CN103268612A - Single image fisheye camera calibration method based on low rank characteristic recovery - Google Patents

Abstract

The invention discloses a single image fisheye camera calibration method based on low rank characteristic recovery. An image with low rank textures is regarded as a matrix, based on an optimizing method of a minimum matrix rank, a low rank image is recovered, exchange is conducted between an original image and the low rank image, and parameters of a fisheye camera is contained in the exchange. The single image fisheye camera calibration method based on the low rank characteristic recovery overcomes the defect that in a traditional method, the fact that angular points are marked manually consumes a large amount of manpower, meanwhile, only a single image is needed, a calibration field does not need to be arranged, and under the premise that certain robustness is ensured, the advantages of being convenient to operate and fast are achieved.

Description

The method of demarcating based on the single image fisheye camera of low-rank characteristic recovery

Technical field

The present invention relates to the camera calibration method, be specifically related to the method that a kind of single image fisheye camera that recovers based on the low-rank texture is demarcated.

Background technology

Camera calibration is problem the most basic in computer vision and the mapping science, only carries out camera calibration, the pixel on the image correctly could be mapped on the three dimensions, or the point on the three dimensions correctly is mapped on the image.Therefore, in computer vision field, as long as relate to the application of 3-d recovery, all need the calibrating parameters of camera, and the precision of camera calibration, also determined the precision of these application to a great extent.Recent decades, the camera calibration problem is a hot issue all the time, and scholars have proposed the method for many camera calibrations.

Current, the fisheye camera scaling method of single image nearly all depends on the correspondence of seeking unique point or line, and by certain geometrical constraint, simultaneous equations are found the solution parameter.If adopt automatic extract minutiae, the method that retrains of then unique point being mapped depends critically upon the precision of extract minutiae and Feature Points Matching, and the unique point of automatically extracting can not extract all unique points that demarcation needs usually, and this has just restricted the precision of camera calibration.Also having a kind of method is the corresponding point of manually selecting among several figure, but this needs the operator very careful and careful, so it makes camera calibration become a very consuming time and warm work.

Summary of the invention

The object of the present invention is to provide a kind of method of demarcating based on the single image fisheye camera of low-rank characteristic recovery, will have the figure of low-rank texture

Picture is regarded a matrix as, based on the optimization method that minimizes rank of matrix, recovers the low-rank image, and between original image and the low-rank image

Conversion, the parameter of fisheye camera just is included among this conversion.

The technical solution used in the present invention is:

(1) manually selects to have among the former figure rectangular area of low-rank texture, only the rectangular area of low-rank texture is operated;

(2) parameter initialization: adopt unified sphere model and double ends degree projection model, and use TILT method initialization transformation parameter, comprising focal distance f _x, f _y, principal point o _x, o _y, minute surface parameter ξ, rotation matrix R;

(3) find the solution the optimization problem that minimizes order:

Wherein I is the image of input, and τ is transformation parameter, and о is the operational symbol of the geometric transformation of the unified sphere model of employing and double precision projection model, I ⁰Be the low-rank image that obtains, λ is a constant, is taken as Width is the width of output image, and E is a sparse matrix, is used for pollution in the token image, and rank () is the order of compute matrix, ‖ ‖ ₀Zeroth order norm for compute matrix;

(4) confidential reference items of taking-up camera from τ.

The concrete grammar of above-mentioned steps (2) parameter initialization is:

Unified sphere model is defined as:

$\left\{\begin{array}{c}x=\frac{X}{\mathrm{\ξ}+Z}\\ y=\frac{Y}{\mathrm{\ξ}+Z}\end{array}\right.---\left(2\right)$

Wherein (x is as the point on the plane y), and (X, Y Z) are the three-dimensional coordinate on the unit sphere in the camera coordinates system;

Double ends degree projection model is defined as:

$\left\{\begin{array}{c}\mathrm{\θ}=\arctan \left(\frac{Z}{Y}\right)\\ \mathrm{\α}=\arctan \left(\frac{Z}{X}\right)\end{array}\right.---\left(3\right)$

Wherein θ is the longitude that is south poles with two end points of X-axis, and the longitude that α is is south poles with two end points of Y-axis tiles θ and the α value of each three-dimensional point at u and v both direction, then obtain the image of projection;

Use the approximate value of TILT method estimation parameter, the camera model of use is the perspective camera model, and minute surface parameter ξ is initialized to 1.

The concrete grammar that above-mentioned steps (3) is found the solution the optimization problem that minimizes order is:

1) formula (1) is carried out protruding relaxing, use nuclear norm to replace order, and use the L1 norm to replace the L0 norm, the problem that separate changes to:

‖ ‖ wherein _*Be the nuclear norm of compute matrix, ‖ ‖ ₁Single order norm for compute matrix.

2) formula (4) is carried out linearization, the problem that separate changes to externally circulation and finds the solution following problem, up to the variation of optimizing variable less than threshold value:

Wherein J is the Jacobian matrix of the τ of I о τ in the current circulation, Δ τ be current circulation find the solution variable quantity, each circulation back uses τ+Δ τ to upgrade current τ;

Formula (3) uses the LADMAP algorithm to find the solution, and its method is externally to optimize variablees with three during circulant solution formula (5) to become two, finds the solution these two variablees respectively separately until convergence in inner loop, each variable find the solution closed solution;

3) after the τ convergence, jump out outer loop.

Above-mentioned steps (4) is taken out the confidential reference items of camera from τ concrete grammar is:

From τ, take out f _x, f _y, o _x, o _y, ξ camera inner parameter, be the result of camera calibration.

Compare with background technology, the beneficial effect that the present invention has is:

The present invention has overcome the shortcoming of a large amount of manpowers of classic method hand labeled angle point consumption, only needs single image simultaneously, and does not need to arrange the demarcation field, under the prerequisite that guarantees certain robustness, has advantage easily and efficiently

Description of drawings

Fig. 1 is the step synoptic diagram of method of the present invention.

Embodiment

Further specify below in conjunction with accompanying drawing and the present invention of embodiment.

Fig. 1 has provided the process flow diagram of the method for demarcating based on the single image fisheye camera of low-rank characteristic recovery.

(1) manually selects to have among the former figure rectangular area of low-rank feature, practical operation only need be selected two summits, upper left and bottom right of this rectangle, document 1(Wright J, Ganesh A, Rao S, et al.Robust principal component analysis:Exact recovery of corrupted low-rank matrices via convex optimization[J] .Advances in neural information processing systems, 2009,22:2080-2088.) prove that selected matrix is more big, the probability that formula (1) obtains finding the solution is more big, and therefore the zone of choosing should be the big as far as possible zone that comprises the low-rank feature.

(2) parameter initialization: adopt unified sphere model and double ends degree projection model, and use branch-and-bound method initialization transformation parameter, comprising focal distance f _x, f _y, principal point o _x, o _y, minute surface parameter ξ, rotation matrix R, unified sphere model is defined as:

$\left\{\begin{array}{c}x=\frac{X}{\mathrm{\ξ}+Z}\\ y=\frac{Y}{\mathrm{\ξ}+Z}\end{array}\right.---\left(1\right)$

Wherein (x is as the point on the plane y), and (X, Y Z) are the three-dimensional coordinate on the unit sphere in the camera coordinates system;

Double ends degree projection model is defined as:

$\left\{\begin{array}{c}\mathrm{\θ}=\arctan \left(\frac{Z}{Y}\right)\\ \mathrm{\α}=\arctan \left(\frac{Z}{X}\right)\end{array}\right.---\left(2\right)$

Wherein θ is the longitude that is south poles with two end points of X-axis, and the longitude that α is is south poles with two end points of Y-axis tiles θ and the α value of each three-dimensional point at u and v both direction, then can obtain the image of projection;

Use document 2(Zhang Z, Liang X, Ganesh A, et al.TILT:transform invariant low-rank textures[M] .Computer Vision – ACCV2010.Springer Berlin Heidelberg, 2011:314-328.) approximate value of the TILT method estimation parameter that proposes, the zone of TILT input is regional identical with this method input, and minute surface parameter ξ is not calculated in TILT, and it is 1 for initialization.

(3) find the solution the optimization problem that minimizes order:

1) formula (3) is carried out protruding relaxing, use nuclear norm to replace order, and use the L1 norm to replace the L0 norm, the problem that separate changes to:

‖ ‖ wherein _*Be the nuclear norm of compute matrix, ‖ ‖ ₁Single order norm for compute matrix.

2) formula (4) is carried out linearization, the problem that separate changes to externally circulation and finds the solution following problem, up to the variation of optimizing variable less than threshold value:

Wherein J is the Jacobian matrix of the τ of I о τ in the current circulation, Δ τ be current circulation find the solution variable quantity, each circulation back uses τ+Δ τ to upgrade current τ;

Formula (3) can use the LADMAP algorithm to find the solution, its thought is externally to optimize variablees with three during circulant solution formula (3) to become two, find the solution these two variablees respectively until convergence in inner loop, the solution of finding the solution closure of each variable, its detailed step is as follows:

1. make J ^⊥=I ₀-J (J ^TJ) ^-1J ^T, formula (3) can be converted to:

2. I is found the solution in circulation ⁰And E, its closed solution is:

$I_{k+1}^0=S_{\frac{1}{{\mathrm{\μ}}_k}}\left(M_k\right)---\left(7\right)$

$E_{k+1}=T_{\frac{\mathrm{\λ}}{{\mathrm{\μ}}_k}}\left(N_k\right)$

（8）

Wherein:

（9）

μ _k+1＝min(μ _max,ρμ _k)（12）

Wherein, k represents the number of times of current circulation, ρ ₀And ε ₂Be two default constants; S () is the singular value contraction operator, is defined as:

S _ε(W)＝UT _ε(Σ)V ^T（14）

T _ε(x) be to be the scalar contraction operator, be defined as:

T _ε(x)＝sgn(x)max(|x|-ε,0)

（15）

3. step circulation termination condition 2. is:

ε wherein ₁Be a default constant, ε ₂With mentioned above identical.

4) confidential reference items of taking-up camera from τ.

Experimental example:

FUJINON FE185C086HA-1 fish eye lens is used in experiment, has carried out two groups of experiments, takes indoor scaling board for first group, takes outdoor well-regulated ceiling for second group.Test the image that collects respectively 10 512 * 512 for two groups.Because camera calibration does not have true value, use this method to all results' of single width figure demarcation average and standard deviation so provided, simultaneously for the validity of this method is described, selection is based on calibration tool case (the document 3:C.Mei and P.Rives of scaling board, inProceedings of IEEE Interna-tional Conference on Robotics and Automation (2007), pp.3945{3950) result and the calibration result of this method compare, the calibration tool case need be imported the angle point of the figure of several scaling boards simultaneously, and needs the size of known calibration plate medium square.

Table 1 has provided the calibration result of this law to scaling board and ceiling, and compares with the result of the calibration tool case that uses scaling board.

The calibration result of table 1 this method calibration result and calibration tool case

Claims (4)

1. the method that the single image fisheye camera that recovers based on the low-rank texture is demarcated is characterized in that: by minimizing the optimization method of order, obtain the transformation parameter of original image and low-rank image, thereby obtain the camera confidential reference items; These method concrete steps are as follows:

(1) manually selects to have among the former figure rectangular area of low-rank texture, only the rectangular area of low-rank texture is operated;

(2) parameter initialization: adopt unified sphere model and double ends degree projection model, and use TILT method initialization transformation parameter, comprising focal distance f _x, f _y, principal point o _x, o _y, minute surface parameter ξ, rotation matrix R;

(3) find the solution the optimization problem that minimizes order:

Wherein I is the image of input, and τ is transformation parameter, and о is the operational symbol of the geometric transformation of the unified sphere model of employing and double precision projection model, I ⁰Be the low-rank image that obtains, λ is a constant, is taken as

Width is the width of output image, and E is a sparse matrix, is used for pollution in the token image, and rank () is the order of compute matrix, ‖ ‖ ₀Zeroth order norm for compute matrix;

(4) confidential reference items of taking-up camera from τ.

2. a kind of single image fisheye camera that recovers based on the low-rank texture according to claim 1 method of demarcating is characterized in that the concrete grammar of described step (2) parameter initialization is:

Unified sphere model is defined as:

$\left\{\begin{array}{c}x=\frac{X}{\mathrm{\ξ}+Z}\\ y=\frac{Y}{\mathrm{\ξ}+Z}\end{array}\right.---\left(2\right)$

Wherein (x is as the point on the plane y), and (X, Y Z) are the three-dimensional coordinate on the unit sphere in the camera coordinates system;

Double ends degree projection model is defined as:

$\left\{\begin{array}{c}\mathrm{\θ}=\arctan \left(\frac{Z}{Y}\right)\\ \mathrm{\α}=\arctan \left(\frac{Z}{X}\right)\end{array}\right.---\left(3\right)$

Wherein θ is the longitude that is south poles with two end points of X-axis, and the longitude that α is is south poles with two end points of Y-axis tiles θ and the α value of each three-dimensional point at u and v both direction, then obtain the image of projection;

Use the approximate value of TILT method estimation parameter, the camera model of use is the perspective camera model, and minute surface parameter ξ is initialized to 1.

3. a kind of single image fisheye camera based on the low-rank characteristic recovery according to claim 1 method of demarcating, it is characterized in that: the concrete grammar that described step (3) is found the solution the optimization problem that minimizes order is:

3.1) formula (1) is carried out protruding relaxing, to use nuclear norm to replace order, and use the L1 norm to replace the L0 norm, the problem that separate changes to:

‖ ‖ wherein _*Be the nuclear norm of compute matrix, ‖ ‖ ₁Single order norm for compute matrix;

3.2) formula (4) is carried out linearization, the problem that separate changes to externally circulation and finds the solution following problem, up to the variation of optimizing variable less than threshold value:

Wherein J is the Jacobian matrix of the τ of I о τ in the current circulation, Δ τ be current circulation find the solution variable quantity, each circulation back uses τ+Δ τ to upgrade current τ;

Formula (3) uses the LADMAP algorithm to find the solution, and its method is externally to optimize variablees with three during circulant solution formula (5) to become two, finds the solution these two variablees respectively separately until convergence in inner loop, each variable find the solution closed solution;

3.3) after the τ convergence, jump out outer loop.

4. a kind of single image fisheye camera based on the low-rank characteristic recovery according to claim 1 method of demarcating, it is characterized in that: described step (4) is taken out the confidential reference items of camera from τ concrete grammar is: take out f from τ _x, f _y, o _x, o _y, ξ camera inner parameter, be the result of camera calibration.

Images