CN107644444B - Single-image camera calibration method based on compressed sensing - Google Patents
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Abstract
The invention relates to the technical field of camera calibration, and particularly discloses a single-image camera calibration method based on compressed sensing.
Description
Technical Field
The invention relates to the technical field of camera calibration, in particular to a single-image camera calibration method based on compressed sensing.
Background
The camera calibration technology originates from lens correction in photogrammetry in the nineteenth century, and is mainly used for solving the problem of accurate matching between a viewpoint coordinate and an image point coordinate corresponding to the viewpoint coordinate. The two-step calibration method proposed by Tsai in 1987 is considered to be an important theoretical work for camera calibration, and is widely applied to the early camera calibration process. Based on the assumption model of collinearity between the radial distortion point and the real point, the method adopts a two-step strategy to solve the internal and external parameters of the camera. The two-step calibration method has the advantages of low calculation complexity and high solving speed of solving parameters, and has the disadvantages of large solving error and low stability when the target plane and the imaging plane are parallel.
In 1999, the planar calibration method proposed by Zhangyingyou (hereinafter referred to as Zhangyingyou planar calibration method) adopts a simple planar object as a target, and takes target images at different positions for many times to estimate camera parameters by a nonlinear optimization method. The calibration method of the plane target combines the ideas of the traditional target calibration method and the self-calibration method, and can obtain higher calibration precision through simple manual operation of the two-dimensional plane target.
The Zhangyingyou plane calibration method is a new, flexible and high-precision method. However, in the process of using the zhangzhengyou plane calibration method, six unknowns are required to be obtained in order to calculate the camera internal reference matrix, so that an equation system for the six unknowns must be established. The Zhangyingyou plane calibration method can only establish 2 equations for each calibration plate image, and under the condition that 6 unknowns need to be solved, only 2 equation sets exist, and obviously the equation set is an underdetermined equation set. Therefore, the Zhangyingyou plane calibration method must take at least 3 photographs of different angles of the calibration plate to obtain at least 6 equation sets to solve the internal reference matrix of the camera, and further solve the external reference matrix and the distortion coefficient through the obtained internal reference matrix.
In the process of manually photographing the calibration plate for multiple times by using the Zhang Zhengyou plane calibration method, useless data can be repeatedly calculated in the subsequent solving process due to repeated or small difference of the placing angles of the calibration plate, and the calibration quality and the calibration efficiency of the camera are low.
Disclosure of Invention
The invention provides a single-image camera calibration method based on compressed sensing, which solves the technical problem that a Zhang Zhengyou plane calibration method in the prior art cannot perform accurate calibration on a single image.
In order to solve the technical problems, the invention provides a single-image camera calibration method based on compressed sensing, which comprises the following steps:
s1, modeling a Zhangyingyou calibration method mathematical model to obtain an equivalent vector expression of a solution of an internal reference matrix of a single image and a constraint relation expression of the equivalent vector expression, and determining the sparsity of a calibration signal;
s2, setting a sensing matrix, and expressing a vector of a solution of the internal reference matrix into an initial compression observation equation according to the sensing matrix;
s3, initializing a camera residual error and an iteration index set, initializing a column set of the sensing matrix, and setting a limiting condition of an unknown quantity in the internal reference matrix according to physical parameters of the camera;
s4, performing inner product operation on the camera residual after t-1 iterations and each column of the sensing matrix to obtain a maximum inner product absolute value, and taking the maximum inner product absolute value as a t-th iteration index of the t-th iteration, wherein t is a natural number more than or equal to 1; all the t-th iteration indexes form the iteration index set;
s5, selecting the column set of the sensing matrix according to the iteration index set obtained in the step S4;
s6, solving a least square solution of the initial compression observation equation according to the column set of the sensing matrix subjected to the step S5;
s7, updating the camera residual after t iterations according to the least square solution;
s8, judging whether the least square solution meets the limiting condition of the unknown quantity in the internal reference matrix; if so, judging the least square solution as an optimal solution, and solving the internal reference matrix according to the optimal solution; if not, the process returns to step S4.
Further, in step S1, the sparsity of the calibration signal is 6.
Further, in the step S3, the physical parameters of the camera include a screen resolution, ideal coordinates of the principal axis point, a sensor size, a focal distance range, and an error range of the ideal coordinates of the principal axis point.
Further, in the step S3, the unknown quantity in the internal reference matrix includes scale factors of the single image on u-axis and v-axis of an image coordinate system, respectively, an ideal coordinate of the principal axis point, and a tilt parameter describing the ideal coordinate of the principal axis point.
The single image camera calibration method based on compressed sensing further comprises the following steps:
and S9, representing the external parameter matrix of the single image according to the internal parameter matrix.
According to the single-image camera calibration method based on compressed sensing, the calibration plate is photographed only once, the constraint conditions are set for 6 unknowns in the underdetermined equation set of the single image through the Zhang Zhengyou plane calibration method, the optimal solution of the single image is obtained through the compressed sensing reconstruction algorithm, the solving process of the internal reference matrix and the external reference matrix of the single image is greatly simplified, the adopted compressed sensing reconstruction algorithm is self-circulation optimized, and the calibration quality and the calibration efficiency of the camera are high.
Drawings
FIG. 1 is a flowchart illustrating steps of a single-image camera calibration method based on compressed sensing according to an embodiment of the present invention;
fig. 2 is a working flow chart of a single-image camera calibration method based on compressed sensing according to an embodiment of the present invention.
Detailed Description
The embodiments of the present invention will be described in detail below with reference to the accompanying drawings, which are given solely for the purpose of illustration and are not to be construed as limitations of the invention, including the drawings which are incorporated herein by reference and for illustration only and are not to be construed as limitations of the invention, since many variations thereof are possible without departing from the spirit and scope of the invention.
Fig. 1 is a flowchart illustrating steps of a single-image camera calibration method based on compressed sensing according to an embodiment of the present invention. In this embodiment, the method for calibrating a single-image camera based on compressed sensing includes the steps of:
s1, modeling a Zhangyingyou calibration method mathematical model to obtain an equivalent vector expression of a solution of an internal reference matrix of a single image and a constraint relation expression of the equivalent vector expression, and determining the sparsity of a calibration signal;
s2, setting a sensing matrix, and expressing a vector of a solution of the internal reference matrix into an initial compression observation equation according to the sensing matrix;
s3, initializing a camera residual error and an iteration index set, initializing a column set of the sensing matrix, and setting a limiting condition of an unknown quantity in the internal reference matrix according to physical parameters of the camera;
s4, performing inner product operation on the camera residual after t-1 iterations and each column of the sensing matrix to obtain a maximum inner product absolute value, and taking the maximum inner product absolute value as a t-th iteration index of the t-th iteration, wherein t is a natural number more than or equal to 1; all the t-th iteration indexes form the iteration index set;
s5, selecting the column set of the sensing matrix according to the iteration index set obtained in the step S4, wherein the column set is a column in the sensing matrix, which is most relevant to the camera residual error;
s6, solving a least square solution of the initial compression observation equation according to the column set of the sensing matrix subjected to the step S5;
s7, updating the camera residual after t iterations according to the least square solution;
s8, judging whether the least square solution meets the limiting condition of the unknown quantity in the internal reference matrix; if so, judging the least square solution as an optimal solution, and solving the internal reference matrix according to the optimal solution; if not, returning to the step S4;
and S9, representing the external parameter matrix of the single image according to the internal parameter matrix.
Wherein, in the step S1, the sparsity of the calibration signal is 6.
In the step S3, the physical parameters of the camera include screen resolution, ideal coordinates of the pivot point, sensor size, focal distance range, and error range of the ideal coordinates of the pivot point.
In step S3, the unknowns in the internal reference matrix include scale factors of the single image on the u-axis and v-axis of the image coordinate system, respectively, ideal coordinates of the principal axis point, and a tilt parameter describing the ideal coordinates of the principal axis point.
Referring to fig. 2, it is a flowchart of a single-image camera calibration method based on compressed sensing according to an embodiment of the present invention.
Fig. 1 and fig. 2 are further detailed in conjunction with the operation process as follows:
corresponding to the step S1, the gnomone scaling mathematical model is represented as:
wherein s is an arbitrary scaling factor, [ R T ]]Referred to as the camera's external reference matrix, R is the rotation matrix and T is the translation matrix.
Is the internal reference matrix of the camera (u)0,v0) Let it be said that the ideal coordinates of the principal axis point, α and β are the scale factors of the single image in the u and v axes, respectively, and γ is the tilt parameter describing the ideal coordinates of the principal axis point
The ith column rotation matrix of R is Ri，R＝[r1r2r3]Then equation (1) may be changed to:
then, let m be [ u v 1 ]]T，M＝[X Y 1]T，H＝K[r1r2t]The following can be obtained:
obviously, H is a matrix of 3 × 3 coefficients, and the H matrix can be found by only 9 sets of M and M data.
Let H be λ K [ r ]1r2t]＝[h1h2h3]The H matrix is a perspective projection matrix, which is a mapping between a point on the calibration plate and its image point, where λ is a scalar scaling factor, and because r is1And r2Orthogonal, formula (4) and formula (5) are obtained:
according to the matrix knowledge, when the number of the taken calibration images is at least more than or equal to 3, the unique solution of the internal reference matrix K containing 5 unknowns can be obtained.
Ordering:
given that the matrix B is a symmetric matrix, it is written in the form of a six-row and one-column vector, i.e. an equivalent vector expression of the solution:
b＝[B11,B12,B22,B13,B23,B33]T(7)
suppose the ith column vector of matrix H is Hi＝[hi1,hi2,hi3]TObtaining:
hi T＝Bhj＝vij Tb (8)
in formula (8):
vij＝[hi1hj1，hi1hj2+hi2hj1，hi2hj2，hi3hj1+hi1hj3，hi3hj2+hi2hj3，hi3hj3](9)
the joint type (4), the formula (5), the formula (8) and the formula (9) obtain the constraint relation expression:
that is, Vb is 0, where the matrix V is a 2 × 6 matrix, that is, a single image needs to establish 2 equation sets including 6 unknowns, the number of the unknowns is 6, and correspondingly, the sparsity Q of the calibration signal is 6. According to the linear algebraic knowledge, the equation set is an underdetermined equation set, and at least 6 equation sets are needed for solving 6 unknowns, so that all unknowns can be solved by at least 3 single images in the calibration process.
In order to take a picture of the calibration plate only once and obtain the optimal solution of the single image by using a compressive sensing reconstruction algorithm, a constraint condition needs to be set for 6 unknowns in an underdetermined equation set of the single image by using a Zhang-Yongyou plane calibration method, and before the constraint condition is set, an initial compression observation equation needs to be constructed.
Corresponding to the step S2, the compressed observation principle expression y ═ Φ x, where y is observed to obtain a vector M × 1 and x is the original signal N × 1(M < N). x is not generally sparse, but is sparse in some transform ψ θ, where θ is Q sparse (the sparsity of the signal is Q, Q is 6), i.e., θ has only Q non-zero terms, when y is φ ψ θ, let a be φ ψ, the initial compression observation equation: and y is A theta, and A is the sensing matrix.
When setting the defining conditions, r is assumed in advancetRepresenting the camera residual, t the number of iterations, O the null set, ΠtSet of indices, λ, representing t iterationstDenotes the index found in the t-th iteration, ajJ-th column representing A, AtIndicating a set pi by indextThe selected column set (matrix of size M x t) of the sensing matrix A, θtThe column vector of t x 1, the symbol ∪ represents the "and" operation of the set,<*，*>indicating an "inner product" operation of the vector.
Corresponding to the step S3, the physical parameters of the camera include screen resolution, ideal coordinates of the principal axis point, sensor size, focal distance range, and error range of the ideal coordinates of the principal axis point; the unknowns in the internal reference matrix include scale factors of the single image on a u-axis and a v-axis of an image coordinate system, respectively, and a tilt parameter describing ideal coordinates of the principal axis point; the known quantities in the internal reference matrix include ideal coordinates and constants of the principal axis points.
For example, the following steps are carried out:
as can be seen from equations (10) and (7), the number of unknowns is 6, and the sparsity Q is set to 6; let M be 64, N be 256; y is initially a 64 x 1 dimensional vector of which 6 are non-zero random numbers, each being [ B [ ]11,B12,B22,B13,B23,B33]；
Initializing camera residual rt：r0When equals 0, index set pit：Π0Column set A ═ Ot：A0O, and the number of iterations t: t is 1.
The iterative index set is illustrated by using a camera model JHSM300M, the screen resolution of the camera is 1600 (length of single image) × 1200 (width of single image), the ideal coordinates of the principal axis point is (u0, v0) ═ 800,600), and the coordinates are allowed to have an error of about 50 pixels, that is, 750< u0<850, 550< v0<650, the sensor size of the camera is 6.55mm (length of sensor) × 4.91mm (width of sensor), the focal length range is 6mm < f <12mm, according to α ═ f/dx, β ═ f/dy, (dx ═ length of sensor/length of single image ═ 6.55/1600 ═ 0.0081875, dy ═ width of sensor/width of single image ═ 4.91/1200, the range of the obtained 638 is 1465.6488< 92, the range of 6866 ═ 1466.4011, the range obtained is nearly equal to the unknown size of β | < 11, the unknown size of β | < 11 |:
corresponding to the step S4, the camera residual r after t-1 iterationst-1With each column a of the sensing matrixj(j ═ 1,2, … …, N) by inner product(s) ((s))<*，*>) Calculating to obtain maximum inner product absolute valueThe value argmaxj＝1,2.....N|<rt-1,aj>And taking it as the t-th iteration index lambda of the t-th iterationtT is a natural number greater than or equal to 1, i.e.:
λt＝argmaxj＝1,2.....N|<rt-1,aj>| (12)
all of the t-th iteration indexes lambdatForming the iterative index set ΠtAnd (3) ordering:
Πt＝Πt-1∪(λt)
corresponding to the step S5, according to the iteration index set Π passing through the step S4tSelecting the column set A of the sensing matrix AtI.e. At＝At-1∪at。
Further, corresponding to the step S6, the column set A of the sensing matrix A according to the step S5tSolving a least squares solution of the initial compressive observation equation (y ═ a θ):
updating the camera residual r over t iterations according to a least squares solution, corresponding to the step S7t：
Finally, corresponding to the step S8, since the formula (7) is a formula including (α, u0, γ, β, v0), the current (α, u0, γ, β, v0) can be solved by the formula (7) and 6 nonzero values of the current y vector, whether the solved current 5 variables (α, u0, γ, β, v0) meet the limit condition of the unknown quantity in the internal reference matrix K is judged, whether the least square solution meets the limit condition of the unknown quantity in the internal reference matrix K is further judged, if yes, a loop is skipped, the least square solution is judged to be the optimal solution, the internal reference matrix K is solved according to the least square solution, if no, the loop is returned to the step S4, and the loop is continued until the optimal solution is obtained.
And further determining an internal reference matrix K of the camera after obtaining the optimal solution, and representing the external reference matrix of the single image according to the internal reference matrix K, namely the external reference matrix of the camera can be represented as follows:
according to the single-image camera calibration method based on compressed sensing provided by the embodiment of the invention, only one-time photographing is needed to be carried out on the calibration plate, the constraint conditions are set for 6 unknown quantities in the underdetermined equation set of the single image by the Zhangyingyou plane calibration method, the optimal solution of the single image is obtained by using the compressed sensing reconstruction algorithm, the solving process of the internal reference matrix and the external reference matrix of the single image is greatly simplified, the adopted compressed sensing reconstruction algorithm is self-circulation optimized, and the calibration quality and the calibration efficiency of the camera are higher.
The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.
Claims (5)
1. A single image camera calibration method based on compressed sensing is characterized by comprising the following steps:
s1, modeling a Zhangyingyou calibration method mathematical model to obtain an equivalent vector expression of a solution of an internal reference matrix of a single image and a constraint relation expression of the equivalent vector expression, and determining the sparsity of a calibration signal;
s2, setting a sensing matrix, and expressing the equivalent vector of the solution of the internal reference matrix into an initial compression observation equation according to the sensing matrix;
s3, initializing a camera residual error and an iteration index set, initializing a column set of the sensing matrix, and setting a limiting condition of an unknown quantity in the internal reference matrix according to physical parameters of the camera;
s4, performing inner product operation on the camera residual after t-1 iterations and each column of the sensing matrix to obtain a maximum inner product absolute value, and taking the maximum inner product absolute value as a t-th iteration index of the t-th iteration, wherein t is a natural number more than or equal to 1; all the t-th iteration indexes form the iteration index set;
s5, selecting the column set of the sensing matrix according to the iteration index set obtained in the step S4;
s6, solving a least square solution of the initial compression observation equation according to the column set of the sensing matrix subjected to the step S5;
s7, updating the camera residual after t iterations according to the least square solution;
s8, judging whether the least square solution meets the limiting condition of the unknown quantity in the internal reference matrix; if so, judging the least square solution as an optimal solution, and solving the internal reference matrix according to the optimal solution; if not, the process returns to step S4.
2. The single-image camera calibration method based on compressed sensing of claim 1, wherein: in step S1, the sparsity of the calibration signal is 6.
3. The single-image camera calibration method based on compressed sensing of claim 1, wherein: in the step S3, the physical parameters of the camera include screen resolution, ideal coordinates of the principal axis point, sensor size, focal distance range, and error range of the ideal coordinates of the principal axis point.
4. A single image camera calibration method based on compressed sensing as claimed in claim 3, characterized in that: in step S3, the unknowns in the internal reference matrix include scale factors of the single image on the u-axis and the v-axis of the image coordinate system, respectively, ideal coordinates of the principal axis points, and tilt parameters describing the ideal coordinates of the principal axis points.
5. The single image camera calibration method based on compressed sensing as claimed in claim 1, further comprising the steps of:
and S9, representing the external parameter matrix of the single image according to the internal parameter matrix.
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| CN104794718A (en) * | 2015-04-27 | 2015-07-22 | 广东省第二人民医院 | Single-image CT (computed tomography) machine room camera calibration method |
| CN105809685A (en) * | 2016-03-09 | 2016-07-27 | 四川巨源科技有限公司 | Single-concentric circle image-based camera calibration method |
| CN105931222A (en) * | 2016-04-13 | 2016-09-07 | 成都信息工程大学 | High-precision camera calibration method via low-precision 2D planar target |
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