CN103985121B - Method for optical calibration of underwater projector structure - Google Patents

Abstract

The invention belongs to the technical field of measuring, and provides a method for calibrating a structure of an underwater projector. The method comprises the following steps of shooting image pairs of a waterproof target and a projection target in the at least three positions, wherein the waterproof target and the projection target are arranged in the same plane; under the coordinate system of a camera, calculating a plane normal vector and three-dimensional coordinates of the projection target, adopting a single-view-point model to initially calibrate the projector and structural parameters, and converting the three-dimensional coordinates of the projection target into the coordinate system of the projector to be used as reference values; under the coordinate system of the projector, setting up the incident ray of the projection target and a refracted ray model, and calculating the three-dimensional coordinates of the projection target; setting up a target function according to the distance between the calculated three-dimensional coordinates of the projection target and the reference value, and performing recursive optimization on all the parameters. According to the method, the refraction effect which happens when the ray of the projector is transmitted to the aqueous medium from the air medium is taken into consideration, and under the condition that the optical axis of the projector is not parallel to a normal vector of a window of a waterproof device, the requirement for calibrating the underwater projector can be met.

Description

One kind projector architecture light scaling method under water

Technical field

The present invention relates to one kind projector architecture light scaling method under water, belong to field of measuring technique.

Background technology

The structure optical mode that projector is combined with video camera, is a kind of important method for three-dimensional measurement and skill in vision measurement Art.Its principle is using projector architecture optical sensor, and projector needs actively to project feature according to measurement, such as dot matrix, grating Striped, encoded mesh etc., the image of video camera capture comprises to produce the projection feature of deformation because of object surface appearance change, Recover the three-dimensional information of body surface according to structure light principle of triangulation.Because the piece image that video camera shoots can comprise A large amount of characteristic informations, therefore measure application for in-plant underwater 3 D, and projector architecture light technology is that a kind of recovery is tested The effective means of object dimensional information.

Projector architecture photo measure environment is different from the air dielectric environment of land under water.The projection of underwater environment operation In the water-tight device that instrument needs be fixed on sealing, by the transparent window before projector lens to the measured object being in water Body projects feature.Because the use of water-tight device is so that testee and projector image planes are located in different medium respectively, I.e. testee is located in aqueous medium, and projector image planes are located in the air dielectric in water-tight device, and light is from projection Instrument photocentre can produce refraction effect when window plane enters aqueous medium.Now, set up on the basis of light is along straightline propagation Haplopia point model no longer applicable.

The projection process of projector is contrary with the imaging process of video camera, can regard reverse video camera as.Due to refraction Light is made to there occurs bending, projector photocentre position and actual photocentre position with the description of haplopia point model are inconsistent. Treibitz etc. is in article " flat refractive geometry.ieee transactions on pattern Analysis and machine intelligence, 2012,34 (1): 51-65 " to analyze and point out, the distortion that refraction produces takes Certainly in the distance between testee and video camera, according to haplopia point model or with this distortion of radial distortion model representation, Larger error then can be produced, therefore haplopia point model is unable to accurate description projector projects process under water.But this article only considered Situation when optical axis is parallel with window plane normal vector, when optical axis and window plane normal vector are not parallel, based on this article Analysis is set up model and is still had deviation.

Knowable to above-mentioned analysis, the refraction effect that light produced due to water-tight device window, and projector optical axis with The uneven impact of window plane normal vector, traditional projector haplopia point model is no longer applicable.Therefore, study a kind of fitting Significant for the model of projector architecture light vision measuring sensor and scaling method under water.

Content of the invention

The technical problem to be solved is: provides a kind of projector for projector architecture optical sensor under water The optimization scaling method of parameter and structural parameters.

The technical solution of the present invention is: one kind under water projector calibrating method it is characterised in that the method comprise with Lower step:

1.1st, adjust positioned at projector architecture optical sensor under water it is ensured that video camera can shoot clearly in measurement range Clear image and projector can project picture rich in detail in measurement range, in the public view field model of projector and calibrating camera In enclosing, using a flat board having waterproof target, projector is to this flat board another target of projection, referred to as projection target, tune simultaneously Leveling Board position, until two target characteristic points are all located in the range of public view field；Move freely target at least three position, often A mobile position, shoots the image pair containing two targets；

1.2nd, extract the image coordinate of waterproof target characteristic point in image, according to the parameter of calibrating camera, ask for putting down Normal vector under camera coordinate system for the plate place plane；

1.3rd, extract the image coordinate projecting target characteristic point in image, using the normal vector tried to achieve in step 1.2, by Camera parameters and the image coordinate of characteristic point, the corresponding point position in space that calculating projection target is incident upon on flat board is sat in video camera Three-dimensional coordinate under mark system；

1.4th, the three-dimensional coordinate of its corresponding spatial point tried to achieve in image coordinate, and step 1.3 according to projection target, Using the structural parameters between haplopia point model preliminary labeling projection instrument parameter and projector and video camera；

1.5th, using the structural parameters obtaining in step 1.4, required normal vector in step 1.2 is represented in projector Under coordinate system；

1.6th, under projector coordinates system, given projector photocentre is along optical axis direction to the distance of water-tight device window plane Initial value, sets up light mould when air dielectric in water-tight device for the light that on projector image, each characteristic point sends is propagated Type, referred to as incident ray；

1.7th, set up the unit vector of refracted light, scale factor is gone out according to Geometric Constraint Solving, determine that refracted light is long Degree, solves the three-dimensional coordinate projecting target characteristic point under projector coordinates system；

1.8th, the three-dimensional coordinate calculating in step 1.3 is changed using the structural parameters in step 1.4 and sit to projector As reference value under mark system；

1.9th, give the initial value that projector optical axis is with respect to drift angle and corner between window plane normal vector, with step The distance between three-dimensional coordinate described in 1.7 and the reference value described in 1.8 set up object function, to proj ector parameters and structure Parameter is optimized, and carries out recursive optimization, that is, the structural parameters tried to achieve are used for step 1.5～1.8, until target function value is full Sufficient given threshold, threshold value requires to set according to certainty of measurement, and generally 10^-5To 0.1mm.

2nd, described one kind under water projector calibrating method it is characterised in that:

2.1st, the plane target drone that the waterproof target described in step 1.1 is made for waterproof material, is fixed on a flat board, waterproof Target thicknesses are negligible compared with measurement distance, and target characteristic point is the lattice point in plane, the design of distance between lattice point Determined by actual measurement distance and camera field of view etc., generally 10～100mm；Described projection target, between its lattice point Image coordinate distance determines according to the resolution of projector image, generally 10～100 pixels；

2.2nd, the waterproof target described in step 1.1 and projection target, rationally make filtering device such as optical filter in video camera Under the premise of, shared region can be overlapping on flat board for two targets；When flat board is in same position, video camera do not use filtering device and When projector does not project target, video camera shoots has to waterproof target image, when video camera uses filtering device and projector During projection target, this target and waterproof target have overlapping region, and video camera shoots to be had to project target image；

2.3rd, the image containing two targets that shoots described in step 1.1 uses filtering device to it is characterised in that working as When, each position shoots two width images, for the image pair containing waterproof target and projection target respectively.

The invention has the advantage that

First it is considered to projector under water operation when air dielectric from water-tight device for the light propagate to outside water-tight device Aqueous medium when the refraction effect that produces, establish projector light refraction model；

Second it is considered to situation when projector optical axis and water-tight device window plane normal vector are not parallel, with optical axis phase Drift angle for normal vector and corner describe this phenomenon, and draw the value of two angles by optimization method；

3rd, reasonable employment filtering device, employ waterproof target that can be overlapping and projection target, allow two targets can Take visual field simultaneously as far as possible, improve stated accuracy.

Brief description

Fig. 1 is the light refraction model schematic diagram of projector under water that the present invention sets up.

Fig. 2 is projector optical axis and the uneven schematic diagram of window plane normal vector under water.

Fig. 3 is projector calibrating method flow diagram under water.

Fig. 4 is to demarcate the target position schematic diagram that projector uses under water.

Specific embodiment

Below the present invention is described in further details.The present invention sets up the light refraction model of projector under water, to light There are proj ector parameters during the anglec of rotation in axle and water-tight device window plane normal vector and structural parameters are optimized demarcation, Achieve high-precision projector calibrating under water.

Fig. 1 show projector light refraction model schematic diagram under water.Set up projector with projector photocentre for initial point to sit Mark system o_p-x_py_pz_p, original image coordinate system is o_u- uv, (u₀,v₀) for principal point coordinate.With the principle point location on projector image Set up image coordinate system o-xy for initial point, have x=u-u₀, y=v-v₀.Define ox | | o_px_p, oy | | o_py_p.X=[x, y]^tRepresent The ideal image coordinate of any on projector image planes, x_d=[x_d,y_d]^tThe image being affected by lens distortion for reality Coordinate.Point x from projector image planes_d=[x_d,y_d]^tThe light projecting, occurs when water-tight device window plane Refraction, note incident ray is r_in, refracted light is r_out.With n=[w₁-w₂0]^tRepresent window plane under projector coordinates system Unit normal vector, wherein w₁And w₂Represent that projector optical axis with respect to the drift angle between window plane normal vector and turns respectively Angle, as shown in Fig. 2 and meetRepresent the angle between optical axis and normal vector.The method of window plane It is also denoted as to vector:

In formula, d represents from projector photocentre along optical axis direction to the distance of window plane.

Assume that center of distortion and principal point overlap it is considered to the radially and tangentially distortion of second order, have a following distortion model:

$x_d=\left[\begin{array}{c}{x}_d\\ y_d\end{array}\right]=(1+k_1{r}^2+k_2{r}^4)\left[\begin{array}{c}x\\ y\end{array}\right]+\left[\begin{array}{c}2p_{1}xy+p_2(r^2+2x^2)\\ p_1(r^2+2y^2)+2p_{1}xy\end{array}\right]---\[2\]$

K in formula₁, k₂For coefficient of radial distortion, p₁, p₂For tangential distortion coefficient, and have:

$r={\left(\frac{x-u_0}{f_x}\right)}^2+{\left(\frac{y-v_0}{f_y}\right)}^2---\[3\]$

Wherein f_xAnd f_yFor projector lens focal length component in the x and y direction.

As shown in figure 1, point (the x from projector photocentre to the plane of delineation_d,y_d) send incident ray r_in, through superrefraction Light is along r afterwards_outDirection continues to propagate until intersecting at point p (x with testee surface_p,y_p,z_p).Represent angle of incidence with γ, γ ' represents refraction angle, is had according to the law of refraction:

$\left\{\begin{array}{c}cos\mathrm{\γ}={\hat{r}}_{in}\·\hat{n}\\ {\mathrm{sin\γ}}^{\′}=\frac{\sin \mathrm{\γ}}{n_{water}}\end{array}\right.---\[4\]$

In formulaRepresent the unit vector in incident ray direction,Represent the unit vector of window plane normal vector.Incident Light r_inCan be expressed as:

$r_{in}=k{\left[\begin{array}{ccc}\frac{x_d}{f_x}& \frac{y_d}{f_y}& 1\end{array}\right]}^t---\[5\]$

In formula, k is a scale factor.Incident ray r_inMeet with window plane normal vector n:

r_inN=1 [6]

Formula [1] and [5] are substituted into [6] scale factor k can be solved.Because the thickness of water-tight device window can compared to d To ignore, then the unit vector of refracted lightCan be expressed as:

${\hat{r}}_{out}=m_1\hat{n}+m_2{\hat{r}}_{in}---\[7\]$

Wherein m₁And m₂For:

$\left\{\begin{array}{c}{m}_1={\mathrm{cos\γ}}^{\′}-m_{2}cos\mathrm{\γ}\\ m_2=\frac{1}{rfn}\end{array}\right.---\[8\]$

Wherein rfn is the refractive index of aqueous medium.

Refracted light continues to propagate, and intersects at point p with testee surface, under projector coordinates system, the coordinate of point p can To be expressed as:

$x_p=\left[\begin{array}{c}{x}_p\\ y_p\\ z_p\end{array}\right]=r_{in}+\mathrm{\β}{\hat{r}}_{out}---\[9\]$

Above formula illustrates the process of light propagation, and wherein β is scale factor, determines the length of refracted light, the value of β by The refracted light of characteristic point together decides on being imaged on the video camera light that on camera review, picture point determines.

According to above-mentioned model, the demarcation of projector under water comprises proj ector parameters (focal length, principal point coordinate, distortion factor, throwing Shadow instrument photocentre along optical axis direction to the drift angle between the distance of window plane and projector optical axis and window plane normal vector and Corner) and projector and video camera between structural parameters (rotation and translation relation) demarcation, specifically comprise the following steps that

1st, using the video camera demarcated, structured light sensor, the i.e. focal length of video camera, principal point are formed with projector Coordinate and distortion factor are it is known that camera marking method is shown in article " a flexible new technique for of zhang camera calibration.ieee transactions on pattern analysis and machine intelligence,2000,22(11):1330-1334”.

2 are attached on a flat board as shown in figure 4, making waterproof gridiron pattern target (waterproof target) red and white, this target On characteristic point be angle point spacing it is known that the setting of angle point spacing is together decided on by camera field of view and operating distance, generally 10～100mm；The red-black alternate gridiron pattern target (projection target) of projector projects, the angle point on this target is in projector image Coordinate under coordinate system is it is known that be designated as x_p=(x_pi, y_pi), i=1 ..., m, angle point spacing setting by projector image resolution Rate determines, generally 10～100 pixels.Specific image acquisition step is:

1) waterproof target is placed in the range of video camera and projector public view field, and takes camera field of view as far as possible.Beat Open projector projects red and black gridiron pattern target, adjust flat position, until projection target and waterproof target are all located at public view field In the range of；

2) red filter paper is placed in front of video camera, due to red filter paper can by the Red absorption in waterproof target, Therefore this waterproof target is rendered as unified background colour in the video camera with red filter paper.Use camera acquisition image, This image comprises only the imaging of projection target, is designated as p_i, (i=1,2,3 ... g)；

3) projector is turned off, removes red filter paper, and gather red white plate lattice waterproof target image, this image containing only There is the imaging of waterproof target, be designated as c_i, (i=1,2,3 ... g)；

4) repeat 1)～3) step, until gathering enough map sheet numbers, need at least gather 3 to image.

It is reasonable employment light filter of the present invention using red white plate lattice waterproof target and red-black gridiron pattern projection target One of example of part, any in a similar manner using filtering device demarcation mode all in protection domain.

3rd, extract image c_iThe image coordinate of middle angle point, according to the video camera of demarcation, calculates image c_iMiddle plateform is located flat Normal vector under camera coordinate system for the face, referring to hartley r.i., zisserman is written for computational methods " multiple view geometry in computer vision, cambridge university press, 2004 ".

4th, extract image p_iBy the image coordinate of camera parameters and angle point, the image coordinate of middle angle point, determines that one is penetrated Line, using the plane normal vector tried to achieve in this ray and step 3, can image in the hope of the projection target being incident upon on flat board Three-dimensional coordinate under machine coordinate system

5th, the projector image coordinate x according to projection target angle point_p, and its corresponding spatial point tried to achieve in step 4 Three-dimensional coordinateUsing haplopia point model, the preliminary labeling projection instrument parameter and projector structure ginseng between video camera Number, concrete grammar writes " " key technology research of binocular stereo vision detection ", BJ University of Aeronautics ＆ Astronautics doctor referring to Zhou Fuqiang Research work report afterwards, 2002 ".

6th, using the structural parameters obtaining in step 5, represent the flat board place plane normal direction under projector coordinates system to Amount

$n_i^p=\frac{r^{-1}\·n_i^c}{1-r^{-1}{t}^t\·r\·n_i^c}---\[10\]$

In formula, structural parameters r and t is respectively spin matrix and the translation vector that camera coordinates are tied to projector coordinates system.

7th, give projector photocentre along optical axis direction to window plane apart from d initial value, such as when projector lens distance When window plane is close, d=0 can be made；Set projector optical axis with respect to the drift angle w between window plane normal vector₁With Corner w₂Initial value be 0.Using image p_iIn angle point image coordinate, set up each angle point and sent by formula [1]～formula [6] Ray model when propagating for the air dielectric in water-tight device for the light, referred to as incident ray r_in.

8th, according to the every incident ray r setting up in step 7_in, corresponding refracted light is set up by formula [7] and formula [8] Unit vectorDetermine the ray trajectory corresponding to each angle point, next it needs to be determined that scale factor β in formula [9], So that it is determined that refracted light is wherein intersected with flat board.

9th, had according to geometrical constraint:

${\left[\begin{array}{ccc}{x}_p& y_p& z_p\end{array}\right]}^t\·n_i^p=1---\[11\]$

Formula [9] is substituted into formula [11], scale factor β can be solved by following formula.

$\mathrm{\β}=\frac{1-{\left(n_i^p\right)}^t\·{\hat{r}}_{in}}{{\left(n_i^p\right)}^t\·{\hat{r}}_{out}}---\[12\]$

10th, scale factor β tried to achieve in step 9 is substituted into [9] formula, you can try to achieve projection target institute under projector coordinates system It is incident upon the three-dimensional coordinate x of corresponding spatial point on flat board_p.

11st, by the three-dimensional coordinate calculating in step 4Changed to projector coordinates system using the structural parameters in step 6 It is down

12nd, willAs reference value, with its three-dimensional coordinate x with gained in step 10_pThe distance between set up target letter Number:

$\underset{i=1}{\overset{g}{\σ}}\underset{j=1}{\overset{m}{\σ}}||x_p-{\tilde{x}}_p(f_x,f_y,u_0,v_0,d,w_1,w_2,k_1,k_2,p_1,p_2,r,t)||---\[13\]$

Using in step 5, proj ector parameters obtained by calibrating and structural parameters are as at the beginning of the initial value of Optimizing Search, distortion factor Value is all set to 0, and other parameters initial value is referring to step 7.Using levenberg-marquardt algorithm, non-thread is carried out to formula [13] Property optimize, the structural parameters r that optimization is obtained, t are applied to the Coordinate Conversion of step 6 and step 11, carry out recursive search parameter Optimal value, until target function value be less than set range error threshold value, threshold value according to certainty of measurement require setting, generally 1e-5 to 0.1mm.

Embodiment

Using the projector of 3500 lumens, resolution is 1024 pixel × 768 pixels.Projector is loaded in water-tight device Fixing, and the fiber optic camera machine being 1024 pixel × 768 pixels with resolution forms structured light sensor.Projector and video camera Relative position is fixed.

The waterproof target making is red white plate lattice target, and between the angle point of target, distance is 34.75mm.The projection of design Target is red-black gridiron pattern target, and the image distance between its angle point is 64 pixels.Using image-pickup method of the present invention, Structured light sensor is put in experiment pond and acquires 10 groups of totally 20 images.Carry out projector using the method for the invention And structural parameters calibration, the results are shown in Table 1.Table 2 is reference value three-dimensional coordinate and is calculated between three-dimensional coordinate using model Root-mean-square error.

Can be seen that using projector calibrating method under water proposed by the present invention from the data of Tables 1 and 2, demarcation obtains Proj ector parameters and structural parameters reliable results, the stated accuracy of the method disclosure satisfy that qualitative monitoring and quantitative measurement under water Task.

Table 1 projector architecture optical sensor calibration result

The root-mean-square error of table 2 three-dimensional coordinate

The above is embodiments of the invention, is not intended to limit protection scope of the present invention.

Claims (2)

1. one kind under water projector calibrating method it is characterised in that the method includes the steps of:

1.1st, adjust positioned at projector architecture optical sensor under water it is ensured that video camera being capable of shooting clear figure in measurement range As and projector can project picture rich in detail in measurement range, in the public view field scope of projector and calibrating camera Interior, using a flat board having waterproof target, projector is to this flat board another target of projection, referred to as projection target, adjustment simultaneously Flat position, until two target characteristic points are all located in the range of public view field；Move freely target at least three position, often move A dynamic position, shoots the image pair containing two targets；

1.2nd, extract the image coordinate of waterproof target characteristic point in image, according to the parameter of calibrating camera, ask for flat board institute In normal vector under camera coordinate system for the plane；

1.3rd, extract the image coordinate projecting target characteristic point in image, using the normal vector tried to achieve in step 1.2, by imaging Machine parameter and the image coordinate of characteristic point, calculate projection target and are incident upon corresponding point position in space on flat board in camera coordinate system Under three-dimensional coordinate；

1.4th, the three-dimensional coordinate of its corresponding spatial point tried to achieve in image coordinate, and step 1.3 according to projection target, utilizes Haplopia point model, is tentatively demarcated to projector architecture optical sensor, and the parameter of demarcation is proj ector parameters and represents throwing The structural parameters of rigid body translation between shadow instrument and video camera；

1.5th, using the structural parameters obtaining in step 1.4, required normal vector in step 1.2 is represented in projector coordinates Under system；

1.6th, under projector coordinates system, given projector photocentre is along optical axis direction at the beginning of the distance of water-tight device window plane Value, sets up ray model when air dielectric in water-tight device for the light that on projector image, each characteristic point sends is propagated, Referred to as incident ray；

1.7th, set up the unit vector of refracted light, scale factor is gone out according to Geometric Constraint Solving, determine refracted light length, ask The three-dimensional coordinate of target characteristic point is projected under solution projector coordinates system；

1.8th, the three-dimensional coordinate calculating in step 1.3 is changed to projector coordinates system using the structural parameters in step 1.4 Lower as reference value；

1.9th, give the initial value that projector optical axis is with respect to drift angle and corner between window plane normal vector, with step 1.7 The distance between reference value described in described three-dimensional coordinate and 1.8 sets up object function, to proj ector parameters and structural parameters It is optimized, and carries out recursive optimization, that is, the structural parameters tried to achieve are used for step 1.5～1.8, set until target function value meets Determine threshold value, threshold value requires to set according to certainty of measurement, in the range from 10^-5～0.1mm.

2. one kind according to claim 1 under water projector calibrating method it is characterised in that:

2.1st, the plane target drone that the waterproof target described in step 1.1 is made for waterproof material, is fixed on a flat board, waterproof target Thickness is negligible compared with measurement distance, and target characteristic point is the lattice point in plane, and between lattice point, the design of distance is by reality Border measurement distance and camera field of view determine, in the range from 10～100mm；Described projection target, the image between its lattice point Coordinate distance determines according to the resolution of projector image, in the range from 10～100 pixels；

2.2nd, the waterproof target described in step 1.1 and projection target, on the premise of video camera reasonable employment filtering device, two targets Being marked on shared region on flat board can be overlapping；When flat board is in same position, video camera does not use filtering device and projector is not thrown Shoot at the target timestamp, video camera shoots has to waterproof target image, when video camera uses filtering device and projector projects target, This target and waterproof target have overlapping region, and video camera shoots to be had to project target image；

2.3rd, shoot the image containing two targets to it is characterised in that when using filtering device, often described in step 1.1 One position shoots two width images, for the image pair containing waterproof target and projection target respectively.