CN102842118A - New robust stereopair correcting method - Google Patents
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- CN102842118A CN102842118A CN201210245305XA CN201210245305A CN102842118A CN 102842118 A CN102842118 A CN 102842118A CN 201210245305X A CN201210245305X A CN 201210245305XA CN 201210245305 A CN201210245305 A CN 201210245305A CN 102842118 A CN102842118 A CN 102842118A
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Abstract
The invention relates to a robust stereopair correcting method which is based on epipolar line matching, and belongs to the field of computer vision. The method is a stereopair correcting algorithm without camera calibration, and only needs to calculate information of matching points between a fundamental matrix and an image pair. The method comprises the following steps of: firstly, mapping an epipolar point e' of a right image to a point at infinity by a selected projection matrix H', wherein an epipolar line on the image is mapped to be a straight line parallel to an X axis; based on a principle that corresponding polar lines of a corrected stereopair are same, deducing a correction matrix H applied to a left image; and finally, resampling the corresponding images according to the obtained projection matrix H' and H, thereby achieving the ultimate correction purpose. The algorithm disclosed by the invention is simple to implement and high in correcting speed, and effectively eliminates vertical errors.
Description
Technical field
The present invention relates to computer vision field, be specifically related to the image correcting technology.
Background technology
Three-dimensional coupling is important and active problem in the computer vision research.Along with solid coupling applied more and more, the efficient that how to improve coupling also becomes a problem of needing solution badly.Image is corrected effective ways that improve matching speed just.The image rectification is called two again and looks rectification; It is meant that stereoscopic image is to implementing a secondary flat projective transformation respectively; Make and corresponding in two images polar curve all is parallel to x axle (perhaps y axle); That is to say that the parallax between image only occurs in x (y) direction, y (x) direction does not have parallax, becomes more convenient thereby make along polar curve search corresponding point.
Image is corrected and can under the situation of camera calibration and no camera calibration, be carried out.Fusiello has an X-rayed matrixes in video camera matrix separately through using two, thereby calculates a pair of rectification projection matrix under the situation of camera calibration.This method has obviously increased the workload and the error of correcting, and the method for therefore not having camera calibration has bigger adaptability.The scaling method of no camera is to be based upon on a series of corresponding point coordinates, and the image that just requires to correct has the common scene of part.Can obtain the corresponding point set of image pair point of interest through image characteristic point extraction and matching technique.In the image correction algorithm of setting up according to corresponding point set; It is polar initial point that people such as Pollefeys propose with antipodal points; Utilize coordinate transform to reach the purpose that image is corrected; This method is positioned at image at antipodal points can obtain better effects when inner, but when the antipodal points schematic diagram as the time precision assurance that just can not get; Francesco etc. have proposed the image antidote of a kind of dependence and corresponding point set information; It need not to calculate fundamental matrix; Use nonlinear optimization to calculate in trimming process and obtain the correlation parameter of correcting matrix; But also existing initial value to choose the shortage confidence level, adopt the very big problem of optimizing process calculated amount of pyramid structure, is a kind of unsettled method; Yu propose to use the RANSAC algorithm correct to image in to avoid because noise matees the mistake that causes with the point of interest mistake, though obtained effect preferably, adopt LM iteration and EP algorithm also to make efficient not high.
Summary of the invention
The present invention is big in order to solve in the image correcting process calculated amount, and operation time is long, and the situation that vertical error is bigger has proposed a kind of based on the stereogram robust antidote to the polar curve coupling.
The present invention at first need computed image to the information of match point; Seek a projection matrix H ' then the antipodal points e ' of right figure is mapped to infinity point, on the right figure of this moment polar curve is mapped as the straight line that is parallel to the x axle; Then the analysis image ultimate principle of correcting is derived the projection matrix H that is applied on the left figure, make on this image to polar curve is matched each other on polar curve and the right figure; Last according to projection matrix H that obtains and the corresponding image of H ' resampling, reach final rectification purpose.
Of the present invention based on as follows to the stereogram robust antidote step of polar curve coupling:
1) extracts matching algorithm through point of interest, confirm the 7 pairs of match points < img TranNum=" 54 " file=" 407833DEST_PATH_IMAGE001.GIF " he=" 21 " img-content=" drawing " img-format=" jpg " inline=" no " orientation=" portrait " wi=" 46 "/> between two width of cloth images at least;
2) use obtains match point to the calculating fundamental matrix, and obtains the antipodal points e and the e' of two width of cloth images;
3) seek a projection matrix H' e' is mapped to infinity point (1,0,0)
T
4) correct the condition < img TranNum=" 59 " file=" 793815DEST_PATH_IMAGE002.GIF " he=" 21 " img-content=" drawing " img-format=" jpg " inline=" no " orientation=" portrait " wi=" 88 "/> that satisfy the back according to image, derive another projection matrix H that is complementary with projection matrix H';
5) use resample the respectively image of correspondence of projection matrix H and H' to obtain correcting image.
Description of drawings
Fig. 1 is the FB(flow block) of the inventive method;
Fig. 2 be stereogram of the present invention to utmost point geometric graph;
Fig. 3 is a correcting process synoptic diagram of the present invention;
Fig. 4 is the output figure as a result of step 1 of the present invention;
Fig. 5 is to polar figure before the rectification of the present invention;
Fig. 6 is that rectification of the present invention back is to polar figure.
Embodiment
In conjunction with Fig. 1 this embodiment is described, its concrete steps are following:
1, extracts matching algorithm through point of interest and confirm 7 pairs of match points between two width of cloth images at least 
The match point of confirming two width of cloth images has a lot of methods, and the SURF algorithm is exactly wherein relatively more popular one.The SURF algorithm can be regarded the acceleration version of famous algorithm SIFT as, and it can handle the extraction and the coupling of two width of cloth image points of interest under suitable condition basically in real time, and it has benefited from integral image calculating and Hessian determinant simplification and approximate in the basis fast.
< b TranNum=" 75 ">2, use and to obtain match point calculating fundamental matrix and obtaining the antipodal points e and the e' of two width of cloth images.</b>
1) fundamental matrix calculates.Fundamental matrix F is the Algebraic Expression to the utmost point how much, and its basic properties is exactly to satisfy following formula:
Wherein x ' and x are exactly the homogeneous coordinates of any a pair of corresponding point in two width of cloth images.Obtain match point just can obtain interior point and use interior putting to try to achieve fundamental matrix through 8 algorithms of normalization afterwards based on formula (1) use RANSAC algorithm.
2) antipodal points calculates.Make that e and e ' are the antipodal points of two video cameras, F is the right fundamental matrix of video camera, then has:
Be that e' is the left zero vector of F, e is the right zero vector of F.Svd decomposition through F just can be in the hope of antipodal points.
3, seek a projection matrix H' e' is mapped to infinity point (1,0,0) T Here construct a projective transformation H ', it can resolve into four processes:
1) translation transformation H
t: with the point
X 0 =(x
0, y
0, 1) and move to initial point;
2) rotational transform H
r: with the initial point is the axle center, rotation antipodal points e' a bit (u, 0,1) to the x axle
T
Make < img TranNum=" 102 " file=" 341471DEST_PATH_IMAGE006.GIF " he=" 30 " img-content=" drawing " img-format=" jpg " inline=" no " orientation=" portrait " wi=" 116 "/>; < img TranNum=" 103 " file=" 540371DEST_PATH_IMAGE007.GIF " he=" 26 " img-content=" drawing " img-format=" jpg " inline=" no " orientation=" portrait " wi=" 110 "/>, then
（4）
3) perspective transform H
p: mapping point (u, 0,1)
TTo infinity point (u, 0,0)
T
4) contrary translation transformation H
-t: will
x 0 Move to original position.
Therefore, projective transformation H is exactly the combination < img TranNum=" 120 " file=" 414994DEST_PATH_IMAGE011.GIF " he=" 26 " img-content=" drawing " img-format=" jpg " inline=" no " orientation=" portrait " wi=" 123 "/> of above four conversion.
4, correct the condition that satisfy the back according to image
, derive another projection matrix H that is complementary with projection matrix H'.
For two width of cloth image P
0And P
0', remember that respectively H and H' are the projective transformation that applies, the image P after the feasible sampling
1And P
1' be rectification effect, then at correcting image P
1And P
1' in to polar curve l
1And l
1' be complementary, be expressed as l
1=l
1', it is right that transfer pair H and the H' that satisfies this condition is called the conversion coupling.More specifically say, if l
0And l
0' be P
0And P
0' in any a pair of correspondence to polar curve, then have:
Make that l and l' are corresponding to polar curve, and k is any straight line of antipodal points e only, k ' is any straight line of antipodal points e ' only, and then the relation between l and l' is
Antipodal points in the summary point 5 and projection matrix are respectively e' and H', just seek the conversion H with the H' coupling now.Can obtain by formula (7) and formula (8):
Because all to polar curve to all satisfying formula (7), therefore to H and all l
0' all satisfy formula (9), thus release:
Wherein first to release number be because H and H' are all invertible matrix; Releasing for second number is establishment because of < img TranNum=" 153 " file=" 801293DEST_PATH_IMAGE016.GIF " he=" 26 " img-content=" drawing " img-format=" jpg " inline=" no " orientation=" portrait " wi=" 81 "/>.Because H is a homogeneous matrix, multiply by any non-zero proportions factor projective transformation is changed again, it is significant only to be the ratio of matrix element, so formula (10) can turn to:
（11）
We can obtain through top derivation, when H satisfies formula (11), have formula (7) to set up, and just two width of cloth images through H and H' resampling match each other to polar curve.Preceding two width of cloth image P of note sampling
0And P
0' in corresponding point be respectively
X 0 With
X 0 ', back image P then samples
1And P
1' in corresponding point
X 1 With
X 1 'Satisfy:
（12）
Corresponding point
X 1 With
X 1 'Only, just have only horizontal parallax, need this moment a constraint to make parallax minimize in the axial gap of x.The projection matrix that note formula (11) obtains is H
0, matrix H
xRepresent as follows:
Minimization problem just can become asks shape such as H
xMake H=H
0H
xSatisfy formula with H'
（14）
Minimize and find the solution.This is a simple linear least-squares parameter minimization problem, can try to achieve x easily
1, x
2And x
3Value.
< b TranNum=" 200 ">5, use projection matrix H and the H' corresponding image that resamples respectively to obtain correcting image.</b>For preceding two width of cloth image P of sampling<sub TranNum=" 201 ">0</sub>And P<sub TranNum=" 202 ">0</sub>' in corresponding point be respectively<b TranNum=" 203 ">X</b><sub TranNum=" 204 "><b TranNum=" 205 ">0</b></sub>With<b TranNum=" 206 ">X</b><sub TranNum=" 207 "><b TranNum=" 208 ">0</b></sub><b TranNum=" 209 ">'</b>, back correcting image P then samples<sub TranNum=" 210 ">1</sub>And P<sub TranNum=" 211 ">1</sub>' in corresponding point<b TranNum=" 212 ">X</b><sub TranNum=" 213 "><b TranNum=" 214 ">1</b></sub>With<b TranNum=" 215 ">X</b><sub TranNum=" 216 "><b TranNum=" 217 ">1</b></sub><b TranNum=" 218 ">'</b>, then correcting image point pixel satisfies with original picture point pixel relationship:
（15）
Claims (7)
1. based on stereogram robust antidote to polar curve coupling, at first need computed image to the information of match point; Seek a projection matrix H ' then the antipodal points e ' of right figure is mapped to infinity point, on the right figure of this moment polar curve is mapped as the straight line that is parallel to the x axle; Then the analysis image ultimate principle of correcting is derived the projection matrix H that is applied on the left figure, make on this image to polar curve is matched each other on polar curve and the right figure; Last according to projection matrix H that obtains and the corresponding image of H ' resampling, reach final rectification purpose.
2. according to claim 1 based on stereogram robust antidote to the polar curve coupling, it is characterized in that may further comprise the steps:
1) extracts matching algorithm through point of interest, confirm the 7 pairs of match points < img TranNum=" 227 " file=" 201210245305X100001DEST_PATH_IMAGE001.GIF " he=" 21 " id=" ifm0001 " img-content=" drawing " img-format=" jpg " inline=" no " orientation=" portrait " wi=" 46 "/> between two width of cloth images at least;
2) use obtains match point to the calculating fundamental matrix, and obtains the antipodal points e and the e' of two width of cloth images;
3) seek a projection matrix H' e' is mapped to infinity point (1,0,0)
T
4) correct the condition < img TranNum=" 232 " file=" 201210245305X100001DEST_PATH_IMAGE002.GIF " he=" 21 " id=" ifm0002 " img-content=" drawing " img-format=" jpg " inline=" no " orientation=" portrait " wi=" 88 "/> that satisfy the back according to image, derive another projection matrix H that is complementary with projection matrix H';
5) use resample the respectively image of correspondence of projection matrix H and H' to obtain correcting image.
3. according to claim 2 based on stereogram robust antidote to the polar curve coupling, it is characterized in that described through 7 pairs of match points < img TranNum=" 236 " file=" 430556DEST_PATH_IMAGE001.GIF " he=" 21 " id=" ifm0003 " img-content=" drawing " img-format=" jpg " inline=" no " orientation=" portrait " wi=" 46 "/> step between definite at least two width of cloth images of point of interest extraction matching algorithm.
The match point of confirming two width of cloth images has a lot of methods, and the SURF algorithm is exactly wherein relatively more popular one; The SURF algorithm can be regarded the acceleration version of famous algorithm SIFT as, and it can handle the extraction and the coupling of two width of cloth image points of interest under suitable condition basically in real time, and it has benefited from integral image calculating and Hessian determinant simplification and approximate in the basis fast.
4. according to claim 2 based on stereogram robust antidote to polar curve coupling, it is characterized in that described use obtains match point to calculating fundamental matrix and obtaining the antipodal points e and the e' step of two width of cloth images.
1) fundamental matrix calculates
Fundamental matrix F is the Algebraic Expression to the utmost point how much, and its basic properties is exactly to satisfy following formula:
Wherein x ' and x are exactly the homogeneous coordinates of any a pair of corresponding point in two width of cloth images. and obtain match point and just can obtain interior point and use interior putting to try to achieve fundamental matrix afterwards according to formula (1) use RANSAC algorithm through 8 algorithms of normalization.
2) antipodal points calculates
Make that e and e ' are the antipodal points of two video cameras, F is the right fundamental matrix of video camera, then has:
Be that e' is the left zero vector of F, e is the right zero vector of F. the svd decomposition through F just can be in the hope of antipodal points.
5. according to claim 2 based on stereogram robust antidote to the polar curve coupling, it is characterized in that projection matrix H' of described searching is mapped to infinity point (1,0,0) with e'
TStep.
Here construct a projective transformation H ', it can resolve into four processes:
1) translation transformation H
t: will put X
0=(x
0, y
0, 1) and move to initial point;
2) rotational transform H
r: with the initial point is the axle center, rotation antipodal points e' a bit (u, 0,1) to the x axle
T
Make < img TranNum=" 266 " file=" DEST_PATH_IMAGE006.GIF " he=" 30 " id=" ifm0007 " img-content=" drawing " img-format=" jpg " inline=" no " orientation=" portrait " wi=" 116 "/>; < img TranNum=" 267 " file=" DEST_PATH_IMAGE007.GIF " he=" 26 " id=" ifm0008 " img-content=" drawing " img-format=" jpg " inline=" no " orientation=" portrait " wi=" 110 "/>, then
3) perspective transform H
p: mapping point (u, 0,1)
TTo infinity point (u, 0,0)
T
4) contrary translation transformation H
-t: with x
0Move to original position
Therefore, projective transformation H is exactly the combination < img TranNum=" 282 " file=" DEST_PATH_IMAGE011.GIF " he=" 26 " id=" ifm0012 " img-content=" drawing " img-format=" jpg " inline=" no " orientation=" portrait " wi=" 123 "/> of above four conversion.
6. according to claim 2 based on stereogram robust antidote to the polar curve coupling; It is characterized in that the described condition < img TranNum=" 285 " file=" 151780DEST_PATH_IMAGE002.GIF " he=" 21 " id=" ifm0013 " img-content=" drawing " img-format=" jpg " inline=" no " orientation=" portrait " wi=" 88 "/> that satisfies according to image rectification back, derive another projection matrix H step that is complementary with projection matrix H'.
For two width of cloth image P
0And P
0', remember that respectively H and H' are the projective transformation that applies, the image P after the feasible sampling
1And P
1' be rectification effect, then at correcting image P
1And P
1' in to polar curve l
1And l
1' be complementary, be expressed as l
1=l
1', it is right that transfer pair H and the H' that satisfies this condition is called the conversion coupling, more specifically says, if l
0And l
0' be P
0And P
0' in any a pair of correspondence to polar curve, then have:
Make that l and l' are corresponding to polar curve, and k is any straight line of antipodal points e only, k ' is any straight line of antipodal points e ' only, and then the relation between l and l' is
Antipodal points in the summary point 5 and projection matrix are respectively e' and H', just seek the conversion H that matees with H' now,
Can obtain by formula (7) and formula (8):
（9）
Because all to polar curve to all satisfying formula (7), therefore to H and all l
0' all satisfy formula (9), thus release:
Wherein first to release number be because H and H' are all invertible matrix; Releasing for second number is establishment because of < img TranNum=" 315 " file=" DEST_PATH_IMAGE016.GIF " he=" 26 " id=" ifm0018 " img-content=" drawing " img-format=" jpg " inline=" no " orientation=" portrait " wi=" 81 "/>
Because H is a homogeneous matrix, multiply by any non-zero proportions factor projective transformation is changed again, it is significant only to be the ratio of matrix element, so formula (10) can turn to:
We can obtain through top derivation, when H satisfies formula (11), have formula (7) to set up, and just two width of cloth images through H and H' resampling match each other to polar curve, preceding two width of cloth image P of note sampling
0And P
0' in corresponding point be respectively
X 0 With
X 0 ', back image P then samples
1And P
1' in corresponding point
X 1 With
X 1 'Satisfy:
Corresponding point
X 1 With
X 1 'Only in the axial gap of x, just have only horizontal parallax, need this moment a constraint to make parallax minimize, the projection matrix that note formula (11) obtains is H
0, matrix H
xRepresent as follows:
（13）
Minimization problem just can become asks shape such as H
xMake H=H
0H
xSatisfy formula with H'
Minimize and find the solution, this is a simple linear least-squares parameter minimization problem, can try to achieve x easily
1, x
2And x
3Value.
7. according to claim 2 based on stereogram robust antidote to polar curve coupling, it is characterized in that resample the respectively image of correspondence of described use projection matrix H and H' obtains the correcting image step; For preceding two width of cloth image P of sampling
0And P
0' in corresponding point be respectively X
0And X
0', back correcting image P then samples
1And P
1' in corresponding point X
1And X
1', then correcting image point pixel satisfies with original picture point pixel relationship
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| CN109785225A (en) * | 2017-11-13 | 2019-05-21 | 虹软科技股份有限公司 | A kind of method and apparatus for image flame detection |
| CN111369447A (en) * | 2020-03-09 | 2020-07-03 | 湖南警察学院 | Correction method for image point in monocular stereoscopic vision image |
| CN111432117A (en) * | 2020-03-23 | 2020-07-17 | 北京迈格威科技有限公司 | Image rectification method, device and electronic system |
| CN112308925A (en) * | 2019-08-02 | 2021-02-02 | 上海肇观电子科技有限公司 | Binocular calibration method and device of wearable device and storage medium |
| CN115115861A (en) * | 2022-08-31 | 2022-09-27 | 中国民航大学 | Image correction method applied to rotating binocular stereoscopic vision system |
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