CN104091308B - Polar line correction method for reducing image distortion - Google Patents
Polar line correction method for reducing image distortion Download PDFInfo
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Abstract
The invention discloses a polar line correction method for reducing image distortion. The method comprises: obtaining two images, i.e., a left image and a right image by use of a binocular camera, and respectively obtaining coordinates of and scale scopes of points corresponding to the left image and the right image by use of a surf algorithm; deleting mismatch points by use of block corresponding consistency and random sampling consistency, and obtaining a basic matrix; according to relations between the basic matrix and a left homography matrix and a right homography matrix, establishing an optimization function which comprises six parameters and is used for polar line correction; solving an initial value of the optimization function by use of a heredity algorithm; obtaining the left homography matrix and the right homography matrix when a comprehensive error is the smallest by use of a pyramid search method and an image distortion performance index; and according to the left homography matrix and the right homography matrix which are obtained in S5, solving a corrected image by use of bilinear interpolation. The method provided by the invention can effectively reduce image distortion after polar line correction.
Description
Technical field
The invention belongs to stereoscopic vision field is and in particular to a kind of method for correcting polar line of minimizing pattern distortion.
Background technology
Stereo matching is to find corresponding point from stereo image pair, in order to improve search speed it is desirable to stereo pairs
EP point is located in same horizontal line, makes two Camera calibrations become preferably to look squarely binocular structure.The applied research of stereoscopic vision
In, method for correcting polar line can be applicable to the aspects such as the video camera attitude process of Stereo matching, 3D TV.
Existing method for correcting polar line, is segmented into two classes, including the method for correcting polar line needing camera calibration and weak
The method for correcting polar line demarcated.Obtain inner parameter and external parameter using camera calibration, including focal length, photocentre coordinate, rotation
Torque battle array, translation matrix etc., obtain the homography matrix solving using the method for explicit physical meaning.The polar curve correction of weak demarcation
Method, only passes through the coupling corresponding point of two images, solves two suitable homography matrixes and carries out projective transformation, allows corresponding point not
There is the parallax of vertical direction.
Classical weak demarcation method for correcting polar line include the corresponding limit of a kind of direct operation of Hartley proposition method its
Algorithm thinking is that the limit of wherein piece image (being set as right figure) is rotated to x-axis, then moves to infinity, obtains making this width
All polar curves of image H parallel with x-axislMatrix；H is gone out according to the relation derivation of fundamental matrix after two correctionsrThe parameter shape of matrix
Formula；Then obtain H using the minimum constraint of the parallax after two image rectificationsrMatrix.
Andrea Fusiello etc. thinks that the homography matrix that the method for correcting polar line of known calibration parameter is tried to achieve is by no
Poor far plane introduces, and the method will not introduce extra y direction parallax it is proposed that the polar curve of Quasi-Euclidean corrects
Method, the structure of infinite homography matrix is retained in majorized function Sampson apart from central, is obtained by nonlinear optimization
The result of approximate known calibration parameter ideal case.This method depends on the solving precision of fundamental matrix, when there is error hiding
When, polar curve can be made to correct result larger pattern distortion occurs, lose matching precision.
Content of the invention
In order to overcome shortcoming and the deficiency of prior art presence, the present invention provides a kind of polar curve reducing pattern distortion to correct
Method.
The technical solution used in the present invention：
A kind of method for correcting polar line reducing pattern distortion, comprises the steps：
S1 use binocular camera obtain same target left and right two images, then using surf algorithm obtain respectively a left side,
The coordinate of right image corresponding point and range scale；
S2 obtains fundamental matrix using block to concordance and the random deletion carrying out Mismatching point using concordance；
S3 according to the relation of fundamental matrix and left and right homography matrix, set up comprise 6 parameters for polar curve correction
Majorized function；
S4 utilizes the initial value of genetic algorithm for solving majorized function；
S5 left singly answers square using what Pyramidal search method and pattern distortion performance indications obtained when synthetic error is minimum
Battle array and right homography matrix；
The left and right homography matrix that S6 obtains according to S5, tries to achieve the image after correction using bilinear interpolation.
If stressing polar curve correction result, select to omit S4.
Described S2 comprises the steps：
S2.1 obtains coordinate and the range scale of corresponding point according to surf algorithm, sets up the topological relation between circle and circle,
Set up corresponding blocks when topological relation is and intersects and comprise；
S2.2 retains the same characteristic features point of the left and right identical corresponding blocks of two figures, rejects Mismatching point；
Left or right image is carried out deblocking by S2.3, extracts at least 8 groups corresponding point from different piecemeals, reduces initial
The excessively intensive situation of point；
S2.4 repeatedly extracts corresponding point using stochastical sampling concordance, and 8 points of algorithms using direct linear transformation obtain
To fundamental matrix and rejecting Mismatching point.
Described S3 is specially：Left and right homography matrix is adopted quasi-Euclidean method according to infinity homography
The form of matrix is decomposed, and sets up the majorized function of 6 parameters using Sampson distance, is carried out non-linear using LM algorithm
Optimize, obtain the majorized function for polar curve correction.
Described S5 is specially：
S5.1 sets minimum zoom ratio, maximum zoom ratio and scaling step-length；
Corresponding point coordinates is zoomed in and out by S5.2, then 6 initial parameter values of majorized function is set to S4 acquired results, that is,
[0,0,0,0,0, w+h] solve, wherein, w represents the width of image, h represent the height of image, affiliated left image and right figure as
Length and width are equal, and computing obtains when time solution of 6 parameters of search；
S5.3 obtains left and right homography matrix and error using the solution of 6 parameters；
S5.4 carries out the scaling of yardstick to left and right homography matrix
With
In formula, HlRepresent left homography matrix, Hr represents right homography matrix, S represents scaling
S5.5 obtains synthetic error err1 according to the performance indications of pattern distortion, and is recorded as current minima；
Wherein, err is to solve the Sampson distance obtaining,
In formula, err1 represents synthetic error, and err represents the distance of Sampson, and subscript l represents left figure, and subscript r represents right figure, and w is
The width of image, h is the height of image, and θ represents the orthogonality of image midpoint line, and ideal value θ not being distorted when image=
90 °,M=Hb-Hd, n=Hc-Ha,
rdRepresent cornerwise length-width ratio, ideal value r not being distorted when imaged=1, rd=m
=Hb-Hd, n=Hc-Ha, a=(0,0,1), b=(w, 0,1), c=(w, h, 1), d=(0, h, 1)；
rwhRepresent the aspect ratio of image, when the ideal value that image is not distorted is width/length,m
=Hb-Hd, n=Hc-Ha,
According to scaling step-size change scaling, scaling order is to scale from big to small to S5.6, repeats S5.2-S5.5, directly
It is to stop during minimum to scaling, the described initial value when time 6 parameters is the solution of last 6 parameters；
S5.7 obtains the minima of err1 under different zoom ratio, and records the left homography matrix when err1 is minimum and the right side
Homography matrix.
Described 6 parameters are specially yL, zL, xR, yR, zR, f, f are the focal length of camera, yL、yRIt is respectively left camera, right phase
The angle that machine rotates around y-axis, zL、zRThe angle that respectively left camera, right camera rotate about the z axis, xRRotate around X-axis for right camera
Angle.
Compared with prior art, the present invention has the advantages that：
1) using block, error hiding is eliminated to concordance and stochastical sampling concordance, obvious Mismatching point can be removed；
2) initial value carrying out nonlinear optimization in conjunction with genetic algorithm solves, when can shorten search to parts of images
Between；
3) homography matrix obtaining in conjunction with Pyramidal search and more suitably performance indications, exists by mistake in corresponding point
Coupling or corresponding point less in the case of, have preferable polar curve calibration result, the image existing after effectively reducing polar curve correction
Distortion, makes the result that polar curve corrects not exclusively rely on the solving precision of fundamental matrix.
Brief description
Fig. 1 is the workflow diagram of the present invention；
Fig. 2 is the flow chart utilizing block to reject Mismatching point to concordance and stochastical sampling concordance in Fig. 1；
Fig. 3 is the flow chart combining genetic algorithm for solving initial parameter values in Fig. 1；
Fig. 4 is the workflow diagram of step S5 in Fig. 1；
Fig. 5 (a) (b) is left and right two images of binocular camera acquisition before correction；
Fig. 6 (c) (d) is that Fig. 5 (a) (b) has Quasi-Euclidean polar curve correction result figure during Mismatching point；
Fig. 7 (e) (f) is that Fig. 5 (a) (b) has the polar curve combining Pyramidal search and pattern distortion performance indications during error hiding
Correction result.
Specific embodiment
With reference to embodiment and accompanying drawing, the present invention is described in further detail, but embodiments of the present invention are not
It is limited to this.
Embodiment
As shown in figure 1, a kind of method for correcting polar line reducing pattern distortion, comprise the steps：
S1 obtains left and right two of same target using the binocular camera of the parallel optical axis structure with fixed base length
Image, left and right two images are respectively left mesh camera and right mesh camera shoots, and are then obtained left and right respectively using surf algorithm
The coordinate of the corresponding point of two images and range scale, described range scale is specially the radius of circle that corresponding point are located.
S2 obtains fundamental matrix, specifically using block to concordance and the random deletion carrying out Mismatching point using concordance
For as shown in Fig. 2 being specially：
S2.1 obtains coordinate and the range scale of corresponding point according to surf algorithm, sets up the topological relation between circle and circle,
Set up corresponding blocks when topological relation is and intersects and comprise；
S2.2 retains the same characteristic features point of the left and right identical corresponding blocks of two figures, rejects Mismatching point；
Left or right image is carried out deblocking by S2.3, is several rectangular mesh specially by left or right image division,
Extract at least 8 groups corresponding point from different piecemeals, reduce the excessively intensive situation of initial point；
S2.4 repeatedly extracts corresponding point using stochastical sampling concordance, and 8 points of algorithms using direct linear transformation obtain
To fundamental matrix and rejecting Mismatching point.Wherein, concrete number of repetitionObtained often by n times iteration
Secondary iteration is no more than the result of 1 exterior point, and confidence level is p, is typically set to 0.99；M is the number of minimum input data, root
Solution according to fundamental matrix is set to 8；U is the probability belonging to interior point in all input points, in the range from 0.5～0.9, may be selected relatively
Few u ensures more number of repetition and preferable result.
S3 according to the relation of fundamental matrix and left and right homography matrix, set up comprise 6 parameters for polar curve correction
Majorized function, specially：
Left and right homography matrix is decomposed in the form of quasi-Euclidean method is according to infinite homography matrixTwo homography matrixes are substituted into
Fundamental matrix can be obtained through mathematical operation
f∈[(w+h)/3,3(w+h)]
I=L, R
Wherein, w is the width of image, and h is the height of image, and f is the focal length in units of pixel.Due to rotating around x-axis
Do not change the parallax in y direction it is possible to 6 parameters of two spin matrixs are reduced into 5, remove left camera around x-axis
The anglec of rotation.Sampson distance by fundamental matrix F As optimization
Function carries out 6 parameters yL,zL,xR,yR,zR, f, nonlinear optimization, initial value be [0,0,0,0,0, w+h].In 6 parameters, f is
The focal length of camera, yL、yRThe angle that respectively left camera, right camera rotate around y-axis, zL、zRIt is respectively left camera, right camera around Z
The angle of axle rotation, xRThe angle rotating around X-axis for right camera, the scope of angle is between -90 °～90 °.Subscript L is left mesh
Video camera, subscript R is right lens camera.
S4 sets up the initial value of majorized function using genetic algorithm for solving sampson distance, thus shortening parts of images correction
Search time, improve search speed.If laying particular emphasis on the effect of polar curve correction, may be selected to abandon carrying out at the beginning of genetic algorithm for solving
The minimizing search time of value is processed.Concretely comprise the following steps：As shown in figure 3,
S4.1 setup parameter.Determine Population Size, iterationses, crossover operation probability, mutation operation probability.
S4.2 determines Phenotype and the genotype of gene, generates initial population at random.6 ginsengs that range of variables is determined
Number, can first pass through the initial value that generating random number obtains population, and the genotype of all genes is carried out with 8 bits
Represent, i.e. 0～255 integer；
S4.3 decodes, and the Phenotype of genes of individuals is converted into genotype.Different Individual to this generation population current, profit
With Sampson distance as direct error function, fitness function is solved from the power function of error；
S4.4 selection operation.According to the fitness function of Different Individual in population, selected at random using roulette selection method
In two Different Individual so that the larger individuality of fitness has larger probability selected；
S4.5 crossover operation.According to the gene being chosen individuality, to every item chromosome all according to certain probability judgment
The need of exchange, follow-on population retains two individualities after exchanging；
S4.6 mutation operation.To the individuality after crossover operation, to every item chromosome according to certain probability judgment
The need of variation, follow-on population retains the individuality after variation；
S4.7 best individual preservation strategy.In order that genetic algorithm is relatively stable, need to protect the optimum individual of every generation
Stay；
S4.8 repeats 4.3～4.7 steps, until iterationses reach requirement；
The optimized parameter that genetic algorithm is found by S4.9 is as initial value.
S5 left singly answers square using what Pyramidal search method and pattern distortion performance indications obtained when synthetic error is minimum
Battle array and right homography matrix, as shown in figure 4, be specially：
S5.1 sets minimum zoom ratio, maximum zoom ratio and scaling step-length；
Corresponding point coordinates is zoomed in and out by S5.2, then 6 initial parameter values of majorized function is set to [0,0,0,0,0, w+
H] solve, described initial value is S4 gained, and wherein, w represents the width of image, and h represents the height of image, affiliated left image and right figure
The length and width of elephant are equal, and computing obtains when time solution of 6 parameters of search；
S5.3 obtains left and right homography matrix and error using the solution of 6 parameters；
S5.4 carries out the scaling of yardstick to left and right homography matrix
With
H in formulalRepresent left homography matrix, Hr represents right homography matrix, S represents scaling
S5.5 obtains synthetic error err1 according to the performance indications of pattern distortion, and is recorded as current minima；
Wherein, err is to solve the Sampson distance obtaining,
In formula, err1 represents synthetic error, and err represents the distance of Sampson, and subscript l represents left figure, and subscript r represents the right side
Figure, w is the width of image, and h is the height of image.
θ represents the orthogonality (ideal value θ=90 ° not being distorted when image) of image midpoint line；M=Hb-Hd, n=Hc-Ha,
rdRepresent cornerwise length-width ratio (ideal value r not being distorted when imaged=1),
M=Hb-Hd, n=Hc-Ha, a=(0,0,1), b=(w, 0,1), c=(w, h, 1), d=(0, h, 1)；
rwhRepresent the aspect ratio (when the ideal value that image is not distorted is width/length) of image,
M=Hb-Hd, n=Hc-Ha, Described
Pattern distortion performance indications include rwh、rd、θ；
According to scaling step-size change scaling, scaling order is from big to small to S5.6, repeats S5.2-S5.5, until contracting
Ratio of putting is to stop during minimum zoom ratio, and the described initial value when time 6 parameters is the solution of last 6 parameters.
S5.7 obtains the minima of err1 under different zoom ratio, and records the left homography matrix when err1 is minimum and the right side
Homography matrix.
The left and right homography matrix that S6 obtains according to S5, tries to achieve the image after correction using bilinear interpolation.After calibration
The rounded coordinate of image obtains the non-integer coordinates of original image using homography matrix, using bilinear interpolation method in target
The nearest coordinate pixel value required for 4 rounded coordinate calculated for pixel values of point.Using formula：
F (x, y)=(f (1) * (64-x) * (64-y)+f (2) * (x) * (64-y)+f (3) * (64-x) * (y)+f (4) * x*
y)/4096
Wherein, f (x, y) is the pixel value of impact point, and f (1), f (2), f (3) and f (4) refer respectively to closest 4
The pixel value of coordinate.
Fig. 5 (a) (b) is the left images of slightly rotation, corresponding point can there is the parallax in y direction as seen from the figure；Fig. 6
C () (d) is because that corresponding point have a small amount of error hiding, existed using the image that original Quasi-Euclidean method obtains and draw
The pattern distortion stretched；Fig. 7 (e) (f) is using the corresponding point that there is a small amount of error hiding with Fig. 6 identical, image after improving
The degree of distortion has been greatly decreased.
Performance comparision before and after correction is as shown in table 1,
Table 1
Performance Evaluating Indexes, the first two index is used for weighing the parallax in y direction, and rear 4 indexs are used for weighing the abnormal of image
Change situation
1) average of the parallax absolute value in y direction：
2) with preferable fundamental matrixSampson distance (video camera meet look squarely binocular
During structure, this numerical value is less)：
3) orthogonality (ideal value θ=90 ° not being distorted when image) of image midpoint line,
M=Hb-Hd, n=Hc-Ha,
4) cornerwise diagonal ratio (ideal value not being distorted when image
M=Hb-Hd, n=Hc-Ha, a=(0,0,1), b=(w, 0,1), c=(w, h, 1), d=(0, h, 1)；
5) aspect ratio (when the ideal value that image is not distorted is width/length=0.75) of image：m
=Hb-Hd, n=Hc-Ha,
6) after triangulation corresponding point in the change (this numerical value is smaller when image is not distorted) in x direction：min
Σ[d(Hlpla-Hlplb)2+d(Hrpra-Hrprb)2]；
Table 2 carries out 100 experiments using three kinds of methods and compares to two figures, illustrates to ask initial value effective with reference to genetic algorithm
Shorten average search time, when so that calibration result is made moderate progress in combination with two kinds of improved methods, also can to a certain degree shorten
Average search time, the part superiority of the present invention lies also in this.In conjunction with two kinds of innovatory algorithm, refer to ask with reference to genetic algorithm
Solve initial value and improve with reference to Pyramidal search and pattern distortion performance indications method, i.e. S4 and S5 of embodiment.Each
Method search refers to the search of the overall plan containing this step.
Table 2 repeats the average search time required for 100 experiments
When there is not Mismatching point, the calibration result of several method is preferable.When there is a small amount of Mismatching point, Quasi-
Euclidean method, the calibration result seeking initial value with reference to genetic algorithm are poor, such as Fig. 6；In conjunction with Pyramidal search and pattern distortion
Performance indications, such as Fig. 7 preferable with reference to the calibration result of two kinds of improved methods.
Above-described embodiment is the present invention preferably embodiment, but embodiments of the present invention are not subject to described embodiment
Limit, other any spirit without departing from the present invention and the change made under principle, modification, replacement, combine, simplify,
All should be equivalent substitute mode, be included within protection scope of the present invention.
Claims (5)
1. a kind of method for correcting polar line reducing pattern distortion is it is characterised in that comprise the steps：
S1 uses binocular camera to obtain left and right two images of same target, then obtains left and right figure respectively using surf algorithm
Coordinate and range scale as corresponding point；
S2 carries out the deletion of Mismatching point using block to concordance and stochastical sampling concordance, obtains fundamental matrix；
S3, according to the relation of fundamental matrix and left and right homography matrix, sets up the optimization for polar curve correction comprising 6 parameters
Function；
S4 utilizes the initial value of genetic algorithm for solving majorized function；
S5 using Pyramidal search method and pattern distortion performance indications obtain left homography matrix when synthetic error is minimum and
Right homography matrix；
The left and right homography matrix that S6 obtains according to S5, tries to achieve the image after correction using bilinear interpolation；
Described S2 comprises the steps：
S2.1 obtains the coordinate of corresponding point and range scale according to surf algorithm, sets up the topological relation between circle and circle, when opening up
Flutter when relation is and intersects and comprise and set up corresponding blocks；
S2.2 retains the same characteristic features point of the left and right identical corresponding blocks of two figures, rejects Mismatching point；
Left or right image is carried out deblocking by S2.3, extracts at least 8 groups corresponding point from different piecemeals, reduces initial point mistake
In intensive situation；
S2.4 repeatedly extracts corresponding point using stochastical sampling concordance, and 8 points of algorithms using direct linear transformation obtain base
This matrix and rejecting Mismatching point.
If 2. a kind of method for correcting polar line reducing pattern distortion according to claim 1 is it is characterised in that stress pole
Line corrects result, selects to omit S4.
3. method according to claim 1 is it is characterised in that described S3 is specially：Left and right homography matrix is adopted
Quasi-Euclidean method is decomposed according to the form of infinite homography matrix, and sets up 6 using Sampson distance
The majorized function of parameter, carries out nonlinear optimization using LM algorithm, obtains the majorized function for polar curve correction.
4. method according to claim 1 is it is characterised in that described S5 is specially：
S5.1 sets minimum zoom ratio, maximum zoom ratio and scaling step-length；
Corresponding point coordinates is zoomed in and out by S5.2, then 6 initial parameter values of majorized function is set to S4 acquired results, that is, [0,
0,0,0,0, w+h] solve, wherein, w represents the width of image, and h represents the height of image, the length of affiliated left image and right figure elephant
Wide equal, computing obtains when time solution of 6 parameters of search；
S5.3 obtains left and right homography matrix and error using the solution of 6 parameters；
S5.4 carries out the scaling of yardstick to left and right homography matrix
With
In formula, HlRepresent left homography matrix, Hr represents right homography matrix, S represents scaling
S5.5 obtains synthetic error err1 according to the performance indications of pattern distortion, and is recorded as current minima；
Wherein, err is to solve the Sampson distance obtaining,
In formula, err1 represents synthetic error, and err represents the distance of Sampson, and subscript l represents left figure, and subscript r represents right figure, and w is image
Width, h is the height of image, and θ represents the orthogonality of image midpoint line, and ideal value θ=90 ° not being distorted when image,M=Hb-Hd, n=Hc-Ha,
rdRepresent cornerwise length-width ratio, ideal value r not being distorted when imaged=1, M=Hb-
Hd, n=Hc-Ha, a=(0,0,1), b=(w, 0,1), c=(w, h, 1), d=(0, h, 1)；
rwhRepresent the aspect ratio of image, when the ideal value that image is not distorted is width/length,m
=Hb-Hd, n=Hc-Ha,
According to scaling step-size change scaling, scaling order is to scale from big to small to S5.6, repeats S5.2-S5.5, until contracting
Put when ratio is minimum and stop, the described initial value when time 6 parameters is the solution of last 6 parameters；
S5.7 obtains the minima of err1 under different zoom ratio, and records left homography matrix when err1 is minimum and right list should
Matrix.
5. the method according to claim 1 or 3 or 4 is it is characterised in that described 6 parameters are specially yL,zL,xR,yR,zR,
F, f are the focal length of camera, yL、yRThe angle that respectively left camera, right camera rotate around y-axis, zL、zRIt is respectively left camera, right phase
The angle that machine rotates about the z axis, xRThe angle rotating around X-axis for right camera.
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