _ζ,3 (x _ζ,3 ,y _ζ,3 )；C _ζ,1min (x _ζ,1min ,y _ζ,1min ) For the characteristic corner of the 2 nd coding region in the ζ th parallelogram coding index, C _ζ,1min (x _ζ,1min ,y _ζ,1min ) Is assigned to C _ζ,2 (x _ζ,2 ,y _ζ,2 )。

4. The decoding method according to claim 1, wherein: in step 18, it is performed in two cases:

(1) Sin omega _ζ ＝＝0,sinξ _ζ Not equal to 0, then C' _ζ,5 (x′ _ζ,5 ,y′ _ζ,5 ) Namely C 'is the characteristic corner point of the 4 th coding area in the ζ th parallelogram coding mark' _ζ,5 (x′ _ζ,5 ,y′ _ζ,5 ) Is assigned to C _ζ,4 (x _ζ,4 ,y _ζ,4 )；C′ _ζ,6 (x′ _ζ,6 ,y′ _ζ,6 ) For the characteristic corner of the 1 st coding region in the ζ -th parallelogram coding indexC's' _ζ,6 (x′ _ζ,6 ,y′ _ζ,6 ) Is assigned to C _ζ,1 (x _ζ,1 ,y _ζ,1 )；

(2) Sin ω _ζ ≠0,sinξ _ζ =0, then C' _ζ,6 (x′ _ζ,6 ,y′ _ζ,6 ) Namely C 'is the characteristic corner point of the 4 th coding area in the ζ th parallelogram coding mark' _ζ,6 (x′ _ζ,6 ,y′ _ζ,6 ) Is assigned to C _ζ,4 (x _ζ,4 ,y _ζ,4 )；C′ _ζ,5 (x′ _ζ,5 ,y′ _ζ,5 ) C 'is a characteristic corner point of a 1 st coding region in a zeta th parallelogram coding mark' _ζ,5 (x′ _ζ,5 ,y′ _ζ,5 ) Is assigned to C _ζ,1 (x _ζ,1 ,y _ζ,1 )。

5. The decoding method according to claim 1, wherein: in step 20, the execution is divided into four cases:

(1) If it is

And is

Then

To orient the pattern centroids for the encoded combination of the 3 rd encoded region

Assign to

(2) If it is

And is

Then

To orient the pattern centroids for the coded combinations of the 2 nd coded region, will

Is assigned to

(3) If it is

And is

Then

To orient the pattern centroids for the encoded combination of the 1 st encoded region

Is assigned to

(4) If it is

And is provided with

Then the

To orient the pattern centroids for the encoded combination of the 4 th encoded region

Is assigned to

6. The decoding method according to claim 1, wherein: in step 23, the execution is divided into four cases:

(1) If it is

And is

Then make it give

Will be provided with

Is assigned to

If i > k _ζ 1, executing step 24, otherwise, assigning i +1 to i, and returning to execute step 23;

(2) If it is

And is provided with

Then order

Will be provided with

Is assigned to

If i > k _ζ 1, executing step 24, otherwise, assigning i +1 to i, and returning to execute step 23;

(3) If it is

And is

Then make it give

Will be provided with

Is assigned to

If i > k _ζ 1, executing step 24, otherwise, assigning i +1 to i, and returning to execute step 23;

(4) If it is

And is

Then order

Will be provided with

Is assigned to

If i > k _ζ 1, then step 24 is executed, otherwise i +1 is assigned to i, and the step 23 is returned to.

7. The decoding method according to claim 1, wherein: in step 24.2, execution is divided into the following cases:

(1) If it is

Then take the integer variable

And

and assign values

(2) If it is

Will array

Elements in the same row which are not-1 are respectively marked as

And

and respectively assigned to _ζ,1 (x _ζ,1 ,y _ζ,1 ) And the abscissa and the ordinate of the computer, and calculating the sine value

And (4) judging:

1) If it is

Then get the integer variable

And

and assign values

2) If it is

Then take the integer variable

And

and assign values

3) If it is

Then take the integer variable

And

and assign values

(3) If it is

Will array

Elements in the same row which are not-1 are respectively marked as

And

and

and respectively assigned to _ζ,1 (x _ζ,1 ,y _ζ,1 ) Abscissa and ordinate of and o _ζ,2 (x _ζ,2 ,y _ζ,2 ) The abscissa and the ordinate of the computer, while calculating the sine value

And

and judging:

(1) If it is

Or

Then take the integer variable

And

and assign values

(2) If it is

Or

Then take the integer variable

And

and assign values

(3) If it is

Or

Then take the integer variable

And

and assign values

(4) If it is

Then take the integer variable

And

and assign values

8. A computer-readable storage medium comprising a computer program for use in conjunction with an electronic device having image processing functionality, the computer program being executable by a processor to perform the decoding method of claim 1.

Images