CN102269587B - Method for controlled light plane-based underwater three-dimensional redrawing device - Google Patents

Abstract

The invention relates to a controlled light plane-based underwater three-dimensional redrawing device and a controlled light plane-based underwater three-dimensional redrawing method. The device comprises a computer control device with software, a light plane control device with a reflecting lens, a charge coupled device (CCD) camera, a light plane generator and a sealed shell of which the front is provided with a glass window and one side is provided with a waterproof interface. The redrawing method comprises the following steps of: establishing a global coordinate system and a camera coordinate system by using the light plane control device and the CCD camera; correcting a light plane equation before refraction, and resolving a light plane equation after refraction; resolving a refraction compensation parameter k, and compensating a pixel coordinate of each point to be detected; and resolving a coordinate of a point to be detected according to the corrected light plane equation and the pixel coordinate of the point to be detected and a geometrical relationship between a light plane and the CCD camera so as to realize the three-dimensional redrawing of an object to be detected. By the invention, the refraction influence is effectively avoided, the three-dimensional redrawing of an underwater object is realized, the structure is simple and the accuracy is high.

Description

Redrawing method of underwater three-dimensional redrawing device based on controllable light plane

Technical Field

The invention relates to an underwater three-dimensional measuring device, in particular to an underwater three-dimensional redrawing device and method based on a controllable light plane.

Background

The existing land three-dimensional redrawing device can not directly measure and redraw underwater objects. Even if the existing land three-dimensional redrawing device is sealed, when the land three-dimensional redrawing device is used for underwater measurement, a glass window of a sealed shell enables a measured object and the measuring device to be respectively positioned in media with different refractive indexes, when light passes through the glass window, refraction can be generated, so that a light plane deflects, and meanwhile, adverse factors such as focusing error, visual angle error, distortion and chromatic aberration are brought to underwater imaging of a CCD camera, so that the imaging quality is reduced, and finally, the underwater three-dimensional redrawing cannot be realized.

Disclosure of Invention

The invention aims to provide an underwater three-dimensional redrawing device and a redrawing method based on a controllable light plane, which overcome the influence of underwater refraction on the light plane and a CCD (charge coupled device) camera and realize accurate three-dimensional redrawing of a measured object underwater.

The underwater three-dimensional redrawing device based on the controllable light plane comprises a computer control device containing software, a light plane control device with a reflecting lens, a CCD camera and a light plane generator, and is characterized by also comprising a sealing shell with a transparent glass window on the front surface and a waterproof interface on one side of the sealing shell, wherein the light plane control device and the CCD camera are fixed at two ends of a base of the sealing shell, the light plane generator is close to the reflecting lens of the light plane control device and is fixed on the base of the sealing shell, and emergent light is just projected onto a rotating axis of the reflecting lens.

The three-dimensional redrawing method comprises the following steps:

1. firstly, a world coordinate system o is respectively established by a light plane control device and a CCD camera_wx_wy_wz_wAnd the camera coordinate system o_cx_cy_cz_cThe relationship of the two coordinate systems can be represented by a rotation matrix and a translation matrix.

2. Considering that when a light plane is projected to a measured object through a glass window, refraction occurs at the glass window, an optical plane equation Ax + By + Cz before refraction must be obtained and then corrected.

The optical plane equation before refraction is obtained by the following formula (I),

<math><mrow> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mi>A</mi> <mo>=</mo> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mi>B</mi> <mo>=</mo> <mi>cos</mi> <mo>[</mo> <mn>2</mn> <mrow> <mo>(</mo> <mi>U</mi> <mo>-</mo> <msub> <mi>U</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mi>&rho;</mi> <mo>]</mo> </mtd> </mtr> <mtr> <mtd> <mi>C</mi> <mo>=</mo> <mi>sin</mi> <mo>[</mo> <mn>2</mn> <mrow> <mo>(</mo> <mi>U</mi> <mo>-</mo> <msub> <mi>U</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mi>&rho;</mi> <mo>]</mo> </mtd> </mtr> <mtr> <mtd> <mi>D</mi> <mo>=</mo> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mi>I</mi> <mo>)</mo> </mrow> </mrow></math>

wherein A, B, C, D is the coefficient of the equation; u is the real-time input voltage of the light plane control device, U₀To make the light plane along z_wThe input voltage of the light plane control device when the shaft is emitted; ρ is the angle the mirror plate rotates for each volt change in the input voltage U.

The light plane is refraction corrected by the following formula (II), specifically, the light plane equation a after refraction at the glass window is solved₃x+b₃y+c₃z＝d₃。

$\left\{\begin{array}{c}{a}_3=\frac{A}{\left|A\right|}\sqrt{\frac{1-\frac{C^2}{n_w^2(A^2+{\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="HDA0000030543540000011.png,HDA0000030543540000021.png"\; state="\{\{state\}\}">B</figure-callout>}}^2+C^2)}}{1+\frac{B^2}{A^2}}}\\ {\mathrm{<figure-callout\; id="3"\; label="b"\; filenames="HDA0000030543540000011.png,HDA0000030543540000012.png"\; state="\{\{state\}\}">b</figure-callout>}}_3=-\frac{a_{3}B}{A}\\ {\mathrm{<figure-callout\; id="3"\; label="c"\; filenames="HDA0000030543540000011.png,HDA0000030543540000012.png"\; state="\{\{state\}\}">c</figure-callout>}}_3=\frac{C}{n_w\sqrt{A^2{+\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="HDA0000030543540000011.png,HDA0000030543540000021.png"\; state="\{\{state\}\}">B</figure-callout>}}^2+C^2}}\\ {\mathrm{<figure-callout\; id="3"\; label="d"\; filenames="HDA0000030543540000011.png,HDA0000030543540000012.png"\; state="\{\{state\}\}">d</figure-callout>}}_3=c_{3}h-{\mathrm{<figure-callout\; id="3"\; label="b"\; filenames="HDA0000030543540000011.png,HDA0000030543540000012.png"\; state="\{\{state\}\}">b</figure-callout>}}_3\frac{\mathrm{hC}+D}{B}\end{array}\right.---\left(\mathrm{II}\right)$

Wherein a is₃x+b₃y+c₃z＝d₃Is the equation of the plane of light after refraction, a₃、b₃、c₃、d₃Are the coefficients of the equation; A. b, C, D is as in formula (I); h is the world coordinate system o_wx_wy_wz_wThe vertical distance from the origin of (a) to the glazing; n is_wIs the refractive index of water to air.

3. Considering that when shooting a target in water, light rays are refracted at a glass window to cause the deviation of an imaging point of the glass window on a CCD target surface and the distortion of pixel coordinates, the refraction compensation must be carried out on an image shot by a CCD camera, the refraction compensation parameters are calculated through a formula (III),

$k=\frac{\tan \left[\arcsin \frac{\sin \left(\arctan \frac{\sqrt{u^2+v^2}}{f}\right)}{n_w}\right)]}{\frac{\sqrt{u^2+v^2}}{f}}---\left(\mathrm{III}\right)$

wherein f is the focal length of the CCD camera; n is_wIs the refractive index of water to air; and (u, v) are pixel coordinates of the measured point on the CCD target surface.

During shooting, the measured point can form an image on a CCD target surface of a CCD camera to obtain pixel coordinates (u, v), the pixel coordinates cannot represent the real position of the point due to refraction at a glass window, and the pixel coordinates are compensated through a CCD camera refraction compensation parameter k in a formula (III) to obtain the real pixel coordinates (ku, kv) of the measured point.

4. Under the premise that the light plane equation is corrected and the pixel coordinates of the CCD camera are compensated, the coordinates of the measured point in the world coordinate system are calculated through a formula (IV) according to the relationship between the light plane equation and the pixel coordinates.

$\left\{\begin{array}{c}(c_1{d}_2-c_2{d}_1)(a_1{c}_3-a_3{c}_1)(a_1{b}_2-a_2{b}_1)\text{-}(c_1{d}_2-c_2{d}_1)(a_1{c}_2-a_2{c}_1)(a_1{b}_3-a_3{b}_1)\\ x=\frac{-(b_2{c}_1-b_1{c}_2)(a_1{d}_2-a_2{d}_1)(a_1{c}_3-a_3{c}_1)+(b_2{c}_2-b_1{c}_2)(a_1{d}_3-a_3{d}_1)(a_1{d}_3-a_3{d}_1)}{(a_2{c}_1-a_1{c}_2)(a_1{c}_3-a_3{c}_1)(a_1{b}_2-a_2{b}_1)-(a_2{c}_1-a_1{c}_2)(a_1{c}_2-a_2{c}_1)(a_1{b}_3-a_3{b}_1)}\\ y=\frac{(a_1{c}_3-a_3{c}_1)(a_1{d}_2-a_2{d}_1)-(a_1{d}_3-a_3{d}_1)(a_1{c}_2-a_2{c}_1)}{(a_1{c}_3-a_3{c}_1)(a_1{b}_2-a_2{b}_1)-(a_1{c}_2-a_2{c}_1)(a_1{b}_3-a_3{b}_1)}\\ z=\frac{(a_1{d}_3-a_3{d}_1)\left(a_1{b}_2{-a}_2{b}_1\right)-(a_1{d}_2-a_2{d}_1)(a_1{b}_3-a_3{b}_1)}{(a_1{c}_3-a_3{c}_1)(a_1{b}_2-a_2{b}_1)-(a_1{c}_2-a_2{c}_1)(a_1{b}_3-a_3{b}_1)}\end{array}\right.----\left(\mathrm{IV}\right)$

Wherein,

$\left\{\begin{array}{c}{a}_1={\mathrm{kur}}_6-{\mathrm{fr}}_0\\ b_1={\mathrm{kur}}_7-{\mathrm{fr}}_1\\ c_1={\mathrm{kur}}_8-f{r}_2\\ d_1=\mathrm{ku}(r_6{t}_0+r_7{t}_1+r_8{t}_2)-f(r_0{t}_0+r_1{t}_1+r_2{t}_2)\end{array}\right.,$ $\left\{\begin{array}{c}{a}_2={\mathrm{kvr}}_6-{\mathrm{fr}}_3\\ {\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="HDA0000030543540000011.png,HDA0000030543540000021.png"\; state="\{\{state\}\}">b</figure-callout>}}_2={\mathrm{kvr}}_7-{\mathrm{fr}}_4\\ {\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA0000030543540000011.png,HDA0000030543540000021.png"\; state="\{\{state\}\}">c</figure-callout>}}_2={\mathrm{kvr}}_8-f{r}_5\\ {\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA0000030543540000011.png,HDA0000030543540000021.png"\; state="\{\{state\}\}">d</figure-callout>}}_2=\mathrm{kv}(r_6{t}_0+r_7{t}_1+r_8{t}_2)-f(r_3{t}_0+r_4{t}_1+r_5{t}_2)\end{array}\right.;$

(u, v) are pixel coordinates of the measured point on the CCD camera CCD target surface; k is as in formula (III); a is₃、b₃、c₃、d₃As in formula (II); r is₀-r₈，t₀-t₂Are the elements of the rotation matrix and the translation matrix of the camera coordinate system to the galvanometer coordinate system, respectively.

According to the modified light plane equation a₃x+b₃y+c₃z＝d₃And the pixel coordinates (ku, kv) of the measured point after refraction compensation can be used for calculating the three-dimensional coordinates (x, y, z') of the measured point under the world coordinates through the formula (IV).

If the input voltage of the light plane control device is increased at a constant speed according to a certain stepping value, the laser plane will uniformly sweep the measured object, and the three-dimensional coordinates of all points of the measured object under the world coordinate system can be measured, i.e. the three-dimensional redrawing is realized.

The first core of the invention is the hardware structure of the device: the light plane control device, the light plane generator and the CCD camera are fixed in a sealed shell with a transparent glass window on one side, and a waterproof interface is arranged on the side surface; the second method is a refraction correction method in the light plane and a refraction compensation method of the CCD camera: according to the formulas (I) and (II), the refraction correction of the optical plane can be realized, and according to the refraction compensation parameter of the formula (III), the refraction compensation of the underwater imaging of the CCD camera is realized; thirdly, a mathematical method for obtaining the three-dimensional coordinates of the measured object through the light plane equation and the internal and external parameters of the CCD camera comprises the following steps: and (3) calculating the three-dimensional coordinates of all measured points through a formula (IV) to finally realize the three-dimensional redrawing of the measured object.

The method overcomes the influence of refraction on the optical plane and the CCD camera, realizes the three-dimensional redrawing of the underwater object, is simple and stable, has high measurement precision, and has the maximum error of not more than 0.5 percent within the distance of 1-10 meters; simple structure, small volume, convenient operation and wide application range.

The invention is further illustrated with reference to the following figures and examples:

drawings

FIG. 1 is a schematic diagram of the basic structure of the present invention.

FIG. 2 is a schematic diagram of the present invention establishing a world coordinate system and a CCD camera coordinate system.

FIG. 3 is a schematic diagram of the optical plane refraction correction and CCD camera refraction compensation of the present invention.

The device comprises a light plane control device 1, a light plane generator 2, a CCD camera 3, a sealing shell 4, a glass window 5, an interface 6, an interface 7, a controllable light plane 8, a reflecting lens 9, a CCD target surface 10 and a computer control device.

Detailed Description

Referring to fig. 1, the device mainly comprises a computer control device 10 containing software, a light plane control device 1 with a reflector 8, a CCD camera 3 and a light plane generator 2, and is characterized by further comprising a sealing shell 4 with a glass window 5 on the front surface and a waterproof interface 6 on one side of the sealing shell 4, wherein the light plane control device 1 and the CCD camera 3 are fixed at two ends of a base of the sealing shell 4, the light plane generator 2 is fixed on the base of the sealing shell 4 close to the reflector 8 of the light plane control device 1, and the emergent light is just projected on a rotating axis of the reflector 8.

The sealed shell 4 is a rectangular frame with the size of 600mm 180mm, the front surface is a glass window 5, the other surfaces are stainless steel, and one side surface is provided with a waterproof interface 6.

Two coordinate systems are established with reference to fig. 2: establishing a conventional camera coordinate system o for the CCD camera 3_cx_cy_cz_cWith the midpoint of the rotation axis of the mirror 8 as the origin o_wIn the direction of the axis of rotation is x_wThe direction of the outgoing light of the axial and light plane generator 2 is y_wAxis, establishing a right-handed rectangular coordinate system o_wx_wy_wz_w. The relationship between the two coordinate systems can be represented by the following formula (V) through a rotation matrix and a translation matrix:

$\left[\begin{array}{c}{x}_w\\ y_w\\ z_w\end{array}\right]=R\left[\begin{array}{c}{x}_c\\ y_c\\ z_c\end{array}\right]+T---\left(V\right)$

wherein,is a rotation matrix between two coordinate systems,is a translation matrix between two coordinate systems.

The angle of rotation of the mirror 8 is controlled by the input voltage to the optical plane control device 1. rho is the angle through which the mirror 8 rotates for each voltage change of one volt, if the optical plane 7 is along z_wInput voltage at the time of shaft ejection is U₀Then, for a certain input voltage U, the optical plane equation is Ax + By + Cz + D equals 0, and the optical plane and z are equal to_wThe included angle of the axes is 2 (U-U)₀) ρ, the A, B, C, D values are obtained separately to obtain formula (I).

Referring to FIG. 3, based on the known light plane equation, the light plane equation a after refraction can be obtained according to the law of refraction₃x+b₃y+c₃z+d₃(II) 0, yielding formula (II).

Referring to fig. 3, a target point P in water is imaged on a CCD target surface 9 at a point Q (u, v) according to the law of refraction, and if the point P is measured on land, the point P is directly imaged on the CCD target surface 9 at a point Q₁(u₁，v₁) Point, Q₁And Q have the following relationshipFor each measured point, only the parameter k is obtained, namelyCompensation for refraction can be achieved.

As can be seen from the view in figure 3,

<math><mrow> <mi>k</mi> <mo>=</mo> <mfrac> <mrow> <mo>|</mo> <msub> <mi>Q</mi> <mn>1</mn> </msub> <msub> <mi>O</mi> <mrow> <mi>c</mi> <mn>1</mn> </mrow> </msub> <mo>|</mo> </mrow> <mrow> <mo>|</mo> <msub> <mi>QO</mi> <mrow> <mi>c</mi> <mn>1</mn> </mrow> </msub> <mo>|</mo> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mi>tan</mi> <mi>&gamma;</mi> </mrow> <mrow> <mi>tan</mi> <mi>&alpha;</mi> </mrow> </mfrac> <mo>=</mo> <mfrac> <mfrac> <mrow> <mo>|</mo> <msub> <mi>QO</mi> <mrow> <mi>c</mi> <mn>1</mn> </mrow> </msub> <mo>|</mo> </mrow> <mrow> <mo>|</mo> <msub> <mi>OO</mi> <mrow> <mi>c</mi> <mn>1</mn> </mrow> </msub> <mo>|</mo> </mrow> </mfrac> <mfrac> <mrow> <mo>|</mo> <mi>NH</mi> <mo>|</mo> <mi>tan</mi> <mi>&beta;</mi> <mo>+</mo> <mo>|</mo> <mi>BH</mi> <mo>|</mo> </mrow> <mrow> <mo>|</mo> <mi>OH</mi> <mo>|</mo> </mrow> </mfrac> </mfrac> </mrow></math>

as is also known, the amount of oxygen present,|OO_c1|＝f，|O_c1N|＝h_c，|OH|＝z_wand are and

through the joint solution of the above types, the relation (III) can be derived, and the image of the CCD camera 3 is further subjected to refraction compensation.

Referring to fig. 3, the geometrical relationship between the light plane 7 and the CCD camera 3:

mathematical relation exists when CCD camera images

From the formula (V), there are

The equation of the plane of the refracted light is a by formula (II)₃x_w+b₃y_w+c₃z_w+d₃＝0；

And solving the equation set of the various types of compositions to obtain a relational expression (IV), solving the coordinates (x, y, z, y and z) of the measured point in a world coordinate system, and obtaining the three-dimensional coordinates of all points of the measured object to realize the three-dimensional redrawing of the measured object.

In conclusion, the invention adopts the method of light plane correction and CCD camera refraction compensation, overcomes the influence of underwater refraction, and realizes the three-dimensional redrawing of underwater objects.

Claims (2)

1. A method for three-dimensional redrawing by using an underwater three-dimensional redrawing device based on a controllable light plane comprises a computer control device (10) containing software, a light plane control device (1) with a reflecting lens (8), a CCD camera (3), a light plane generator (2), a sealing shell (4) with a glass window (5) on the front surface and a waterproof interface (6) on one side of the sealing shell (4), wherein the light plane control device (1) and the CCD camera (3) are fixed at two ends of the base of the sealing shell (4), the light plane generator (2) is close to the reflecting lens (8) of the light plane control device (1) and is fixed on the base of the sealing shell (4), and emergent light is just projected on a rotating axis of the reflecting lens (8),

it is characterized in that firstly, a world coordinate system o is established by a light plane control device (1) and a CCD camera (3) respectively_wx_wy_wz_wAnd the camera coordinate system o_cx_cy_cz_c(ii) a Then correcting the light plane equation Ax + By + Cz = D before refraction, and solving the light plane equation a after refraction₃x+b₃y+c₃z=d₃(ii) a Then, a refraction compensation parameter k is obtained, and the pixel coordinates (u, v) of each measured point are compensated to be (ku, kv); finally according to the corrected light plane equation a₃x+b₃y+c₃z=d₃And the pixel coordinates (ku, kv) of the measured point and the geometric relationship between the light plane (7) and the CCD camera (3) are solved to obtain the coordinates (x, y, z) of the measured point, so as to obtain the coordinates of all the measured points, namely, the three-dimensional redrawing of the measured object is realized;

the above world coordinate system o_wx_wy_wz_wAnd the camera coordinate system o_cx_cy_cz_cThe relationship between them is expressed by the following formula (v) through a rotation matrix and a translation matrix:

r₀-r₈，t₀-t₂respectively are elements of a rotation matrix and a translation matrix from a camera coordinate system to a galvanometer coordinate system;

the light plane equation Ax + By + Cz = D before refraction is corrected to obtain the light plane equation a after refraction₃x+b₃y+c₃z=d₃And then obtaining a refraction compensation parameter k, comprising:

the plane equation of light before refraction is obtained by the following formula (i),

wherein A, B, C, D is the coefficient of the equation; u is the real-time input voltage of the light plane control device, U₀To make the light plane along z_wThe input voltage of the light plane control device when the shaft is emitted; ρ is the angle the mirror plate rotates for each volt change in the input voltage U,

the light plane is subjected to refraction correction through the following formula (II), and specifically, the light plane equation a after refraction at the glass window is solved₃x+b₃y+c₃z=d₃,

Wherein a is₃x+b₃y+c₃z=d₃Is the equation of the plane of light after refraction, a₃、b₃、c₃、d₃Are the coefficients of the equation; A. b, C, D is as in formula (I); h is the world coordinate system o_wx_wy_wz_wThe vertical distance from the origin of (a) to the glazing; n is_wIs the refractive index of water to air;

calculating refraction compensation parameters by formula (III),

wherein f is the focal length of the CCD camera; n is_wIs the refractive index of water to air; (u, v) are pixel coordinates of the measured point on the CCD target surface;

the geometrical relationship between the light plane (7) and the CCD camera (3) is as follows: for a point P on the light plane (7), the coordinate is (x) under the world coordinate system_w,y_w,z_w) The coordinate under the camera coordinate system is (x)_c,y_c,z_c) When the pixel coordinates on the CCD target surface (9) are (u, v) and the focal length of the CCD camera (3) is f, the conditions are metThe following mathematical relationship:

the above equation a based on the corrected light plane₃x+b₃y+c₃z=d₃And the pixel coordinates (ku, kv) of the measured point and the geometrical relationship between the light plane (7) and the CCD camera (3) are solved to obtain the coordinates (x, y, z,) of the measured point, which comprises:

calculating the coordinate of the measured point in the world coordinate system through a formula (IV),

wherein,

(u, v) are pixel coordinates of the measured point on the CCD camera CCD target surface; k is as in formula (III); a is₃、b₃、c₃、d₃As formula (II); r is₀-r₈，t₀-t₂Are the elements of the rotation matrix and translation matrix from the camera coordinate system to the galvanometer coordinate system,

according to the modified light plane equation a₃x+b₃y+c₃z=d₃And refraction compensated pixel coordinates (ku, kv) of the measured point can be obtained by the formula (IV) under the world coordinateCoordinates (x, y, z,).

2. An underwater three-dimensional redrawing method according to claim 1, wherein said sealed casing (4) is a rectangular frame with dimensions of 600mm x 180 mm.

Images