CN107423772A - A kind of new binocular image feature matching method based on RANSAC - Google Patents

A kind of new binocular image feature matching method based on RANSAC Download PDF

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CN107423772A
CN107423772A CN201710668389.0A CN201710668389A CN107423772A CN 107423772 A CN107423772 A CN 107423772A CN 201710668389 A CN201710668389 A CN 201710668389A CN 107423772 A CN107423772 A CN 107423772A
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王辉
郭山红
谢仁宏
芮义斌
李鹏
周文忠
蔡璐
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Nanjing University of Science and Technology
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    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
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    • G06F18/22Matching criteria, e.g. proximity measures
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    • G06V10/40Extraction of image or video features
    • G06V10/46Descriptors for shape, contour or point-related descriptors, e.g. scale invariant feature transform [SIFT] or bags of words [BoW]; Salient regional features
    • G06V10/462Salient features, e.g. scale invariant feature transforms [SIFT]
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00Indexing scheme for image analysis or image enhancement
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Abstract

The invention discloses a kind of binocular image feature matching method based on RANSAC, this method, to carrying out selection matching by the binocular feature of SIFT operator extractions, can efficiently be improved the accuracy of matching, greatly reduce erroneous matching using stochastical sampling uniformity.Specifically comprise the steps of:First, image calibration, using Zhang Zhengyou chessboard calibration methods, the nominal data of two cameras of binocular image is obtained;Secondly, image distortion correction, binocular image is read, image distortion correction is carried out using nominal data;Then, feature detection and extraction, are detected using SIFT operators and extract the feature of two images;Finally, RANSAC images match, match point is selected using RANSAC methods.This method principle is simple, and accuracy is high, and erroneous matching can be significantly reduced in SIFT images match, strengthens matching effect.

Description

A kind of new binocular image feature matching method based on RANSAC
Technical field
The invention belongs to a kind of image matching technology, particularly a kind of binocular image characteristic matching side based on RANSAC Method.
Background technology
In recent years, computer vision was in Mobile Robotics Navigation, remote sensing survey, medical imaging, industrial detection, recognition of face It is widely used Deng numerous areas, shows good development prospect.Stereoscopic vision is one of important branch of computer vision, its Major function is to recover real three-dimensional scene information from two dimensional image.
Currently, many mobile robots are exactly to use binocular stereo vision airmanship, and U.S.'s jet-propulsion in addition is tested The unmanned Autonomous Vehicles of DEMOIII of room (JPL) development, " Jade Hare number " lunar rover of Chinese goddess in the moon team independent research, Microsoft The complete autonomous football location instrument and have been put into that the wide Baseline Stereo vision guided navigation instrument of development, Harbin Institute of Technology develop Human body three-dimensional size non-contact measuring instrument of production and application etc. has all applied to technique of binocular stereoscopic vision.Moreover, instantly Binocular stereo vision is exactly combined the newest frontier science and technology such as bionical, digital hologram to people by popular VR virtual technologies the most Bring 360 ° of scene experience effects true to nature, be it is a kind of change our life styles disruptive technology, even more to such as medical science, Many key areas such as military aerospace, industrial simulation, education, amusement bring subversive reform tide.Although people in recent years Stereoscopic vision research is achieved noticeable achievement, but research level is still not mature enough, and application effect can't reach full level of intelligence, grind Study carefully technology there is also it is many problem of and bottleneck.In fact, accurately identify and understand that environmental information is very tired for computer Difficulty, to construct the stronger stereo visual system of practicality also much needs the place of Improvement.Wherein camera calibration Technology and Stereo Matching Technology are the mostly important research modules of stereoscopic vision research field.The accuracy of calibration result is three The basic guarantee of Information recovering is tieed up, robustness, accuracy and the density of Stereo matching are the foundations of three-dimensional reconstruction.However, mesh Before there is no practicality, robustness and accuracy to be attained by demarcation and the Stereo matching universal method of perfect effect.
The content of the invention
Technical problem solved by the invention is to provide a kind of new binocular image characteristic matching side based on RANSAC Method.
The technical solution for realizing the object of the invention is:A kind of new binocular image characteristic matching side based on RANSAC Method, comprise the following steps:
Step 1:Binocular image gathers;
Step 2:Binocular image is effectively demarcated using Zhang Zhengyou image calibrations method.23 of shooting different angle are Know the black and white chessboard trrellis diagram piece of accurate dimension, choose clearly 20 pictures therefrom, utilize the side of Corner Detection Method finds the characteristic point in each image, then calculates each five inner parameters of camera and all external parameters respectively, Followed by least square method primary Calculation coefficient of radial distortion, finally by minimization, optimize all parameters;Obtain Parameter represented with following matrix;Transition matrix is:
It is outer ginseng matrix be:
Step 3:The binocular image of input is subjected to distortion correction respectively using image calibration data obtained by step 2 kind, so Two images binocular is corrected afterwards, reads in nominal data in binocular image, and step 2 first, then each image is carried out abnormal Become and correct and preserve correction chart picture, the two images for eliminating distortion are finally subjected to binocular correction according to epipolar-line constraint.
Step 4:Using SIFT operator extraction detection image characteristic points, and characteristic point is extracted, first to every width figure As carrying out being utilized respectively SIFT operators detection characteristic point, and key point is saved as, the key point for then detecting to obtain is calculated 128 dimensional feature vectors;
Step 5:Binocular ranging, the point of debug matching is reduced using RANSAC methods, two images is carried out just to match, Matching pair is obtained, and affine transformation matrix is generated to calculating by matching, then by assigned error scope, obtains correctly matching pair Set, judges whether cycle-index is more than threshold value, if being not more than, recalculates affine matrix, if being more than, take all numbers In obtain correctly matching to most one group, the equation that the affine matrix finally obtained using least square solution is formed, finally The high characteristic matching of the degree of accuracy is obtained to group.
Compared with prior art, its remarkable advantage is the present invention:1) method of the invention is detected and extracted using SIFT methods The feature of binocular image, there is preferable robustness;2) present invention by RANSAC methods to match to further being screened, Substantially increase the degree of accuracy of matching.
The present invention is described in further detail below in conjunction with the accompanying drawings.
Brief description of the drawings
Fig. 1 is the inventive method flow chart.
Fig. 2 is inventive algorithm flow chart.
Fig. 3 is the left and right cameras image after three-dimensional correction, wherein figure (a) is the left view after correction, figure (b) is Right view after correction.
Fig. 4 is result figure of the embodiment of the present invention, wherein figure (a) is left image, figure (b) is right image.
Embodiment
With reference to accompanying drawing, a kind of binocular image feature matching method based on RANSAC of the invention, comprise the following steps:
Step 1, using binocular camera image is acquired;
Step 2, using Zhang Zhengyou image calibrations method the binocular image that step 1 collects is demarcated, obtain binocular Image inner parameter and external parameter;Specially:
Step 2-1, the black and white chessboard trrellis diagram piece of M known accurate dimensions of different angle is shot, therefrom Choose clearly N pictures;Wherein, M>N>15;
Step 2-2, the characteristic point in each image is found using the method for Corner Detection;
Step 2-3, each five inner parameters of camera are calculated respectively, and result of calculation is:
Wherein αx、αyFor camera focal length, μ0、ν0For main point coordinates, γ is reference axis tilt parameters;
External parameter is:
Spin matrixTranslation matrix
Step 2-4, the radial distortion parameter of picture is corresponded to using each camera of least square method calculating;
Step 2-5, every width picture is corrected using distortion parameter, is then recalculated and taken the photograph using the image after correction The inner parameter and external parameter of camera.
Step 3, binocular image is read, image is corrected using calibrating parameters;Specially:
Step 3-1, binocular image, binocular image inner parameter and external parameter are read in;
Step 3-2, distortion correction is carried out to binocular image using binocular image inner parameter and external parameter and preserves school Positive image, its updating formula are:
Wherein, k1And k2For coefficient of radial distortion, (u0, v0) be main point coordinates, (u, v) andFor preferable and reality In the case of pixel coordinate, (x, y) andFor preferable and actual image coordinate;
Step 3-3, the two images for eliminating distortion are subjected to binocular correction according to epipolar-line constraint, finally obtain correction chart Picture, its updating formula are:
Wherein, R1And R2For the synthesis spin matrix of binocular image, R1' and R'2For corresponding two integral-rotation matrixes;
RrectIt is as obtained from being converted translation matrix T for transformation matrix, conversion is as follows,
Wherein 3=e1×e2
Step 4, using SIFT operators detect binocular image in characteristic point, characteristic point is extracted;Specially:
Step 4-1, each image is carried out being utilized respectively SIFT operators detection characteristic point, and saves as key point;
Step 4-2,128 dimensional feature vectors are calculated by the key point for detecting to obtain in step 4-1.
Step 5, binocular image is matched, the characteristic point of erroneous matching is removed using RANSAC methods, generate design sketch, Complete the binocular image characteristic matching based on RANSAC.Specially:
Step 5-1, two images are carried out just matching, it, which is matched, is combined into collection:
P={ (xi,yi),(xi',yi'), i=1,2, N, wherein N is the number of initial matching pair, is chosen initial To m, n and o, its set expression is for any three groups of matchings in P set:
S1={ ((xm,ym);(x'm,y'm)),((xn,yn);(x'n,y'n)),((xo,yo);(x'o,y'o))}
3 groups of matchings are substituted into following affine equation of change to coordinate data:
If X=(h11,h12,h21,h22,tx,ty)T, above formula can be written as:AX=b, then obtain affine transformation matrix;
Step 5-2, assigned error scope T, the P of condition subset is met, i.e., correctly matched to set:
Step 5-3, judge whether cycle-index is more than threshold value H, if being not more than, jump procedure 5-1, if being more than, jump Go to step 5-4;
Step 5-4, take element number in K secondary subsets is most to be designated as
Step 5-5, set is utilizedAX=b is solved equation, its least square solution is:X=[ATA]-1ATb;It is final to obtain just The high matching point set X of true rate, completes matching.
On the one hand the method for the present invention have selected method of the good SIFT methods of stability as extraction feature and detection feature, With good robustness;On the other hand, matching is substantially increased to matching to further being screened by RANSAC methods The degree of accuracy.
It is described in more detail below.
With reference to Fig. 2, detailed process of the invention is as follows:
Step 1:Binocular image gathers;
Step 2:Binocular image is effectively demarcated using Zhang Zhengyou image calibrations method.23 of shooting different angle are Know the black and white chessboard trrellis diagram piece of accurate dimension, choose clearly 20 pictures therefrom, utilize the side of Corner Detection Method finds the characteristic point in each image, then calculates each five inner parameters of camera and all external parameters respectively, Followed by least square method primary Calculation coefficient of radial distortion, finally by minimization, optimize all parameters;Obtain Parameter represented with following matrix;Transition matrix is:
It is outer ginseng matrix be:
Step 3:Distortion correction is carried out to the binocular image of input respectively using gained image calibration data in step 2, so Two images binocular is corrected afterwards.
Nominal data in binocular image, and step 2 is read in first, and distortion correction then is carried out using following formula to each image And correction chart picture is preserved,
The two images for eliminating distortion carry out binocular correction according to epipolar-line constraint, and its updating formula is:
Wherein, R1And R2For the synthesis spin matrix of binocular image, R1' and R'2For corresponding two integral-rotation matrixes.
RrectIt is as obtained from being converted translation matrix T for transformation matrix, conversion is as follows,
Whereine3=e1×e2
Image after the final correction obtained as shown in implementation illustration 3.
Step 4:Using SIFT operator extraction detection image characteristic points, and characteristic point is extracted, first to every width figure As carrying out being utilized respectively SIFT operators detection characteristic point, and key point is saved as, the key point for then detecting to obtain is calculated 128 dimensional feature vectors;
Step 5:Binocular ranging, the point of debug matching is reduced using RANSAC methods, two images are carried out just first Matching, it is matched is combined into collection:
P={ (xi,yi),(xi',yi'), i=1,2, N,
Wherein N is the number of initial matching pair, chooses any three groups of matchings in initial p set to its collection table of m, n and o It is shown as:
S1={ ((xm,ym);(x'm,y'm)),((xn,yn);(x'n,y'n)),((xo,yo);(x'o,y'o))}
3 groups of matchings are substituted into following affine equation of change to coordinate data:
If X=(h11,h12,h21,h22,tx,ty)T, above formula can be written as:AX=b, then obtain affine transformation matrix.
By assigned error scope T (taking 4), it is met the P of condition subset (correctly matching is to set):
Then, judge whether cycle-index is more than threshold value (choosing 30), if being not more than, return starts, if being more than, after It is continuous;Take the conduct that element number is most in K secondary subsets
Finally, set is utilizedAX=b is solved equation, its least square solution is:X=[ATA]-1ATb;It is final to obtain accuracy High matching point set.
Verified through embodiment, RANSAC binocular images feature matching method of the invention not only has good robustness also There is very high accuracy.

Claims (5)

1. a kind of binocular image feature matching method based on RANSAC, it is characterised in that comprise the following steps:
Step 1, using binocular camera image is acquired;
Step 2, using Zhang Zhengyou image calibrations method the binocular image that step 1 collects is demarcated, obtain binocular image Inner parameter and external parameter;
Step 3, binocular image is read, image is corrected using calibrating parameters;
Step 4, using SIFT operators detect binocular image in characteristic point, characteristic point is extracted;
Step 5, binocular image is matched, the characteristic point of erroneous matching is removed using RANSAC methods, generate design sketch, completed Binocular image characteristic matching based on RANSAC.
2. the binocular image feature matching method according to claim 1 based on RANSAC, schemed in step 2 using Zhang Zhengyou As scaling method is demarcated to binocular image, binocular image inner parameter and external parameter are obtained, is specially:
Step 2-1, the black and white chessboard trrellis diagram piece of M known accurate dimensions of different angle is shot, is chosen therefrom Clearly N pictures;Wherein, M>N>15;
Step 2-2, the characteristic point in each image is found using the method for Corner Detection;
Step 2-3, each five inner parameters of camera are calculated respectively, and result of calculation is:
<mrow> <mi>A</mi> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>&amp;alpha;</mi> <mi>x</mi> </msub> </mtd> <mtd> <mi>&amp;gamma;</mi> </mtd> <mtd> <msub> <mi>&amp;mu;</mi> <mn>0</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <msub> <mi>&amp;alpha;</mi> <mi>y</mi> </msub> </mtd> <mtd> <msub> <mi>v</mi> <mn>0</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> </mrow>
Wherein αx、αyFor camera focal length, μ0、ν0For main point coordinates, γ is reference axis tilt parameters;
External parameter is:
Spin matrixTranslation matrix
Step 2-4, the radial distortion parameter of picture is corresponded to using each camera of least square method calculating;
Step 2-5, every width picture is corrected using distortion parameter, then recalculates video camera using the image after correction Inner parameter and external parameter.
3. the binocular image feature matching method according to claim 1 based on RANSAC, step 3 reads binocular image, Image is corrected using calibrating parameters, is specially:
Step 3-1, binocular image, binocular image inner parameter and external parameter are read in;
Step 3-2, distortion correction is carried out to binocular image using binocular image inner parameter and external parameter and preserves correction chart Picture, its updating formula are:
<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mover> <mi>u</mi> <mo>&amp;OverBar;</mo> </mover> <mo>=</mo> <mi>u</mi> <mo>+</mo> <mo>(</mo> <mi>u</mi> <mo>-</mo> <msub> <mi>u</mi> <mn>0</mn> </msub> <mo>)</mo> <mo>&amp;lsqb;</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>(</mo> <msup> <mi>x</mi> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>y</mi> <mn>2</mn> </msup> <mo>)</mo> <mo>+</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <msup> <mrow> <mo>(</mo> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>y</mi> <mn>2</mn> </msup> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>&amp;rsqb;</mo> </mtd> </mtr> <mtr> <mtd> <mover> <mi>v</mi> <mo>&amp;OverBar;</mo> </mover> <mo>=</mo> <mi>v</mi> <mo>+</mo> <mo>(</mo> <mi>v</mi> <mo>-</mo> <msub> <mi>v</mi> <mn>0</mn> </msub> <mo>)</mo> <mo>&amp;lsqb;</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>(</mo> <msup> <mi>x</mi> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>y</mi> <mn>2</mn> </msup> <mo>)</mo> <mo>+</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <msup> <mrow> <mo>(</mo> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>y</mi> <mn>2</mn> </msup> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>&amp;rsqb;</mo> </mtd> </mtr> </mtable> </mfenced>
Wherein, k1And k2For coefficient of radial distortion, (u0, v0) be main point coordinates, (u, v) andFor preferable and actual conditions Under pixel coordinate, (x, y) andFor preferable and actual image coordinate;
Step 3-3, the two images for eliminating distortion are subjected to binocular correction according to epipolar-line constraint, it is final to obtain correction chart picture, its Updating formula is:
<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>R</mi> <mn>1</mn> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <msub> <mi>R</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>c</mi> <mi>t</mi> </mrow> </msub> <mo>&amp;times;</mo> <msub> <mi>R</mi> <mn>1</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>R</mi> <mn>2</mn> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <msub> <mi>R</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>c</mi> <mi>t</mi> </mrow> </msub> <mo>&amp;times;</mo> <msub> <mi>R</mi> <mn>2</mn> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced>
Wherein, R1And R2For the synthesis spin matrix of binocular image, R '1And R'2For corresponding two integral-rotation matrixes;
RrectIt is as obtained from being converted translation matrix T for transformation matrix, conversion is as follows,
Whereine3=e1×e2
4. the binocular image feature matching method based on RANSAC according to claim 1, step 4 utilizes SIFT operator extractions Detection image characteristic point, and characteristic point is extracted, it is specially:
Step 4-1, each image is carried out being utilized respectively SIFT operators detection characteristic point, and saves as key point;
Step 4-2,128 dimensional feature vectors are calculated by the key point for detecting to obtain in step 4-1.
5. the binocular image feature matching method according to claim 1 based on RANSAC, step 5 is carried out to binocular image Matching, the characteristic point of erroneous matching is removed using RANSAC methods, be specially:
Step 5-1, two images are carried out just matching, it, which is matched, is combined into collection:
P={ (xi,yi),(x′i,y′i), i=1,2 ..., N, wherein N are the number of initial matching pair, are chosen in initial p set To m, n and o, its set expression is for any three groups of matchings:
S1={ ((xm,ym);(x'm,y'm)),((xn,yn);(x'n,y'n)),((xo,yo);(x'o,y'o))}
3 groups of matchings are substituted into following affine equation of change to coordinate data:
<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>x</mi> <mi>m</mi> </msub> </mtd> <mtd> <msub> <mi>y</mi> <mi>m</mi> </msub> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <msub> <mi>x</mi> <mi>m</mi> </msub> </mtd> <mtd> <msub> <mi>y</mi> <mi>m</mi> </msub> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mi>n</mi> </msub> </mtd> <mtd> <msub> <mi>y</mi> <mi>n</mi> </msub> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <msub> <mi>x</mi> <mi>n</mi> </msub> </mtd> <mtd> <msub> <mi>y</mi> <mi>n</mi> </msub> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mi>o</mi> </msub> </mtd> <mtd> <msub> <mi>y</mi> <mi>o</mi> </msub> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <msub> <mi>x</mi> <mi>o</mi> </msub> </mtd> <mtd> <msub> <mi>y</mi> <mi>o</mi> </msub> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>h</mi> <mn>11</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>h</mi> <mn>12</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>h</mi> <mn>21</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>h</mi> <mn>22</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>t</mi> <mi>x</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>t</mi> <mi>y</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msubsup> <mi>x</mi> <mi>m</mi> <mo>&amp;prime;</mo> </msubsup> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>y</mi> <mi>m</mi> <mo>&amp;prime;</mo> </msubsup> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>x</mi> <mi>n</mi> <mo>&amp;prime;</mo> </msubsup> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>y</mi> <mi>n</mi> <mo>&amp;prime;</mo> </msubsup> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>x</mi> <mi>o</mi> <mo>&amp;prime;</mo> </msubsup> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>y</mi> <mi>o</mi> <mo>&amp;prime;</mo> </msubsup> </mtd> </mtr> </mtable> </mfenced> </mrow>
If X=(h11,h12,h21,h22,tx,ty)T, above formula can be written as:AX=b, then obtain affine transformation matrix;
Step 5-2, assigned error scope T, the P of condition subset is met, i.e., correctly matched to set:
<mrow> <msubsup> <mi>S</mi> <mn>1</mn> <mo>*</mo> </msubsup> <mo>=</mo> <mo>{</mo> <mrow> <mo>(</mo> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> </mrow> <mo>)</mo> <mo>;</mo> <mo>(</mo> <mrow> <msubsup> <mi>x</mi> <mi>i</mi> <mo>&amp;prime;</mo> </msubsup> <mo>,</mo> <msubsup> <mi>y</mi> <mi>i</mi> <mo>&amp;prime;</mo> </msubsup> </mrow> <mo>)</mo> <mo>)</mo> </mrow> <mo>,</mo> <mo>|</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msubsup> <mi>x</mi> <mi>i</mi> <mo>&amp;prime;</mo> </msubsup> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>y</mi> <mi>i</mi> <mo>&amp;prime;</mo> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>h</mi> <mn>11</mn> </msub> </mtd> <mtd> <msub> <mi>h</mi> <mn>12</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>h</mi> <mn>21</mn> </msub> </mtd> <mtd> <msub> <mi>h</mi> <mn>22</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>x</mi> <mi>i</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>y</mi> <mi>i</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>t</mi> <mi>x</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>t</mi> <mi>y</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>|</mo> <mo>&lt;</mo> <mi>T</mi> <mo>}</mo> </mrow>
Step 5-3, judge whether cycle-index is more than threshold value H, if being not more than, jump procedure 5-1, if being more than, redirect step Rapid 5-4;
Step 5-4, take element number in K secondary subsets is most to be designated as
Step 5-5, set is utilizedAX=b is solved equation, its least square solution is:X=[AT A]-1ATb;It is final to obtain accuracy High matching point set X, complete matching.
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