CN1203292C - Method and system for measruing object two-dimensiond surface outline - Google Patents

Abstract

The present invention relates to a method and a system for measuring the outline of the three-dimensional surface of an object, which belongs to the technical field of the three-dimensional measurement of the object. The present invention is characterized in that the present invention uses the combination of a phase and stereo vision technique for projecting a grating on the object surface, grating images occurring aberrance are shot by using two cameras, and each point of phase on the images shot by a left camera and a right camera is obtained by using encoding light and a phase-shifting method. The phase and an outer polar line are used for realizing point matching on two images so that a calibrated camera system can be used for calculating the coordinate of the point in three-dimensional space to measure the three-dimensional outline of the object surface. The present invention has the advantages of non-contact, high speed, large data quantity, high precision, simple operation, easy realization, etc. Only 2 seconds are needed to measure the single surface of the object, high-density data can be obtained and reaches 400, 000 points, and measured precision is more than 0.05mm.

Description

The method of Measuring Object three-dimensional surface profile

Technical field

The method of Measuring Object surface tri-dimensional profile belongs to three-dimensional measurement of objects method and technology field.

Background technology

The three-dimensional measurement technology of object is very universal in fields such as product design and manufacturing, quality testing and control, robot vision.It used product image, rapid manufacture system, the anti-fields such as design, online detection, clothing making, video display stunt, virtual reality, artistic sculpture of asking of product of also being extended in the last few years.

It is contact and contactless that measuring three-dimensional profile mainly contains two class methods.The main method of contact type measurement is a three-coordinates measuring machine, and its measuring accuracy height can reach 0.5 μ m.But this method is not suitable for soft in kind measurement, and measuring speed is slow, working environment is required very high, must be shockproof, anti-gray, constant temperature etc., so range of application is subjected to bigger restriction.As a whole, the demand that the mechanical type three-coordinates measuring machine is difficult to satisfy now fast, high-level efficiency is measured.

Non-contacting method for three-dimensional measurement has: optical sensor method, laser scanning method, stereo vision method, projection gate phase method etc.

1. optical sensor method

The principle of work of this method is similar to the mechanical type three-coordinates measuring machine, only adopts special optic probe to come the inspected object surface configuration.Its optic probe can directly obtain the distance between measured point and the probe, obtains coordinate on other both direction by its working position.Japan Toshiba company has developed one and has been used for the non-contact optical detection instrument that the large-scale high-precision optical surface is measured, and the surface shape measurement precision reaches 0.1 μ m, and roughness is to 1nmRa, is installed on the worktable of super smart CNC lathe to use.Its gordian technique is the manufacturing of optic probe, belongs to precision instrument and equipment, therefore involves great expense.

2. laser scanning method

This method is utilized the laser scanning body surface, determines the three-dimensional coordinate of object each point by the geometry imaging relations between eye point, subpoint and the imaging point three.Characteristics and character according to the work LASER Light Source can be divided into point type laser scanning, linear laser scanning etc.The speed of laser scanning is than piece, but scanning accuracy but is subjected to the influence of factors such as the material of workpiece and character of surface.In addition, the price of laser scanning system is very expensive, and non-general user can bear.

3. stereo vision method

Stereo vision method is to set up according to the bionics principle of people's binocular vision system, and this method can reach certain measuring accuracy.It utilizes the parallax of corresponding point can calculate steric information within the vision according to principle of triangulation, is used for binocular and used for multi-vision visual.

This method requires looser to the application scenario, once can obtain the three-dimensional information in a zone, particularly has the advantage that not influenced by the body surface reflection characteristic.But being difficult to resolve, the matching problem of corresponding point wherein determines, the algorithm complexity is consuming time longer.When the body surface unique point is more sparse, also be difficult to obtain accurate shape.

4. projection gate phase method

Projection gate adopts at body surface projection grid line, utilizes the phase distortion information of modulating grid line to obtain the three-dimensional information of object, and its adopts the method demodulation phase of mathematics, and utilizes phase value to calculate each height value with respect to reference surface.The very big problem that the projection gate phase method exists is that its system operation is bad, is difficult to realize practicability.

Summary of the invention

The purpose of this method is to provide a kind of method of measuring accurately, being convenient to operate and be easy to the Measuring Object three-dimensional surface profile of practicability, to utilize the combination of phase place and stereovision technique for the proposition that reaches this purpose initiative of the present invention, at body surface projection grating, adopt twin camera to take image, utilize phase place and polar curve to realize coupling, thereby reach the counter of object dimensional coordinate asked and reconstruct, developed that operability is good, measuring accuracy is higher, speed is fast, be suitable for the novel three-dimensional noncontacting measurement system of different big wisps.

Light (being called structured light) with certain specific character projects on the object, and the point of differing heights is modulated grating grating is distorted on the object.Take the raster image that distortion takes place with two video cameras, utilize encoded light and phase shifting method to obtain left and right cameras and take the phase place that image is gone up every bit.Utilize phase place and outer polar curve to realize the coupling of the point on two width of cloth images for how much.To the camera chain of having calibrated, just can calculate it at three-dimensional coordinate.

The method of the Measuring Object three-dimensional surface profile that the present invention proposes, it is characterized in that it is a kind of combination that utilizes phase place and stereovision technique, at body surface projection grating, adopt twin camera to take the raster image that distortion takes place again, utilize encoded light and phase shifting method to obtain the phase place of every bit on the left and right cameras photographic images.Utilize phase place and outer polar curve to realize the coupling of the point on two width of cloth images, thereby reach the anti-method of asking body surface point three-dimensional coordinate; It comprises the steps:

(1) utilizes computing machine to generate virtual grating,, utilize projector that the grating that generates is incident upon on the object comprising encode grating and phase-shifted grating;

The light intensity of phase-shifted grating is as shown in the formula expressing:

I _i(u，v)＝a(u，v)+b(u，v)cos(φ(u，v)+φ _i)

Wherein:

(u v) is the coordinate of certain point;

I _i(u v) is (u, a light intensity v) in the i width of cloth image;

(u v) is the bias light majorant to a;

(u v) is a fringe contrast to b;

(u v) represents the phase place of each point to φ, and the cycle is T; φ _iBe angle of phase displacement;

Encode grating has the N width of cloth, and building method is that first width of cloth is partly to deceive partly in vain, and each width of cloth of back segments gradually, and divided method is the black part of a last width of cloth, is divided into partly deceiving partly in vain, and the white of a last width of cloth is divided into partly and partly deceives in vain.To each point, according to then being encoded to 1 still for encoding in vain for deceiving for black on each width of cloth image in each width of cloth image, for then being encoded to 0 in vain, thereby obtain the coded sequence of this point; N width of cloth encode grating can have 2 ^NIndividual coded sequence, whole image is divided into 2 ^NIndividual rectangular, each rectangular width is the period T of phase-shifted grating; To n rectangular (n=1,2 ... 2 ^N, claim periodicity again), according to the corresponding unique encoding sequence of such encoded light building method, its decimal-coded digit is nc, sets up the mapping relations between periodicity n and the coded number nc, can realize both mutual conversions;

(2) utilize the raster image of two ccd video camera collection projections, and be kept in the array of distributing in the program;

(3) each width of cloth image that each camera is taken is handled respectively, obtain the phase value of each point, phase value adds that by the phase main value periodicity multiply by 2 π, be 2n π, because the phase value of each point that two video cameras are taken should equate, take each some phase value of obtaining as the foundation of mating with two video cameras;

(4) two video cameras are calibrated, obtained the intrinsic parameter of video camera and with respect to the outer parameter of world coordinate system: f ^(j), R ^(j), T ^(j), j=1,2

f ^(j): lens focus length, j is a camera number;

R ^(j): rotation matrix, $R=\left[\begin{array}{ccc}{r}_1& r_2& r_3\\ r_4& r_5& r_6\\ r_7& r_8& r_9\end{array}\right];$

T ^(j): translation vector, T=[TxTyTz] ';

Calculate R, Tx, Ty earlier;

(4.1) calculate the image coordinate of each point

u＝u ₀+x/dx

v＝v ₀+y/dy

To the point in space (Xw, Yw, Zw), after video camera is taken, image coordinate (mm) be (x, y), pixel coordinates be (u, v), (u ₀, v ₀) be the pixel coordinate of initial point in pixel coordinate system of image coordinate system, (dx is the x between the CCD adjacent image point and the distance of y direction dy), is provided by CCD producer.

(4.2) calculate five unknown quantity Ty ^-1r ₁, Ty ^-1r ₂, Ty ^-1Tx, Ty ^-1r ₄, Ty ^-1r ₅

For each three dimensional object point (Xw _k, Yw _k, Zw _k) (because the some coplane, so the Z coordinate is got work 0) and corresponding image coordinate (x _k, y _k), by collinearity equation:

$x_k=f\frac{r_{1}X{w}_k+r_{2}Y{w}_k+\mathrm{Tx}}{r_{7}X{w}_k+r_{8}Y{w}_k+\mathrm{Tz}}$

$y_k=f\frac{r_{4}X{w}_k+r_{5}Y{w}_k+\mathrm{Ty}}{r_{7}X{w}_k+r_{8}Y{w}_k+\mathrm{Tz}}$

Top two formulas are divided by obtain: utilize least square method to try to achieve above-mentioned 5 unknown quantitys; (4.3) calculate r ₁..., r ₉, Tx, Ty

(4.31) calculate | Ty|

The definition matrix:

$C=\left[\begin{array}{cc}{r_1}^{\&prime;}& {{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="C0315350400191.png"\; state="\{\{state\}\}">r</figure-callout>}}_2}^{\&prime;}\\ {{\mathrm{<figure-callout\; id="4"\; label="r"\; filenames="C0315350400191.png"\; state="\{\{state\}\}">r</figure-callout>}}_4}^{\&prime;}& {r_5}^{\&prime;}\end{array}\right]=\begin{array}{c}\left[\begin{array}{cc}{r}_1/\mathrm{Ty}& {\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="C0315350400191.png"\; state="\{\{state\}\}">r</figure-callout>}}_2/\mathrm{Ty}\\ {\mathrm{<figure-callout\; id="4"\; label="r"\; filenames="C0315350400191.png"\; state="\{\{state\}\}">r</figure-callout>}}_4/\mathrm{Ty}& r_5/\mathrm{Ty}\end{array}\right]\end{array}$

Then have:

${\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="C0315350400191.png"\; state="\{\{state\}\}">y</figure-callout>}}^2=\frac{Sr-{[S{r}_2-4{({r_1}^{\&prime;}{r_5}^{\&prime;}-{{\mathrm{<figure-callout\; id="4"\; label="r"\; filenames="C0315350400191.png"\; state="\{\{state\}\}">r</figure-callout>}}_4}^{\&prime;}{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="C0315350400191.png"\; state="\{\{state\}\}">r</figure-callout>}}_2}^{\&prime;})}^2]}^{1/2}}{2{({r_1}^{\&prime;}{r_5}^{\&prime;}-{{\mathrm{<figure-callout\; id="4"\; label="r"\; filenames="C0315350400191.png"\; state="\{\{state\}\}">r</figure-callout>}}_4}^{\&prime;}{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="C0315350400191.png"\; state="\{\{state\}\}">r</figure-callout>}}_2}^{\&prime;})}^2}$

Wherein:

Sr＝r ₁′ ²+r ₂′ ²+r ₅′ ²+r ₄′ ²，

If certain row of Matrix C or certain column element are calculated as follows for being 0 entirely:

Ty ²=(r _i' ²+ r _j' ²) ^-1, r wherein _i', r _j', be remaining two elements in addition of Matrix C.

(4.32) symbol of decision Ty

1. suppose that Ty is a positive sign;

2. select in the captured image, from picture centre far away a bit.If its image coordinate is (x _k, y _k), the coordinate in three-dimensional world is (Xw _k, Yw _k, Zw _k).

3. calculate following various value by top result:

r ₁＝(Ty ^-1r ₁)*Ty，r ₂＝(Ty ^-1r ₂)*Ty，r ₄＝(Ty ^-1r ₄)*Ty

r ₅＝(Ty ^-1r ₅)*Ty，Tx＝(Ty ^-1Tx)*Ty，

x _k′＝r ₁Xw _k+r ₂Yw _k+Tx

y _k′＝r ₄Xw _k+r ₅Yw _k+Ty

If x _kAnd x _k', y _kAnd y _k' jack per line all, sgn (Ty)=+ 1 so, otherwise sgn (Ty)=-1;

(4.33) calculate rotation matrix R

Value according to Ty recomputates r ₁, r ₂, r ₄, r ₅, Tx.

$R=\left[\begin{array}{ccc}{r}_1& r_2& {(1-{r_1}^2-{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="C0315350400191.png"\; state="\{\{state\}\}">r</figure-callout>}}_2}^2)}^{1/2}\\ r_4& r_5& s{(1-{{\mathrm{<figure-callout\; id="4"\; label="r"\; filenames="C0315350400191.png"\; state="\{\{state\}\}">r</figure-callout>}}_4}^2-{r_5}^2)}^{1/2}\\ r_7& r_8& r_9\end{array}\right]$

S=sgn (r wherein ₁r ₄+ r ₂r ₅)

r ₇, r ₈, r ₉Be to obtain by preceding two appositions of going.

If calculating following focal distance f according to such R is negative value, then:

$R=\left[\begin{array}{ccc}{r}_1& r_2& -{(1-{r_1}^2-{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="C0315350400191.png"\; state="\{\{state\}\}">r</figure-callout>}}_2}^2)}^{1/2}\\ r_4& r_5& -s{(1-{{\mathrm{<figure-callout\; id="4"\; label="r"\; filenames="C0315350400191.png"\; state="\{\{state\}\}">r</figure-callout>}}_4}^2-{r_5}^2)}^{1/2}\\ -r_7& -r_8& r_9\end{array}\right]$

Then calculate focal length f and T _zValue

To each calibration point, foundation comprises f and T _zLinear equation as unknown parameter:

$[Y_i-y_i]\left[\begin{array}{c}f\\ \mathrm{Tz}\end{array}\right]=w_i{y}_i$

Wherein:

Y _i＝r ₄x _wi+r ₅y _wi+r ₆*0+Ty

w _i＝r ₇x _wi+r ₈y _wi+r ₉*0

By solving an equation, can ask f and T _z

(5) carry out three-dimensionalreconstruction according to phase place and outer polar curve geometry to every, obtain the three-dimensional coordinate of body surface point:

(5.1) calculate basis matrix F

F＝A ₂ ^-TEA ₁ ^-1

Wherein

$A_2=\left[\begin{array}{ccc}{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="C0315350400191.png"\; state="\{\{state\}\}">f</figure-callout>}}_2/\mathrm{<figure-callout\; id="2"\; label="d\; x"\; filenames="C0315350400191.png"\; state="\{\{state\}\}">d</figure-callout>}{x}_{}{}_2& 0& u_{02}\\ 0& {\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="C0315350400191.png"\; state="\{\{state\}\}">f</figure-callout>}}_2/d{y}_2& v_{02}\\ 0& 0& 1\end{array}\right],$ $A_1=\left[\begin{array}{ccc}{f}_1/d{x}_1& 0& u_{01}\\ 0& f_1/d{y}_1& v_{01}\\ 0& 0& 1\end{array}\right]$

F wherein ₁, (u ₀₁, v ₀₁), dx ₁, dy ₁Be the intrinsic parameter of first video camera,

f ₂, (u ₀₂, v ₀₂), dx ₂, dy ₂It is the intrinsic parameter of second video camera;

$E={\left[T\right]}_x{R}^{\left(2\right)}{R}^{{\left(1\right)}^{-1}}$ (being called essential matrix, Essential Matrix)

$T=T^{\left(2\right)}-R^{\left(2\right)}{R}^{{\left(1\right)}^{-1}}{T}^{\left(1\right)}$

T is expressed as [Tx, Ty, Tz], then antisymmetric matrix is [T] _x

${\left[T\right]}_x=\left[\begin{array}{ccc}0& -\mathrm{Tz}& \mathrm{Ty}\\ \mathrm{Tz}& 0& -\mathrm{Tx}\\ -\mathrm{Ty}& \mathrm{Tx}& 0\end{array}\right]$

(5.2) calculate 1 P on the right video camera photographic images, its coordinate is

Its polar curve equation parameter on left video camera photographic images.And on above-mentioned straight line, seek its match point Q point, method is that the phase value of a P and some Q equates.

Known

According to following straight-line equation, look for the some Q of some P on left video camera photographic images on the right video camera photographic images, its coordinate is

${{\tilde{m}}_2}^{T}F{\tilde{m}}_1=0,$

Wherein:

Be the pixel coordinate (u that P is ordered ₂, v ₂, 1) ^T

Be Q point pixel coordinate (u ₁, v ₁, 1) ^T

According to a P and the equal principle of some Q phase place, on straight line, seek the Q point by above-mentioned straight-line equation decision.

(5.3) find the Q point, then store this match point, according to following three dimensions point S (Xw, Yw, Zw) and the pass of the correspondence image coordinate of two video camera photographic images be:

$x^{\left(j\right)}=f^{\left(j\right)}\frac{{R^{\left(j\right)}}_{11}\mathrm{Xw}+{R^{\left(j\right)}}_{12}\mathrm{Yw}+{R^{\left(j\right)}}_{13}\mathrm{Zw}+T^{\left(j\right)}x}{{R^{\left(j\right)}}_{31}\mathrm{Xw}+{R^{\left(j\right)}}_{32}\mathrm{Yw}+{R^{\left(j\right)}}_{33}\mathrm{Zw}+T^{\left(j\right)}z},$

$y^{\left(j\right)}=f^{\left(j\right)}\frac{{R^{\left(j\right)}}_{21}\mathrm{Xw}+{R^{\left(j\right)}}_{22}\mathrm{Yw}+{R^{\left(j\right)}}_{23}\mathrm{Zw}+T^{\left(j\right)}y}{{R^{\left(j\right)}}_{31}\mathrm{Xw}+{R^{\left(j\right)}}_{32}\mathrm{Yw}+{R^{\left(j\right)}}_{33}\mathrm{Zw}+T^{\left(j\right)}z},$

J=1,2, be the numbering of video camera.

The angle of phase displacement φ of described phase-shifted grating _i=i*90, i=1 ... 4, promptly the phase-shifted grating image has 4 width of cloth, and its phase main value computing formula is:

$\mathrm{\&phi;}(u,v)=a\tan \left(\frac{I_2-I_4}{I_3-I_1}\right),$ I wherein ₁, I ₂, I ₃, I ₄, be point (u, the v) phase place in four width of cloth phase-shifted gratings.

Described encode grating has 7 width of cloth, and the binary code sequence of every bit can change into this position in image, i.e. periodicity.

The system of the Measuring Object three-dimensional surface profile that the present invention proposes is characterized in that it contains computing machine, projector, two ccd video cameras.

Experimental results show that the present invention has noncontact, speed is fast, data volume is big, precision is high, simple to operate, be easy to advantages such as realization.

Description of drawings

Fig. 1: the synoptic diagram of system of the present invention.

Fig. 2: the calibrating block that camera calibration is used.

Fig. 3: two-phase method camera calibration program flow diagram.

Fig. 4: three-dimensionalreconstruction algorithm flow chart.

Fig. 5: staff measurement result synoptic diagram.

Embodiment

The embodiment of the method for a kind of three-dimensional measurement that the present invention proposes is in conjunction with being described as follows:

The measuring system of present embodiment as shown in Figure 1.Native system is by ccd video camera 1,3, projector 2, computing machine 4 compositions such as grade.

Computing machine has 1394 image cards for PIII 1G, and video card is supported dual screen output.

The ASKC20+ HD digital projector that system adopts, its brightness is the 1500ANSI lumen, resolution is 800 * 600.

CCD adopts the A302f digital camera of German Basler company, and its resolution has reached 780 * 582, meets the IEEE1394 industrial standard, cooperates Computar M1214-MP tight shot to use.

The step that method is taked is as follows, and wherein the realization of software adopts Visual C++6.0 platform to develop:

1) utilizes computing machine to generate virtual grating,, utilize projector that the grating that generates is incident upon on the object comprising encode grating and phase-shifted grating;

The light intensity of phase-shifted grating is as shown in the formula expressing:

I _i(u，v)＝a(u，v)+b(u，v)cos(φ(u，v)+φ _i) (1)

Wherein:

(u v) is the coordinate of certain point;

I _i(u v) is (u, a light intensity v) in the i width of cloth image;

(u v) is the bias light majorant to a;

(u v) is a fringe contrast to b;

(u v) represents the phase place of each point to φ, and the cycle is T;

For the phase shift of every interval 90 degree, φ _i=i*90, i=1 ... 4,

During phase-shifted grating, the rastered picture size is 1024 * 768 at structure, and the cycle size of grating is 8 promptly the integers of coordinate x span between (1,1024), the integer of y value between (1,768).(x y) gets 0 to a, and (x y) gets 255 to b.Each some phase value φ (x, y) be set to x divided by 8 remainders that obtain divided by 8, multiply by 2 π again.

Encode grating has 7 width of cloth, and building method is that first width of cloth is partly to deceive partly in vain, and each width of cloth of back segments gradually, and divided method is the black part of a last width of cloth, is divided into partly deceiving partly in vain, and the white of a last width of cloth is divided into partly and partly deceives in vain.To each point, according to then being encoded to 1 still for encoding in vain for deceiving for black on each width of cloth image in each width of cloth image, for then being encoded to 0 in vain, thereby obtain the coded sequence of this point; 7 width of cloth encode gratings can have 2 ⁷Individual coded sequence, whole image is divided into 2 ⁷Individual rectangular, each rectangular width is the cycle 8 of phase-shifted grating; To n rectangular (n=1,2 ... 2 ⁷), according to the corresponding unique encoding sequence of such encoded light building method, its decimal-coded digit is nc, sets up mapping relations between each periodicity n and the coded number nc according to such method, can realize both mutual conversions;

2) utilize the rastered picture of two ccd video camera collection projections, and be kept in the array of distributing in the program.

3) 11 images that each camera is taken are handled respectively, obtain the phase value of each point, and phase value adds that by the phase main value periodicity multiply by 2 π.

Phase main value computing formula is in the phase-shift method:

$\mathrm{\&phi;}(u,v)=a\tan \left(\frac{I_2-I_4}{I_3-I_1}\right)---\left(2\right)$

I wherein ₁, I ₂, I ₃, I ₄, be point (u, the v) light intensity in four width of cloth phase-shifted gratings.

To seven width of cloth encode gratings, pass through image processing technique, image is carried out binary conversion treatment, can try to achieve each point to each is stain (being encoded to 1) or white point (being encoded to 0) in every images, comprehensive 7 images, can obtain coded sequence,, coded sequence is converted into periodicity n then according to the mapping relations between coded number and the periodicity.The phase place of each point adds that by the phase main value 2n π can obtain.

Concerning same point, according to the phase place of calculating above the location independent taken with video camera, that is to say should equate at each point that two video cameras are taken.Thereby the phase value of our each point of taking with two video cameras is as the foundation of coupling.

4) two video cameras are calibrated, the calibrating block of using in the calibration as shown in Figure 2.Camera calibration is to try to achieve the intrinsic parameter of video camera and with respect to the process of the outer parameter of world coordinate system.To the point in space (Xw, Yw, Zw), after video camera is taken, image coordinate (mm) be (x, y), pixel coordinates (pixel) be (u, v):

$x=f\frac{r_1\mathrm{Xw}+{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="C0315350400191.png"\; state="\{\{state\}\}">r</figure-callout>}}_2\mathrm{Yw}+{\mathrm{<figure-callout\; id="3"\; label="r"\; filenames="C0315350400191.png"\; state="\{\{state\}\}">r</figure-callout>}}_3\mathrm{Zw}+\mathrm{Tx}}{r_7\mathrm{Xw}+r_8\mathrm{Yw}+r_9\mathrm{Zw}+\mathrm{Tz}}$

$y=\mathrm{<figure-callout\; id="4"\; label="f\; r"\; filenames="C0315350400191.png"\; state="\{\{state\}\}">f</figure-callout>}\frac{r_{}}{}\frac{{}_4\mathrm{Xw}+r_5\mathrm{Yw}+r_6\mathrm{Zw}+\mathrm{Ty}}{r_7\mathrm{Xw}+r_8\mathrm{Yw}+r_9\mathrm{Zw}+\mathrm{Tz}}---\left(3\right)$

u＝u ₀+x/dx

v＝v ₀+y/dy (4)

Wherein:

$R=\left[\begin{array}{ccc}{r}_1& r_2& r_3\\ r_4& r_5& r_6\\ r_7& r_8& r_9\end{array}\right],$ T=[TxTyTz] ' be rotation matrix and translation vector, f is a lens focus, is the parameter that will demarcate.

(u ₀, v ₀) be the pixel coordinate of initial point in pixel coordinate system of image coordinate system, be 780*582 to our resolution of video camera, (u ₀, v ₀) value is (390,291).(dx is the x between the CCD adjacent image point and the distance of y direction dy), can be provided by CCD producer.

Calibrating block in the calibration is a Precision Machining, and the three-dimensional coordinate of each point is accurately to know, utilizes the image processing radix can obtain the image coordinate of each point.In native system, take the dual stage process of Tsai to obtain the rotation matrix R of video camera, translation matrix T, focal distance f.Idiographic flow as shown in Figure 3, its process is as follows:

Stage 1: calculate rotation matrix R, Tx, Ty

(4.1) computed image coordinate

According to (4) formula calculate each monumented point image coordinate (x, y).

(4.2) calculate five unknown quantity Ty ^-1r ₁, Ty ^-1r ₂, Ty ^-1T _x, Ty ^-1r ₄, Ty ^-1r ₅For each three dimensional object point (Xw _k, Yw _k, Zw _k) (because the some coplane, so the Z coordinate is got work 0) and corresponding image coordinate (x _k, y _k), by collinearity equation:

$x_k=f\frac{r_{1}X{w}_k+r_{2}Y{w}_k+\mathrm{Tx}}{r_{7}X{w}_k+r_{8}Y{w}_k+\mathrm{Tz}}$

$y_k=f\frac{r_{4}X{w}_k+r_{5}Y{w}_k+\mathrm{Ty}}{r_{7}X{w}_k+r_{8}Y{w}_k+\mathrm{Tz}}---\left(5\right)$

Top two formulas are divided by obtain:

[y _kXw _k y _kYw _k y _k -x _kXw _k -x _kYw _k]L＝x _k (6)

Wherein:

L＝[Ty ^-1r ₁ Ty ^-1r ₂ Ty ^-1Tx Ty ^-1r ₄ Ty ^-1r ₅] ^T (7)

In following formula, 5 unknown numbers are arranged, the number of our point is generally a lot, utilizes least square method to try to achieve solution of equations.

(4.3) calculate r ₁..., r ₉, Tx, Ty

(4.31) calculate | Ty|

The definition matrix:

$C=\left[\begin{array}{cc}{r_1}^{\&prime;}& {{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="C0315350400191.png"\; state="\{\{state\}\}">r</figure-callout>}}_2}^{\&prime;}\\ {{\mathrm{<figure-callout\; id="4"\; label="r"\; filenames="C0315350400191.png"\; state="\{\{state\}\}">r</figure-callout>}}_4}^{\&prime;}& {r_5}^{\&prime;}\end{array}\right]=\left[\begin{array}{cc}{r}_1/\mathrm{<figure-callout\; id="2"\; label="Ty\; r"\; filenames="C0315350400191.png"\; state="\{\{state\}\}">Ty</figure-callout>}& r_{}{}_2/\mathrm{<figure-callout\; id="4"\; label="Ty\; r"\; filenames="C0315350400191.png"\; state="\{\{state\}\}">Ty</figure-callout>}& \\ r_{}{}_4/\mathrm{Ty}& r_5/\mathrm{Ty}\end{array}\right]---\left(8\right)$

Then have:

$\mathrm{<figure-callout\; id="2"\; label="T\; y"\; filenames="C0315350400191.png"\; state="\{\{state\}\}">T</figure-callout>}{y}^{}{}^2=\frac{{\mathrm{Sr}-[S{r}_2-4{({r_1}^{\&prime;}{r_5}^{\&prime;}-{{\mathrm{<figure-callout\; id="4"\; label="r"\; filenames="C0315350400191.png"\; state="\{\{state\}\}">r</figure-callout>}}_4}^{\&prime;}{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="C0315350400191.png"\; state="\{\{state\}\}">r</figure-callout>}}_2}^{\&prime;})}^2]}^{1/2}}{2{({r_1}^{\&prime;}{r_5}^{\&prime;}-{{\mathrm{<figure-callout\; id="4"\; label="r"\; filenames="C0315350400191.png"\; state="\{\{state\}\}">r</figure-callout>}}_4}^{\&prime;}{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="C0315350400191.png"\; state="\{\{state\}\}">r</figure-callout>}}_2}^{\&prime;})}^2}---\left(9\right)$

Wherein:

Sr＝r ₁′ ²+r ₂′ ²+r ₅′ ²+r ₄′ ²， (10)

If certain row of Matrix C or certain column element are calculated as follows for being 0 entirely:

Ty ²=(r _i' ²+ r _j' ²) ^-1, r wherein _i', r _j', be remaining two elements in addition of Matrix C.

(4.32) symbol of decision Ty

1. suppose that Ty is a positive sign;

2. select in the captured image, from picture centre far away a bit.If its image coordinate is (x _k, y _k), the coordinate in three-dimensional world is (Zw _k, Yw _k, Zw _k).

3. calculate following various value by top result:

r _i＝(Ty ^-1r ₂)*Ty，r ₂＝(Ty ^-1r ₂)*Ty，r ₄＝(Ty ^-1r ₄)*Ty

r ₅＝(Ty ^-1r ₅)*Ty，Tx＝(Ty ^-1Tx)*Ty， (11)

x _k′＝r ₁Xw _k+r ₂Yw _k+Tx

y _k′＝r ₄Xw _k+r ₅Yw _k+Ty

If x _kAnd x _k', y _kAnd y _k' jack per line all, sgn (Ty)=+ 1 so, otherwise sgn (Ty)=-1;

(4.33) calculate rotation matrix R

Value according to Ty recomputates r ₁, r ₂, r ₄, r ₅, Tx.

$R=\left[\begin{array}{ccc}{r}_1& r_2& {(1-{r_1}^2-{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="C0315350400191.png"\; state="\{\{state\}\}">r</figure-callout>}}_2}^2)}^{1/2}\\ r_4& r_5& s{(1-{{\mathrm{<figure-callout\; id="4"\; label="r"\; filenames="C0315350400191.png"\; state="\{\{state\}\}">r</figure-callout>}}_4}^2-{r_5}^2)}^{1/2}\\ r_7& r_8& r_9\end{array}\right]---\left(12\right)$

S=sgn (r wherein ₁r ₄+ r ₂r ₅)

r ₇, r ₈, r ₉Be to obtain by preceding two appositions of going.

If calculating following focal distance f according to such R is negative value, then:

$R=\left[\begin{array}{ccc}{r}_1& r_2& -{(1-{r_1}^2-{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="C0315350400191.png"\; state="\{\{state\}\}">r</figure-callout>}}_2}^2)}^{1/2}\\ r_4& r_5& -s{(1-{{\mathrm{<figure-callout\; id="4"\; label="r"\; filenames="C0315350400191.png"\; state="\{\{state\}\}">r</figure-callout>}}_4}^2-{r_5}^2)}^{1/2}\\ -r_7& -r_8& r_9\end{array}\right]---\left(13\right)$

Then calculate focal length f and T _zValue

To each calibration point, foundation comprises f and T _zLinear equation as unknown parameter:

$[Y_k-y_k]\left[\begin{array}{c}f\\ \mathrm{Tz}\end{array}\right]=w_k{y}_k---\left(14\right)$

Wherein:

Y _k＝r ₄x _wk+r ₅y _wk+r ₆*0+Ty (15)

w _k＝r ₇x _wk+r ₈y _wk+r ₉*0

By solving an equation, can ask f and T _z

5) carry out three-dimensionalreconstruction according to phase place and outer polar curve geometry to every, obtain the three-dimensional coordinate of body surface point.To the image that two video cameras are taken, three dimensions point S (Zw) pass with the correspondence image coordinate is for Xw, Yw:

$x^{\left(j\right)}=f^{\left(j\right)}\frac{{R^{\left(j\right)}}_{11}\mathrm{Xw}+{R^{\left(J\right)}}_{12}\mathrm{Yw}+{R^{\left(j\right)}}_{13}\mathrm{Zw}+T^{\left(j\right)}x}{{R^{\left(j\right)}}_{31}\mathrm{Xw}+{R^{\left(j\right)}}_{32}\mathrm{Yw}+{R^{\left(j\right)}}_{33}\mathrm{Zw}+T^{\left(j\right)}z},$

$y^{\left(j\right)}=f^{\left(j\right)}\frac{{R^{\left(j\right)}}_{21}\mathrm{Xw}+{R^{\left(j\right)}}_{22}\mathrm{Yw}+{R^{\left(j\right)}}_{23}\mathrm{Zw}+T^{\left(j\right)}y}{{R^{\left(j\right)}}_{31}\mathrm{Xw}+{R^{\left(j\right)}}_{32}\mathrm{Yw}+{R^{\left(j\right)}}_{33}\mathrm{Zw}+T^{\left(j\right)}z}---\left(16\right)$

J=1 wherein, the image that two video cameras of 2 expressions are taken.

Behind the camera calibration, f ^(j), R ^(j), T ^(j)Be known, the image to individual video camera is taken has four equations, to the video camera of demarcating, utilizes least square method can obtain the coordinate of three-dimensional point.

This is the ultimate principle of stereo vision three-dimensional rebuilding, and wherein Zui Da problem is how to find two points that are complementary, and that is to say how to realize some corresponding relation on two images in the three dimensions.Know that by the outer polar curve theory in the computer vision to a point in first width of cloth image, the corresponding point in second width of cloth image are point-blank.Its relation can have following The Representation Equation:

${{\tilde{m}}_2}^{T}F{\tilde{m}}_1=0---\left(17\right)$

Wherein,

Be the pixel coordinate (u of certain point in first width of cloth image ₁, v ₁, 1) ^T,

Be the pixel coordinate (u of certain point in second width of cloth image ₂, v ₂, 1) ^T, F is basis matrix (Fundamental Matrix), its element is a camera interior and exterior parameter.

F＝A ₂ ^-TEA ₁ ^-1 (18)

Wherein

$A_2=\left[\begin{array}{ccc}{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="C0315350400191.png"\; state="\{\{state\}\}">f</figure-callout>}}_2/\mathrm{<figure-callout\; id="2"\; label="d\; x"\; filenames="C0315350400191.png"\; state="\{\{state\}\}">d</figure-callout>}{x}_{}{}_2& 0& u_{02}\\ 0& {\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="C0315350400191.png"\; state="\{\{state\}\}">f</figure-callout>}}_2/d{y}_2& v_{02}\\ 0& 0& 1\end{array}\right],$ $A_1=\left[\begin{array}{ccc}{f}_1/d{x}_1& 0& u_{01}\\ 0& f_1/d{y}_1& v_{01}\\ 0& 0& 1\end{array}\right]$

F wherein ₁, (u ₀₁, v ₀₁), dx ₁, dy ₁Be the intrinsic parameter of first video camera, f ₂, (u ₀₂, v ₀₂), dx ₂, dy ₂Be the intrinsic parameter of second video camera, the meaning of parameter is described with the front.

$E={\left[T\right]}_x{R}^{\left(2\right)}{R}^{{\left(1\right)}^{-1}}$ (being called essential matrix, Essential Matrix)

$T=T^{\left(2\right)}-R^{\left(2\right)}{R}^{{\left(1\right)}^{-1}}{T}^{\left(1\right)}---\left(19\right)$

T is expressed as [Tx, Ty, Tz], [T] _xBe antisymmetric matrix, be defined as:

${\left[T\right]}_x=\left[\begin{array}{ccc}0& -\mathrm{Tz}& \mathrm{Ty}\\ \mathrm{Tz}& 0& -\mathrm{Tx}\\ -\mathrm{Ty}& \mathrm{Tx}& 0\end{array}\right]---\left(20\right)$

Basis matrix is determined by camera interior and exterior parameter as can be seen, and by camera calibration, we just can obtain the polar curve equation.

From the polar curve equation as can be seen, right video camera is taken last 1 P of image, its coordinate

If it is taken on the image at left video camera corresponding point Q is arranged, should be by On the straight line of basis matrix F decision.

Key is which point on this straight line

When phase place is obtained in front, once mentioned, same when different cameras is taken phase value should be identical.And to the phase value of each point, we have phase place to obtain to have obtained, and we utilize this point to realize the accurate coupling of putting on two images just.

Algorithm flow chart is seen accompanying drawing 4.

After finding match point, utilize the three-dimensional coordinate that formula (16) can calculation level.

According to said process staff is carried out three-dimensional measurement, the point that measures as shown in Figure 5.

Characteristics such as the three-dimension measuring system that the present invention constituted has noncontact, speed is fast, data volume is big, precision is high, simple to operate.Single face to object is measured as long as can obtain the data (400,000 points) of very high-density 2 seconds, and the precision of measurement is more than 0.05mm.

Claims (3)

1. the method for Measuring Object surface tri-dimensional profile, it is characterized in that: it is a kind of combination that utilizes phase place and stereovision technique, at body surface projection grating, adopt twin camera to take the raster image that distortion takes place again, utilize encoded light and phase shifting method to obtain the phase place of every bit on the left and right cameras photographic images; Utilize phase place and outer polar curve to realize the coupling of the point on two width of cloth images, thereby reach the anti-method of asking body surface point three-dimensional coordinate; It comprises the steps:

(1) utilizes computing machine to generate virtual grating,, utilize projector that the grating that generates is incident upon on the object comprising encode grating and phase-shifted grating;

The light intensity of phase-shifted grating is as shown in the formula expressing:

I _i(u，v)＝a(u，v)+b(u，v)cos(φ(u，v)+φ _i)

Wherein:

(u v) is the coordinate of certain point;

I _i(u v) is (u, a light intensity v) in the i width of cloth image;

(u v) is the bias light majorant to a;

(u v) is a fringe contrast to b;

(u v) represents the phase place of each point to φ, and the cycle is T;

φ _iBe angle of phase displacement;

Encode grating has the N width of cloth, and building method is that first width of cloth is partly to deceive partly in vain, and each width of cloth of back segments gradually, and divided method is the black part of a last width of cloth, is divided into partly deceiving partly in vain, and the white of a last width of cloth is divided into partly and partly deceives in vain; To each point, according to then being encoded to 1 still for encoding in vain for deceiving for black on each width of cloth image in each width of cloth image, for then being encoded to 0 in vain, thereby obtain the coded sequence of this point; N width of cloth encode grating can have 2 ^NIndividual coded sequence, whole image is divided into 2 ^NIndividual rectangular, each rectangular width is the period T of phase-shifted grating; Individual rectangular to n, n=1,2 ... 2 ^N, claim periodicity again, according to the corresponding unique encoding sequence of such encoded light building method, its decimal-coded digit is nc, sets up the mapping relations between periodicity n and the coded number nc, can realize both mutual conversions;

(2) utilize the raster image of two ccd video camera collection projections, and be kept in the array of distributing in the program;

(3) each width of cloth image that each camera is taken is handled respectively, obtain the phase value of each point, phase value adds that by the phase main value periodicity multiply by 2 π, be 2n π, because the phase value of each point that two video cameras are taken should equate, take each some phase value of obtaining as the foundation of mating with two video cameras;

(4) two video cameras are calibrated, obtained the intrinsic parameter of video camera and with respect to the outer parameter of world coordinate system: f ^(j), R ^(j), T ^(j), j=1,2

f ^(j): lens focus length, j is a camera number;

R ^(j): rotation matrix, $R=\left[\begin{array}{ccc}{r}_1& r_2& r_3\\ r_4& r_5& r_6\\ r_7& r_8& r_9\end{array}\right];$

T ^(j): translation vector, T=[Tx Ty Tz] ';

Calculate R, Tx, Ty earlier;

(4.1) calculate the image coordinate of each point

u＝u ₀+x/dx

v=v ₀+y/dy

To the point in space (Xw, Yw, Zw), after video camera is taken, image coordinate (mm) be (x, y), pixel coordinates be (u, v), (u ₀, v ₀) be the pixel coordinate of initial point in pixel coordinate system of image coordinate system, (dx is the x between the CCD adjacent image point and the distance of y direction dy), is provided by CCD producer;

(4.2) calculate five unknown quantity Ty ^-1r ₁, Ty ^-1r ₂, Ty ^-1Tx, Ty ^-1r ₄, Ty ^-1r ₅

For each three dimensional object point (Xw _k, Yw _k, Zw _k), because the some coplane, so the Z coordinate is got work 0, and corresponding image coordinate (x _k, y _k), by collinearity equation:

$x_k=f\frac{r_{1}X{w}_k+r_{2}Y{w}_k+\mathrm{Tx}}{r_{7}X{w}_k+r_{8}Y{w}_k+\mathrm{Tz}}$

$y_k=f\frac{r_4{\mathrm{Xw}}_k+r_{5}Y{w}_k+\mathrm{Ty}}{r_{7}X{w}_k+r_{8}Y{w}_k+\mathrm{Tz}}$

Top two formulas are divided by obtain: utilize least square method to try to achieve above-mentioned 5 unknown quantitys;

(4.3) calculate r ₁..., r ₉, Tx, T _y

(4.31) calculate | Ty|

The definition matrix:

$C=\left[\begin{array}{cc}{r_1}^{\&prime;}& {r_2}^{\&prime;}\\ {r_4}^{\&prime;}& {r_5}^{\&prime;}\end{array}\right]=\left[\begin{array}{cc}{r}_1/\mathrm{Ty}& r_2/\mathrm{Ty}\\ r_4/\mathrm{Ty}& r_5/\mathrm{Ty}\end{array}\right]$

Then have:

${\mathrm{Ty}}^2=\frac{\mathrm{Sr}-{[{\mathrm{Sr}}_2-4{({r_1}^{\&prime;}{r_5}^{\&prime;}-{r_4}^{\&prime;}{r_2}^{\&prime;})}^2]}^{1/2}}{2{({r_1}^{\&prime;}{r_5}^{\&prime;}-{r_4}^{\&prime;}{r_2}^{\&prime;})}^2}$

Wherein:

Sr＝r ₁′ ²+r ₂′ ²+r ₅′ ²+r ₄′ ²，

If certain row of Matrix C or certain column element are calculated as follows for being 0 entirely:

Ty ²=(r _i' ²+ r _j' ²) ^-1, r wherein _i', r _j', be remaining two elements in addition of Matrix C;

(4.32) symbol of decision Ty

1. suppose that Ty is a positive sign;

2. select in the captured image, from picture centre far away a bit; If its image coordinate is (x _k, y _k), the coordinate in three-dimensional world is (Xw _k, Yw _k, Zw _k);

3. calculate following various value by top result:

r ₁＝(Ty ^-1r ₁)*Ty，r ₂＝(Ty ^-1r ₂)*Ty，r ₄＝(Ty ^-1r ₄)*Ty

r ₅＝(Ty ^-1r ₅)*Ty，Tx＝(Ty ^-1Tx)*Ty，

x _k′＝r ₁Xw _k+r ₂Yw _k+Tx

y _k′＝r ₄Xw _k+r ₅Yw _k+Ty

If x _kAnd x _k', y _kAnd y _k' jack per line all, sgn (Ty)=+ 1 so, otherwise sgn (Ty)=-1;

(4.33) calculate rotation matrix R

Value according to Ty recomputates r ₁, r ₂, r ₄, r ₅, Tx;

$R=\left[\begin{array}{ccc}{r}_1& r_2& {(1-{r_1}^2-{r_2}^2)}^{1/2}\\ r_4& r_5& s{(1-{r_4}^2-{r_5}^2)}^{1/2}\\ r_7& r_8& r_9\end{array}\right]$

S=sgn (r wherein ₁r ₄+ r ₂r ₅)

r ₇, r ₈, r ₉Be to obtain by preceding two appositions of going;

If calculating following focal distance f according to such R is negative value, then:

$R=\left[\begin{array}{ccc}{r}_1& r_2& {-(1-{r_1}^2-{r_2}^2)}^{1/2}\\ r_4& r_5& -s{(1-{r_4}^2-{r_5}^2)}^{1/2}\\ -r_7& {-r}_8& r_9\end{array}\right]$

Then calculate focal length f and T _zValue

To each calibration point, foundation comprises f and T _zLinear equation as unknown parameter:

$\left[\begin{array}{cc}{Y}_k& -y_k\end{array}\right]\left[\begin{array}{c}f\\ \mathrm{Tz}\end{array}\right]=w_k{y}_k$

Wherein:

Y _k＝r ₄x _wk+r ₅y _wk+r ₆*0+Ty

w _k＝r ₇x _wk+r ₈y _wk+r ₉*0

By solving an equation, can ask f and T _z

(5) carry out three-dimensionalreconstruction according to phase place and outer polar curve geometry to every, obtain the three-dimensional coordinate of body surface point:

(5.1) calculate basis matrix F

F＝A ₂ ^-TEA ₁ ^-1

Wherein

$A_2=\left[\begin{array}{ccc}{f}_2/{\mathrm{dx}}_2& 0& u_{02}\\ 0& f_2/{\mathrm{dy}}_2& v_{02}\\ 0& 0& 1\end{array}\right],A_1=\left[\begin{array}{ccc}{f}_1/{\mathrm{dx}}_1& 0& u_{01}\\ 0& f_1/{\mathrm{dy}}_1& v_{01}\\ 0& 0& 1\end{array}\right]$

F wherein ₁, (u ₀₁, v ₀₁), dx ₁, dy ₁Be the intrinsic parameter of first video camera,

f ₂, (u ₀₂, v ₀₂), dx ₂, dy ₂It is the intrinsic parameter of second video camera;

E=[T] _xR ⁽²⁾R ^(1)-1, be called essential matrix;

T＝T ⁽²⁾-R ⁽²⁾R ^(1)-1T ⁽¹⁾

T is expressed as [Tx, Ty, Tz], then antisymmetric matrix is [T] _x

${\left[T\right]}_x=\left[\begin{array}{ccc}0& -\mathrm{Tz}& \mathrm{Ty}\\ \mathrm{Tz}& 0& -\mathrm{Tx}\\ -\mathrm{Ty}& \mathrm{Tx}& 0\end{array}\right]$

(5.2) calculate 1 P on the right video camera photographic images, its coordinate is Look for its polar curve equation parameter on left video camera photographic images; And on above-mentioned straight line, seek its match point Q point, method is that the phase value of a P and some Q equates;

Known According to following straight-line equation, look for the some Q of some P on left video camera photographic images on the right video camera photographic images, its coordinate is

${{\tilde{m}}_2}^{T}F{\tilde{m}}_1=0,$

Wherein: Be the pixel coordinate (u that P is ordered ₂, v ₂, 1) ^T:

Be Q point pixel coordinate (u ₁, v ₁, 1) ^T

According to a P and the equal principle of some Q phase place, on straight line, seek the Q point by above-mentioned straight-line equation decision;

(5.3) find the Q point, then store this match point, according to following three dimensions point S (Xw, Yw, Zw) and the pass of the correspondence image coordinate of two video camera photographic images be:

$x^{\left(j\right)}=f^{\left(j\right)}\frac{{R^{\left(j\right)}}_{11}\mathrm{Xw}+{R^{\left(j\right)}}_{12}\mathrm{Yw}+{R^{\left(j\right)}}_{13}\mathrm{Zw}+T^{\left(j\right)}x}{{R^{\left(j\right)}}_{31}\mathrm{Xw}+{R^{\left(j\right)}}_{32}\mathrm{Yw}+{R^{\left(j\right)}}_{33}\mathrm{Zw}+T^{\left(j\right)}z},$

$y^{\left(j\right)}=f^{\left(j\right)}\frac{{R^{\left(j\right)}}_{21}\mathrm{Xw}+{R^{\left(j\right)}}_{22}\mathrm{Yw}+{R^{\left(j\right)}}_{23}\mathrm{Zw}+T^{\left(j\right)}y}{{R^{\left(j\right)}}_{31}\mathrm{Xw}+{R^{\left(j\right)}}_{32}\mathrm{Yw}+{R^{\left(j\right)}}_{33}\mathrm{Zw}+T^{\left(j\right)}z},$

J=1,2, be the numbering of video camera.

2. the method for surface measurements three-D profile according to claim 1 is characterized in that the angle of phase displacement φ of described phase-shifted grating _i=i*90, i=1 ... 4, promptly the phase-shifted grating image has 4 width of cloth, and its phase main value computing formula is: $\mathrm{\&phi;}(x,y)=a\tan \left(\frac{I_2-I_4}{I_3-I_1}\right),$

I wherein ₁, I ₂, I ₃, I ₄, be point (u, the v) light intensity in four width of cloth phase-shifted gratings.

3. the method for Measuring Object three-dimensional surface profile according to claim 1 is characterized in that described encode grating has 7 width of cloth, and the binary code sequence of every bit can change into this position in image, i.e. periodicity.

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