CN103310215A - Detecting and identifying method for annular coding mark point - Google Patents

Abstract

The invention belongs to the field of close-range photogrammetry and relates to a detecting and identifying method for an annular coding mark point. The method includes that first, canny edge detection is conducted on a collected image, an outline centroid is closed through a series of limiting conditions and calculation, and noise and non-coding mark points are filtered; then least square ellipse fitting is adopted, coding mark point location is conducted, an ellipse fitting error is combined to judge a partition coding mark point outline, and the outline is filled; finally, ALPC transformation for transforming a local concentric ellipse into parallel straight lines is provided, the ALPC transformation is conducted on the partitioned coding mark point, and transformed image characteristics are used for decoding. By means of the detecting and identifying method, location of the coding mark point can reach a sub pixel level, local shape characteristics of a concentric ellipse are transformed into shape characteristics of parallel straight lines which are easy to detect and calculate, coding mark point identifying speed is improved, and effects of an included angle of a camera optical axis and a coding mark point normal on the coding mark point identifying accuracy can be reduced.

Description

A kind of detection of ring-type coded markings point and recognition methods

Technical field

The present invention relates to detection and the recognition methods of ring-type coded markings point, more particularly, the present invention relates to a kind of ring-type coded markings point for the large full-scale splicing of workpiece and detect and recognition methods.

Background technology

In the machine dimensional visual measurement, for the image that large visual field, multi-angle gather, the accuracy of images match is to improve the important step of three-dimensional data splicing accuracy.In the process of images match, require the image corresponding point are carried out accurate detection and Identification.Yet for high-resolution large view field image, the corresponding point that identify two width of cloth images are very difficult, this just need to be by a kind of gauge point with unique encoded radio, be attached to artificially on the testee key feature points and take pictures, by detection and Identification coded markings point 2 width of cloth Characteristic of Image points are identified.

It is simple that ring-type coded markings point has a Design and manufacture, the advantage that is easy to identify, and have good translation rotation, convergent-divergent independence.Therefore ring-type coded markings point is used comparatively extensive in close-range photogrammetry.The detection and Identification of coded markings point are one of difficult points of close-range photogrammetry, the at present both at home and abroad research of this respect mainly contains (1) Forbes K and used the coded markings point to carry out timing signal in 2002 to have proposed the arc fragmenting method, it is inhomogeneous that the method is easy to cause cutting apart, thereby affect final decoded result.(2) people such as Thomas Doring is applied in 12 coded markings points of Forbes K in the scanner calibration, adopt the coding collar split plot design to increase the number of samples of sampling, but will increase calculation cost simultaneously, and the method affected by photo angle larger; (3) people such as beam Shanxi, Liu Jianxin and Hu Hao of Xi'an Communications University are applied to ring-type coded markings point in the camera calibration, and its coding/decoding method is higher to shooting angle and the environmental requirement of coded markings point.(4) people such as Wang Man and Ye Zhenglin uses morphological operator to identify, but that this method is affected by photo angle is larger, and relatively poor for the image recognition effect of background complexity.

Therefore seek that a kind of affected by photo angle less, and be applicable to the recognition methods of this shape facility of concentration ellipse of ring-type coded markings point, seeming in the detection of ring-type coded markings point and recognition methods are studied is even more important.The present invention is on the basis of oval least square fitting, affined transformation and log-polar transform combined propose a kind of conversion ALPC conversion, this conversion is applicable to this local shape feature of concentration ellipse is converted into this shape of easily identifying of parallel lines in two dimensional image, has improved recognition rate and precision.

Summary of the invention

The invention provides a kind of detection and recognition methods of ring-type coded markings point, location for coded markings point can reach the sub-pix rank, and can reduce camera optical axis and coded markings point normal angle to the impact of coded markings point recognition accuracy, fully satisfy the bearing accuracy of coded markings point in the close-range photogrammetry and the requirement of recognition accuracy.

The detection of described ring-type coded markings point and the hardware system of recognition system comprise:

Be used for pasting the large-scale workpiece of coded markings point;

Bad shape coded markings point for detection of identification is some;

Be used for to gather one of the colour of image or B/W camera;

Be used for the computing machine that precision control, image acquisition and data are processed.

Detection and the recognition methods of the ring-type coded markings point that the present invention is designed, concrete operation step is as follows:

Step 1: the ring-type coded markings point that will have the different coding value sticks on the testee, uses video camera to take testee, gathers image, with the image transmitting that gathers in computing machine;

Step 2: adopt the Canny operator that the image that gathers is carried out edge extracting, edge extracts girth l, the area s that the profile that obtains calculates profile, suitable contour area and girth threshold value are set, the profile of threshold condition is not satisfied in deletion, calculate its center-of-mass coordinate for the profile that satisfies threshold condition, the profile that contains N pixel, its barycenter (cx, cy) is:

$\mathrm{cx}=\frac{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_1}{N},\mathrm{cy}=\frac{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{y}_1}{N}---\left(1\right)$

(x _i, y _i) be the coordinate of i pixel on the profile, as the centroid distance δ＜δ of any two profiles ₀The time, filter out simultaneously this two profiles, so just the non-coding gauge point can be removed, thereby tentatively reach the purpose that coded target is separated;

Step 3: described ring-type coded markings point is in actual measurement, because the angle problem of taking, the inner marker circle overwhelming majority is imaged as ellipse, in order to obtain the round central coordinate of circle of described inner marker and described external encode ring to be decoded, need to carry out the least square ellipse match to described ellipse

For the ellipse of optional position, its equation is designated as:

f(x，y)＝x ²+Axy+By ²+Cx+Dy+E＝0 (2)

Suppose that the number of putting on the profile is N (N 〉=6), carries out least square ellipse match, then objective function for these points

$F(A,B,C,D,E)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{f}^2(x_i,y_i)---\left(3\right)$

By extremum principle, so that F is minimum, then must have

, can calculate parameter A, B, C, D, E by this formula, then the complete elliptic equation of match can be determined;

The centre coordinate of supposing described ellipse is (x _c, y _c), the major and minor axis radius is respectively a, b, and the angle of major axis and x axle i.e. the bias angle theta of ellipse, obtains five oval basic parameters by the A that calculates, B, C, D, E

$x_c=\frac{\mathrm{AD}-2\mathrm{BC}}{4B-A^2}---\left(4\right)$

$y_c=\frac{\mathrm{AC}-2D}{4B-A^2}---\left(5\right)$

$\mathrm{\θ}=\arctan \sqrt{\frac{{\mathrm{Bb}}^2-a^2}{b^2-{\mathrm{Ba}}^2}}---\left(6\right)$

$a=\sqrt{\frac{2({\mathrm{BC}}^2+D^2-\mathrm{ACD}-4\mathrm{BE}+A^{2}E)}{(4B-A^2)(B+1-\sqrt{A^2+{(B-1)}^2})}}---\left(7\right)$

$b=\sqrt{\frac{2({\mathrm{BC}}^2+D^2-\mathrm{ACD}-4\mathrm{BE}+A^{2}E)}{(4B-A^2)(B+1+\sqrt{A^2+{(B-1)}^2})}}---\left(8\right)$

Geometric distance represents certain point to the distance of curve closest approach, and namely normal distance is seen formula (15),

${d^{\left(i\right)}}_{\min }=\sqrt{{(x_i-x)}^2+{(y_i-y)}^2}---\left(9\right)$

The present invention uses a little to the standard of oval geometric distance as this error of fitting of evaluation, travel through all point and ask for the error of fitting of each point, if greater than certain threshold value, it is considered as non-matching point, when the ratio of non-matching some number and the total number of point reaches threshold alpha %, think that then the ellipse fitting of this profile is undesirable, carry out next profile ellipse fitting, when reaching the ellipse fitting requirement, then this profile is described inner marker circle, centered by this oval center, is partitioned into a rectangular, all profile informations that will comprise this ring-type coded markings point in this rectangle, and fill closed outline;

Step 4: the present invention is combined affined transformation with log-polar transform, for original image (x, y), if transform center is (x ₀, x ₀), obtain image (x ', y ') after the conversion through the ALPC conversion, then transformation relation is suc as formula shown in (10) (11),

$x\′=M\log \left(\sqrt{\begin{array}{c}{((x-x_0)\cos \mathrm{\θ}+(y-y_0)\sin \mathrm{\θ})}^2+\\ \frac{a^2}{b^2}{((-x+x_0)\sin \mathrm{\θ}+(y-y_0)\cos \mathrm{\θ})}^2\end{array}}\right)---\left(10\right)$

$y\′=\arctan \left(\frac{\frac{a}{b}((-x+x_0)\sin \mathrm{\θ}+(y-y_0)\cos \mathrm{\θ})}{(x-x_0)\cos \mathrm{\θ}+(y-y_0)\sin \mathrm{\θ}}\right)---\left(11\right)$

For original image can be shown well along transform center characteristics of image radially, amplify in the image transverse features after conversion, wherein M is a scaling, described transform center is the elliptical center of match gained in the step 3, a/b is the axial ratio of concentration ellipse, and θ is the drift angle of concentration ellipse;

Step 5: with the ALPC conversion process in the ring-type coded markings point process step 4 that is partitioned in the step 3, its result presents is on the image after the black and white bulk fitly is arranged in conversion, we are called code pattern, encoding block in this code pattern order correspondence from top to bottom the order of coding collar arranged clockwise, in code pattern, detect coding endless belt region, by vertical direction straight line in the scanning area, obtain the number of each section monochrome pixels, suppose to have the M piece, every section number of pixels that contains leaves array P[M in] in, the corresponding array Flag[M that contains the encoding block monochrome informatio with it simultaneously], Flag[i wherein]=0, represent that the i section is black, Flag[i]=1 expression i section is white, P[i] be the number of i section pixel, because be encoded to loop coding, so if Flag[M-1]=Flag[0], then number of pixels is end to end merged, P[0]=P[M-1]+P[0], the array P[M after the adjustment] and, the code value of i section is by n _iIndividual 0 or 1 forms, as Flag[i]=then form Flag[i by 11 the time]=then formed by 0 in 0 o'clock,

Wherein height is vertical number of pixels of image after the conversion, finally calculate every 0 and 1 number, order forms a L bit, according to cryptoprinciple, cyclic ordering obtains the binary number of L L position, and the decimal system minimum value that calculates correspondence in this L binary number i.e. the encoded radio of ring-type coded markings point for this reason;

Step 6: get back to the ellipse fitting that carries out next profile in the step 3, until next profile is empty.

The invention has the beneficial effects as follows: the present invention can reach the sub-pix rank for the location of coded markings point, this local shape feature of concentration ellipse is converted into the shape facility of this easy detection of parallel lines and calculating, improve the speed of coded markings point identification, and can reduce camera optical axis and coded markings point normal angle to the impact of coded markings point recognition accuracy.

Description of drawings

Fig. 1: system diagram of the present invention;

Fig. 2: concentration ellipse ALPC conversion and ring-type coded markings point ALPC transformation results;

Fig. 3: ring-type coded markings point decoding schematic diagram;

Fig. 4: ring-type coded markings point detects and the recognition methods process flow diagram.

Embodiment

System diagram of the present invention as shown in Figure 1, the invention provides a kind of detection and recognition methods of ring-type coded markings point, location for coded markings point can reach the sub-pix rank, and can reduce camera optical axis and coded markings point normal angle to the impact of coded markings point recognition accuracy, fully satisfy the bearing accuracy of coded markings point in the close-range photogrammetry and the requirement of recognition accuracy.

The detection of described ring-type coded markings point and the hardware system of recognition system comprise:

Be used for pasting the large-scale workpiece of coded markings point;

Ring-type coded markings point for detection of identification is some;

Be used for to gather one of the colour of image or B/W camera;

Be used for the computing machine that precision control, image acquisition and data are processed.

Detection and the recognition methods of the ring-type coded markings point that the present invention is designed, concrete operation step is as follows:

Step 1: the ring-type coded markings point that will have the different coding value sticks on the testee, uses video camera to take testee, gathers image, with the image transmitting that gathers in computing machine;

Step 2: adopt the Canny operator that the image that gathers is carried out edge extracting, edge extracts girth l, the area s that the profile that obtains calculates profile, suitable contour area and girth threshold value are set, the profile of threshold condition is not satisfied in deletion, calculate its center-of-mass coordinate for the profile that satisfies threshold condition, the profile that contains N pixel, its barycenter (cx, cy) is:

$\mathrm{cx}=\frac{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_i}{N},\mathrm{cy}=\frac{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{y}_i}{N}---\left(1\right)$

(x _i, y _i) be the coordinate of i pixel on the profile, as the centroid distance δ＜δ of any two profiles ₀The time, filter out simultaneously this two profiles, so just the non-coding gauge point can be removed, thereby tentatively reach the purpose that coded target is separated;

Step 3: described ring-type coded markings point is in actual measurement, because the angle problem of taking, the inner marker circle overwhelming majority is imaged as ellipse, in order to obtain the round central coordinate of circle of described inner marker and described external encode ring to be decoded, need to carry out the least square ellipse match to described ellipse

For the ellipse of optional position, its equation is designated as:

f(x，y)＝x ²+Axy+By ²+Cx+Dy+E＝0 (2)

Suppose that the number of putting on the profile is N (N 〉=6), carries out least square ellipse match, then objective function for these points

$F(A,B,C,D,E)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{f}^2(x_i,y_i)---\left(3\right)$

By extremum principle, so that F is minimum, then must have

, can calculate parameter A, B, C, D, E by this formula, then the complete elliptic equation of match can be determined;

The centre coordinate of supposing described ellipse is (x _c, y _c), the major and minor axis radius is respectively a, b, and the angle of major axis and x axle i.e. the bias angle theta of ellipse, obtains five oval basic parameters by the A that calculates, B, C, D, E

$x_c=\frac{\mathrm{AD}-2\mathrm{BC}}{4B-A^2}---\left(4\right)$

$y_c=\frac{\mathrm{AC}-2D}{4B-A^2}---\left(5\right)$

$\mathrm{\θ}=\arctan \sqrt{\frac{{\mathrm{Bb}}^2-a^2}{b^2-{\mathrm{Ba}}^2}}---\left(6\right)$

$a=\sqrt{\frac{2({\mathrm{BC}}^2+D^2-\mathrm{ACD}-4\mathrm{BE}+A^{2}E)}{(4B-A^2)(B+1-\sqrt{A^2+{(B-1)}^2})}}---\left(7\right)$

$b=\sqrt{\frac{2({\mathrm{BC}}^2+D^2-\mathrm{ACD}-4\mathrm{BE}+A^{2}E)}{(4B-A^2)(B+1+\sqrt{A^2+{(B-1)}^2})}}---\left(8\right)$

Geometric distance represents certain point to the distance of curve closest approach, and namely normal distance is seen formula (15),

${d^{\left(i\right)}}_{\min }=\sqrt{{(x_i-x)}^2+{(y_i-y)}^2}---\left(9\right)$

The present invention uses a little to the standard of oval geometric distance as this error of fitting of evaluation, travel through all point and ask for the error of fitting of each point, if greater than certain threshold value, it is considered as non-matching point, when the ratio of non-matching some number and the total number of point reaches threshold alpha %, think that then the ellipse fitting of this profile is undesirable, carry out next profile ellipse fitting, when reaching the ellipse fitting requirement, then this profile is described inner marker circle, centered by this oval center, is partitioned into a rectangular, all profile informations that will comprise this ring-type coded markings point in this rectangle, and fill closed outline;

Step 4: the present invention is combined affined transformation with log-polar transform, for original image (x, y), if transform center is (x ₀, y ₀), obtain image (x ', y ') after the conversion through the ALPC conversion, then transformation relation is suc as formula shown in (10) (11),

$x\′=M\log \left(\sqrt{\begin{array}{c}{((x-x_0)\cos \mathrm{\θ}+(y-y_0)\sin \mathrm{\θ})}^2+\\ \frac{a^2}{b^2}{((-x+x_0)\sin \mathrm{\θ}+(y-y_0)\cos \mathrm{\θ})}^2\end{array}}\right)---\left(10\right)$

$y\′=\arctan \left(\frac{\frac{a}{b}((-x+x_0)\sin \mathrm{\θ}+(y-y_0)\cos \mathrm{\θ})}{(x-x_0)\cos \mathrm{\θ}+(y-y_0)\sin \mathrm{\θ}}\right)---\left(11\right)$

For original image can be shown well along transform center characteristics of image radially, amplify in the image transverse features after conversion, wherein M is a scaling, described transform center is the elliptical center of match gained in the step 3, a/b is the axial ratio of concentration ellipse, θ is the drift angle of concentration ellipse, and concentration ellipse ALPC conversion and ring-type coded markings point ALPC transformation results are as shown in Figure 2;

Step 5: with the ALPC conversion process in the ring-type coded markings point process step 4 that is partitioned in the step 3, its result presents is on the image after the black and white bulk fitly is arranged in conversion, we are called code pattern, encoding block in this code pattern order correspondence from top to bottom the order of coding collar arranged clockwise, in code pattern, detect coding endless belt region, by vertical direction straight line in the scanning area, obtain the number of each section monochrome pixels, suppose to have the M piece, every section number of pixels that contains leaves array P[M in] in, the corresponding array Flag[M that contains the encoding block monochrome informatio with it simultaneously], Flag[i wherein]=0, represent that the i section is black, Flag[i]=1 expression i section is white, P[i] be the number of i section pixel, because be encoded to loop coding, so if Flag[M-1]=Flag[0], then number of pixels is end to end merged, P[0]=P[M-1]+P[0], the array P[M after the adjustment] and, the code value of i section is by n _iIndividual 0 or 1 forms, as Flag[i]=then form Flag[i by 11 the time]=then formed by 0 in 0 o'clock,

Wherein height is vertical picture number of image after the conversion, finally calculate every 0 and 1 number, order forms a L bit, according to cryptoprinciple, cyclic ordering obtains the binary number of L L position, calculate in this L binary number the i.e. encoded radio of ring-type coded markings point for this reason of corresponding decimal system minimum value, the decoding schematic diagram of ring-type coded markings point as shown in Figure 3;

Step 6: get back to the ellipse fitting that carries out next profile in the step 3, until next profile is empty.

The detection of the ring-type coded markings point that the present invention is designed and recognition methods process flow diagram are as shown in Figure 4.

The detection of the present invention and existing ring-type coded markings point and the difference of the maximum of recognition methods are: it is larger that existing ring-type coded markings point detection and recognition methods are affected by measurement environment, shooting angle.The present invention can reach the sub-pix rank for the location of coded markings point, this local shape feature of concentration ellipse is converted into the shape facility of this easy detection of parallel lines and calculating, improve the speed of coded markings point identification, and can reduce camera optical axis and coded markings point normal angle to the impact of coded markings point recognition accuracy.

In sum, ring-type coded markings point detection of the present invention with the advantage of recognition methods is:

1) this local shape feature of concentration ellipse is converted into the shape facility of this easy detection of parallel lines and calculating, has improved the speed of coded markings point identification.

2) compare the impact of camera subject shooting angle with existing method less, improved the accuracy rate of coded markings point identification.

Below schematically the present invention and embodiment thereof are described, this description does not have limitation, and shown in the accompanying drawing also is one of embodiments of the present invention.So; if those of ordinary skill in the art is enlightened by it; in the situation that do not break away from the invention aim; adopt the same base part of other form or each component layouts mode of other form; without the creationary technical scheme similar to this technical scheme and the embodiment of designing, all should belong to protection scope of the present invention.

Claims (1)

1. the detection of a ring-type coded markings point and recognition methods, the feature of described ring-type coded markings point is to be made of inner marker circle and external encode ring, the central coordinate of circle of described inner marker circle is the place, position of described ring-type coded markings point, described external encode ring is one and all is divided into L with the concentric annulus of described inner marker circle (described L can be 10,12,15,18 etc.) individual encoding block, each described encoding block can be white (described white code value is 1), also can be black (described black code value is 0), encode clockwise as start bit with any one described encoding block, can access the binary number of L L position, corresponding decimal system minimum value namely is the encoded radio that described external encode ring has in this L the described binary number, the detection of described ring-type coded markings point and recognition methods, it is characterized in that, comprise the following steps:

Step 1: the ring-type coded markings point that will have the different coding value sticks on the testee, uses video camera to take testee, gathers image, with the image transmitting that gathers in computing machine;

Step 2: adopt the Canny operator that the image that gathers is carried out edge extracting, edge extracts girth l, the area s that the profile that obtains calculates profile, suitable contour area and girth threshold value are set, the profile of threshold condition is not satisfied in deletion, calculate its center-of-mass coordinate for the profile that satisfies threshold condition, the profile that contains N pixel, its barycenter (cx, cy) is:

$\mathrm{cx}=\frac{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_i}{N},\mathrm{cy}=\frac{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{y}_i}{N}---\left(1\right)$

(x _i, y _i) be the coordinate of i pixel on the profile, as the centroid distance δ＜δ of any two profiles ₀The time, δ ₀Can get 1, filter out simultaneously this two profiles, so just the non-coding gauge point can be removed, thereby tentatively reach the purpose that coded target is separated;

Step 3: described ring-type coded markings point is in actual measurement, because the angle problem of taking, the inner marker circle overwhelming majority is imaged as ellipse, in order to obtain the round central coordinate of circle of described inner marker and described external encode ring to be decoded, need to carry out the least square ellipse match to described ellipse

For the ellipse of optional position, its equation is designated as:

f(x，y)＝x ²+Axy+By ²+Cx+Dy+E＝0 (2)

Suppose that the number of putting on the profile is N (N 〉=6), carries out least square ellipse match, then objective function for these points

$F(A,B,C,D,E)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{f}^2(x_i,y_i)---\left(3\right)$

By extremum principle, so that F is minimum, then must have , can calculate parameter A, B, C, D, E by this formula, then the complete elliptic equation of match can be determined;

The centre coordinate of supposing described ellipse is (x _c, y _c), the major and minor axis radius is respectively a, b, and the angle of major axis and x axle i.e. the bias angle theta of ellipse, obtains five oval basic parameters by the A that calculates, B, C, D, E

$x_c=\frac{\mathrm{AD}-2\mathrm{BC}}{4B-A^2}---\left(4\right)$

$y_c=\frac{\mathrm{AC}-2D}{4B-A^2}---\left(5\right)$

$\mathrm{\θ}=\arctan \sqrt{\frac{{\mathrm{Bb}}^2-a^2}{b^2-{\mathrm{Ba}}^2}}---\left(6\right)$

$a=\sqrt{\frac{2({\mathrm{BC}}^2+D^2-\mathrm{ACD}-4\mathrm{BE}+A^{2}E)}{(4B-A^2)(B+1-\sqrt{A^2+{(B-1)}^2})}}---\left(7\right)$

$b=\sqrt{\frac{2({\mathrm{BC}}^2+D^2-\mathrm{ACD}-4\mathrm{BE}+A^{2}E)}{(4B-A^2)(B+1+\sqrt{A^2+{(B-1)}^2})}}---\left(8\right)$

Geometric distance represents certain point to the distance of curve closest approach, and namely normal distance is seen formula (15),

${d^{\left(i\right)}}_{\min }=\sqrt{{(x_i-x)}^2+{(y_i-y)}^2}---\left(9\right)$

The present invention uses a little to the standard of oval geometric distance as this error of fitting of evaluation, travel through all point and ask for the error of fitting of each point, if greater than certain threshold value, it is considered as non-matching point, when the ratio of non-matching some number and the total number of point reaches threshold alpha %, think that then the ellipse fitting of this profile is undesirable, carry out next profile ellipse fitting, when reaching the ellipse fitting requirement, then this profile is described inner marker circle, centered by this oval center, is partitioned into a rectangular, all profile informations that will comprise this ring-type coded markings point in this rectangle, and fill closed outline;

Step 4: the present invention is combined affined transformation with log-polar transform, for original image (x, y), if transform center is (x ₀, y ₀), obtain image (x ', y ') after the conversion through the ALPC conversion, then transformation relation is suc as formula shown in (10) (11),

$x\′=M\log \left(\sqrt{\begin{array}{c}{((x-x_0)\cos \mathrm{\θ}+(y-y_0)\sin \mathrm{\θ})}^2+\\ \frac{a^2}{b^2}{((-x+x_0)\sin \mathrm{\θ}+(y-y_0)\cos \mathrm{\θ})}^2\end{array}}\right)---\left(10\right)$

$y\′=\arctan \left(\frac{\frac{a}{b}((-x+x_0)\sin \mathrm{\θ}+(y-y_0)\cos \mathrm{\θ})}{(x-x_0)\cos \mathrm{\θ}+(y-y_0)\sin \mathrm{\θ}}\right)---\left(11\right)$

For original image can be shown well along transform center characteristics of image radially, amplify in the image transverse features after conversion, wherein M is a scaling, described transform center is the elliptical center of match gained in the step 3, a/b is the axial ratio of concentration ellipse, and θ is the drift angle of concentration ellipse;

Step 5: with the ALPC conversion process in the ring-type coded markings point process step 4 that is partitioned in the step 3, its result presents is on the image after the black and white bulk fitly is arranged in conversion, we are called code pattern, encoding block in this code pattern order correspondence from top to bottom the order of coding collar arranged clockwise, in code pattern, detect coding endless belt region, by vertical direction straight line in the scanning area, obtain the number of each section monochrome pixels, suppose to have the M piece, every section number of pixels that contains leaves array P[M in] in, the corresponding array Flag[M that contains the encoding block monochrome informatio with it simultaneously], Flag[i wherein]=0, represent that the i section is black, Flag[i]=1 expression i section is white, P[i] be the number of i section pixel, because be encoded to loop coding, so if Flag[M-1]=Flag[0], then number of pixels is end to end merged, P[0]=P[M-1]+P[0], the array P[M after the adjustment] and, the code value of i section is by n _iIndividual 0 or 1 forms, as Flag[i]=then form Flag[i by 11 the time]=then formed by 0 in 0 o'clock,

Wherein height is vertical number of pixels of image after the conversion, finally calculate every 0 and 1 number, order forms a L bit, according to cryptoprinciple, cyclic ordering obtains the binary number of L L position, and the decimal system minimum value that calculates correspondence in this L binary number i.e. the encoded radio of ring-type coded markings point for this reason;

Step 6: get back to the ellipse fitting that carries out next profile in the step 3, until next profile is empty.

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