CN104240233A - Method for solving camera homography matrix and projector homography matrix - Google Patents
Method for solving camera homography matrix and projector homography matrix Download PDFInfo
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Abstract
The invention relates to a method for solving a camera homography matrix and a projector homography matrix. The method for solving the camera homography matrix and the projector homography matrix is characterized in that a camera and a projector are both connected with a computer through cables, and the method comprises the following steps that in the computer, a camera calibration image is generated, in the computer, a projector calibration image is generated, and the camera calibration image and the projector calibration image are stored in the computer; the camera and the projector are fixedly placed on the front portion of a calibration plate, and it is guaranteed that the calibration plate is placed within the view field range of the camera and the projector; the calibration plate is taken through the camera, and a camera calibration plate image is obtained; the calibration plate is kept not be moved, the projector calibration image is all projected to the calibration plate through the projector, the camera is used for shooting the calibration plate, and a projector calibration plate image is obtained. According to the method for solving the camera homography matrix and the projector homography matrix, the camera and the projector can be quickly calibrated, and therefore the camera homography matrix and the projector homography matrix can be obtained.
Description
Technical field
The present invention relates to the method for solving of a kind of video camera homography matrix and projector's homography matrix, belong to technical field of computer vision.
Background technology
Structural light measurement method is one of the most promising and most popular method for three-dimensional measurement, has the advantages such as noncontact, precision is high, speed is fast.Structural light measurement method can adopt technique of binocular stereoscopic vision or single eye stereo vision technology, and monocular vision technique has structure and simply, without the need to considering that video camera stationary problem, process data volume are little, put cloud rebuilds efficiency advantages of higher and be widely used.From following formula,
In order to determine camera review coordinate system and projector optical coordinate system respectively with the corresponding relation of world coordinate system, and then obtain the actual physical size of object under test, first will solve video camera homography matrix
with the homography matrix of projector
.
In order to solve the homography matrix of video camera and projector, need to demarcate video camera and projector.The wherein scaling method comparative maturity of video camera, is generally divided into based on the traditional scaling method demarcating thing, the self-calibrating method based on image sequence and the scaling method based on active vision.It is simple that tradition scaling method has principle, stated accuracy advantages of higher, but need high-precision calibrating block, can not break away from artificial interference.Self-calibrating method based on image sequence relies on the relation between multiple image corresponding point directly to demarcate, the strong but poor robustness of dirigibility.Camera marking method based on active vision calculates simply, robustness is higher, but needs to use high precision mobile platform.Projector is generally regarded as reverse video camera, and because it belongs to non-imaged equipment, it demarcates difficulty higher than video camera, and precision is also lower.According to mode getparms, projector's scaling method has based on the scaling method of phase techniques, based on Cross ration invariability scaling method, based on the projector's scaling method etc. of video camera demarcated.Scaling method based on phase techniques needs repeatedly to project sinusoidal grating, and stated accuracy depends on the precision of Absolute phase-unwrapping; Need to do fitting a straight line and gray-level interpolation based on Cross ration invariability scaling method, directly cannot be calculated the full-size(d) of object under test by calibration result; Projector's scaling method based on the video camera demarcated uses relatively more extensive, and need the scaling board of particular design, the design of scaling board affects stated accuracy and robustness.Based on special video camera and projector's uncalibrated image, the present invention proposes the method for solving of a kind of video camera homography matrix and projector's homography matrix, it is simple that the method has method, precision is high, the advantages such as strong robustness, and the true three-dimension information that directly can be calculated object under test by the homography matrix obtained.
Summary of the invention
The object of the invention is to the method for solving proposing a kind of video camera homography matrix and projector's homography matrix, it can be demarcated video camera and projector rapidly, thus obtains video camera homography matrix and projector's homography matrix.
Technical scheme of the present invention is achieved in that the method for solving of a kind of video camera homography matrix and projector's homography matrix, computing machine, video camera, projector, scaling board; It is characterized in that: video camera is all connected with computing machine by cable with projector, realize according to the following steps:
Step 1, in a computer, produce a width camera calibration image, the rgb value of camera calibration image background color is respectively 100,100,100; Camera calibration image comprises the identical white circle of 48 radiuses, and radius is 9mm, arranges arrangement by 8 row 6, distance between adjacent two centers of circle is 23.5mm, uses A4 paper, by camera calibration image printing out, and be pasted onto on a surface plate, form scaling board;
Step 2, in a computer, produce a width projector uncalibrated image, and store in a computer.The rgb value of projector's uncalibrated image background color is all 0; Projector's uncalibrated image comprises the identical white circle of 48 radiuses, and radius is 9mm, and arrange arrangement by 8 row 6, the distance between adjacent two centers of circle is 23.5mm;
Step 3, video camera and projector fixedly to be put in scaling board front, ensure that scaling board is positioned at the field range of video camera and projector;
Step 4, absorb scaling board by video camera, obtain camera calibration plate image;
Step 5, maintenance scaling board are motionless, are all projected on scaling board by projector's uncalibrated image by projector, use video camera shooting scaling board, obtain projector's scaling board image;
Step 6, under ensureing that scaling board is positioned at the prerequisite of the field range of video camera and projector, change the position of scaling board or angle, repeat step 4 and step 5 obtains several camera calibration plate images and projector's scaling board image;
Step 7, the cvThreshold function used in OpenCV1.0, carry out binaryzation to camera calibration plate image and projector's scaling board image successively; Use the cvFindContours function in OpenCV1.0, in camera calibration plate image after binarization and projector's scaling board image, find out the point set of the profile of each figure successively; Use the cvCvtSeqToArray function in OpenCV1.0, successively the point set of the profile of each figure is converted to one-dimension array, in one-dimension array, the type of element is all CvPoint; Finally, use the cvFitEllipse function in OpenCV1.0, ellipse fitting is carried out to each one-dimension array, obtains the center of circle of each ellipse;
Step 8, the camera calibration function CalibrateCamera2 three-dimensional coordinate in the oval center of circle corresponding on the two-dimensional coordinate in the center of circle of circle each in camera calibration image and every width camera calibration plate image passed in OpenCV1.0, Z axis coordinate figure in the world coordinate system in wherein corresponding on the every width camera calibration plate image oval center of circle gets 1.0, be set to WorldZ, just can calculate 3 × 3 rank video camera internal reference matrixes, 3 rank video camera rotating vectors and 3 rank camera translation vectors;
Step 9, the cvRodrigues2 function used in OpenCV1.0, convert 3 × 3 rank video camera rotation matrixs to by video camera rotating vector.Structure 3 × 4 rank video cameras join matrix outward, and wherein first three column vector is three column vectors that video camera rotation matrix is corresponding, and the 4th column vector is camera translation vector; Use the cvGEMM function in OpenCV1.0, video camera internal reference matrix and video camera are joined the video camera homography matrix that matrix conversion becomes 3 × 4 rank outward, is designated as CameraMatrix;
Step 10, according to following formulae discovery temporary variable tmp1 and tmp2
tmp1?=?(FeatureV?*?CameraMatrix[2][1]?–?CameraMatrix[1][1]);
tmp2?=?(FeatureU?*?CameraMatrix[2][1]?–?CameraMatrix[0][1]);
Wherein FeatureV is the V axial coordinate of the oval center of circle under projector's coordinate system in projector's scaling board image, and FeatureU is the U axial coordinate of the oval center of circle under projector's coordinate system in projector's scaling board image;
According to the X-axis coordinate figure WorldX in the world coordinate system in the oval center of circle in projection on following formulae discovery scaling board and Y-axis coordinate figure WorldY;
WorldX?=?(tmp2?*?WorldZ?*?CameraMatrix[1][2]?+?tmp2?*?CameraMatrix[1][3]?-?tmp2?*?FeatureV?*?WorldZ?*?CameraMatrix[2][2]?-?tmp2?*?FeatureV?*?CameraMatrix[2][3]?-?tmp1?*?WorldZ?*?CameraMatrix[0][2]?-?tmp1?*?CameraMatrix[0][3]?+?tmp1?*?FeatureU?*?WorldZ?*?CameraMatrix[2][2]?+?tmp1?*?FeatureU?*?CameraMatrix[2][3])?/?(tmp1?*?CameraMatrix[0][0]?-?tmp1?*?FeatureU?*?CameraMatrix[2][0]?-?tmp2?*?CameraMatrix[1][0]?+?tmp2?*?FeatureV?*?CameraMatrix[2][0]);
WorldY?=?(WorldX?*?CameraMatrix[2][0]?+?WorldZ?*?CameraMatrix[1][2]?+?CameraMatrix[1][3]?-?FeatureV?*?WorldX?*?CameraMatrix[2][0]?-?FeatureV?*?WorldZ?*?CameraMatrix[2][2]?-?FeatureV?*?CameraMatrix[2][3])?/?(FeatureV?*?CameraMatrix[2][1]?–?CameraMatrix[1][1]);
Step 11, the camera calibration function CalibrateCamera2 three-dimensional coordinate in the oval center of circle corresponding on the two-dimensional coordinate in the center of circle of circle each in projector's uncalibrated image and Mei Fu projector scaling board image passed in OpenCV1.0, Z axis coordinate figure in the world coordinate system in wherein corresponding on the Mei Fu projector scaling board image oval center of circle also gets WorldZ, calculates 3 × 3 rank projector internal reference matrixes, 3 rank projector rotating vectors and 3 rank projector translation vectors;
Step 12, the cvRodrigues2 function used in OpenCV1.0, convert 3 × 3 rank projector rotation matrixs to by projector's rotating vector.Join matrix outside structure projector, wherein first three column vector is three column vectors that projector's rotation matrix is corresponding, and the 4th column vector is projector's translation vector; Use the cvGEMM function in OpenCV1.0, projector's internal reference matrix is become projector's homography matrix on 3 × 4 rank with outer ginseng matrix conversion, be designated as ProjectorMatrix;
The homography matrix of video camera and the homography matrix of projector is obtained successively by above step.
Good effect of the present invention is based on special video camera and projector's uncalibrated image, has method simple, the advantages such as precision is high, strong robustness, and the true three-dimension information that directly can be calculated object under test by the homography matrix obtained.
Accompanying drawing explanation
Fig. 1 is the method for solving equipment needed thereby pie graph of a kind of video camera homography matrix and projector's homography matrix.This figure is also specification digest accompanying drawing.Wherein: 1 is computing machine, 2 is video camera, and 3 is projector, and 4 is scaling board.
Fig. 2 is camera calibration image.
Tu3Shi projector uncalibrated image.
Embodiment
Below in conjunction with accompanying drawing, the present invention will be further described: as shown in Figure 1, the method for solving of a kind of video camera homography matrix and projector's homography matrix, computing machine 1, video camera 2, projector 3, scaling board 4; It is characterized in that: video camera 2 is all connected with computing machine 1 by cable with projector 3, realize according to the following steps:
Step 1, in computing machine 1, produce a width camera calibration image, as shown in Figure 2, the rgb value of camera calibration image background color is respectively 100,100,100; Camera calibration image comprises the identical white circle of 48 radiuses, and radius is 9mm, and arrange arrangement by 8 row 6, the distance between adjacent two centers of circle is 23.5mm.Use A4 paper, by camera calibration image printing out, and be pasted onto on a surface plate, form scaling board 4.
Step 2, in computing machine 1, produce a width projector uncalibrated image, as shown in Figure 3, and be stored in computing machine 1.The rgb value of projector's uncalibrated image background color is all 0; Projector's uncalibrated image comprises the identical white circle of 48 radiuses, and radius is 9mm, and arrange arrangement by 8 row 6, the distance between adjacent two centers of circle is 23.5mm.
Step 3, video camera 2 and projector 3 are fixedly put in scaling board 4 front, ensure that scaling board 4 is positioned at the field range of video camera 2 and projector 3.
Step 4, absorb scaling board 4 by video camera 2, obtain camera calibration plate image.
Step 5, maintenance scaling board 4 are motionless, all project on scaling board 4 by projector 3 by projector's uncalibrated image, use video camera 2 to take scaling board 4, obtain projector's scaling board image.
Step 6, under scaling board 4 is positioned at the prerequisite of the field range of video camera 2 and projector 3 in guarantee, change position or the angle of scaling board 4, repeat step 4 and step 5 obtains several camera calibration plate images and projector's scaling board image.
Step 7, the cvThreshold function used in OpenCV1.0, carry out binaryzation to camera calibration plate image and projector's scaling board image successively; Use the cvFindContours function in OpenCV1.0, in camera calibration plate image after binarization and projector's scaling board image, find out the point set of the profile of each figure successively; Use the cvCvtSeqToArray function in OpenCV1.0, successively the point set of the profile of each figure is converted to one-dimension array, in one-dimension array, the type of element is all CvPoint; Finally, use the cvFitEllipse function in OpenCV1.0, ellipse fitting is carried out to each one-dimension array, obtains the center of circle of each ellipse;
Step 8, the camera calibration function CalibrateCamera2 three-dimensional coordinate in the oval center of circle corresponding on the two-dimensional coordinate in the center of circle of circle each in camera calibration image and every width camera calibration plate image passed in OpenCV1.0, Z axis coordinate figure in the world coordinate system in wherein corresponding on the every width camera calibration plate image oval center of circle gets 1.0, be set to WorldZ, just can calculate 3 × 3 rank video camera internal reference matrixes, 3 rank video camera rotating vectors and 3 rank camera translation vectors.
Step 9, the cvRodrigues2 function used in OpenCV1.0, convert 3 × 3 rank video camera rotation matrixs to by video camera rotating vector.Structure 3 × 4 rank video cameras join matrix outward, and wherein first three column vector is three column vectors that video camera rotation matrix is corresponding, and the 4th column vector is camera translation vector; Use the cvGEMM function in OpenCV1.0, video camera internal reference matrix and video camera are joined the video camera homography matrix that matrix conversion becomes 3 × 4 rank outward, is designated as CameraMatrix.
Step 10, according to following formulae discovery temporary variable tmp1 and tmp2
tmp1?=?(FeatureV?*?CameraMatrix[2][1]?–?CameraMatrix[1][1]);
tmp2?=?(FeatureU?*?CameraMatrix[2][1]?–?CameraMatrix[0][1]);
Wherein FeatureV is the V axial coordinate of the oval center of circle under projector's coordinate system in projector's scaling board image, and FeatureU is the U axial coordinate of the oval center of circle under projector's coordinate system in projector's scaling board image.
According to the X-axis coordinate figure WorldX in the world coordinate system in the oval center of circle in projection on following formulae discovery scaling board and Y-axis coordinate figure WorldY.
WorldX?=?(tmp2?*?WorldZ?*?CameraMatrix[1][2]?+?tmp2?*?CameraMatrix[1][3]?-?tmp2?*?FeatureV?*?WorldZ?*?CameraMatrix[2][2]?-?tmp2?*?FeatureV?*?CameraMatrix[2][3]?-?tmp1?*?WorldZ?*?CameraMatrix[0][2]?-?tmp1?*?CameraMatrix[0][3]?+?tmp1?*?FeatureU?*?WorldZ?*?CameraMatrix[2][2]?+?tmp1?*?FeatureU?*?CameraMatrix[2][3])?/?(tmp1?*?CameraMatrix[0][0]?-?tmp1?*?FeatureU?*?CameraMatrix[2][0]?-?tmp2?*?CameraMatrix[1][0]?+?tmp2?*?FeatureV?*?CameraMatrix[2][0]);
WorldY?=?(WorldX?*?CameraMatrix[2][0]?+?WorldZ?*?CameraMatrix[1][2]?+?CameraMatrix[1][3]?-?FeatureV?*?WorldX?*?CameraMatrix[2][0]?-?FeatureV?*?WorldZ?*?CameraMatrix[2][2]?-?FeatureV?*?CameraMatrix[2][3])?/?(FeatureV?*?CameraMatrix[2][1]?–?CameraMatrix[1][1]);
Step 11, the camera calibration function CalibrateCamera2 three-dimensional coordinate in the oval center of circle corresponding on the two-dimensional coordinate in the center of circle of circle each in projector's uncalibrated image and Mei Fu projector scaling board image passed in OpenCV1.0, Z axis coordinate figure in the world coordinate system in wherein corresponding on the Mei Fu projector scaling board image oval center of circle also gets WorldZ, calculates 3 × 3 rank projector internal reference matrixes, 3 rank projector rotating vectors and 3 rank projector translation vectors.
Step 12, the cvRodrigues2 function used in OpenCV1.0, convert 3 × 3 rank projector rotation matrixs to by projector's rotating vector.Join matrix outside structure projector, wherein first three column vector is three column vectors that projector's rotation matrix is corresponding, and the 4th column vector is projector's translation vector; Use the cvGEMM function in OpenCV1.0, projector's internal reference matrix is become projector's homography matrix on 3 × 4 rank with outer ginseng matrix conversion, be designated as ProjectorMatrix.
The homography matrix of video camera 2 and the homography matrix of projector 3 is obtained successively by above step.
Claims (1)
1. a method for solving for video camera homography matrix and projector's homography matrix, the method for solving of a kind of video camera homography matrix and projector's homography matrix, computing machine, video camera, projector, scaling board; It is characterized in that: video camera is all connected with computing machine by cable with projector, realize according to the following steps:
Step 1, in a computer, produce a width camera calibration image, the rgb value of camera calibration image background color is respectively 100,100,100; Camera calibration image comprises the identical white circle of 48 radiuses, and radius is 9mm, and arrange arrangement by 8 row 6, the distance between adjacent two centers of circle is 23.5mm;
Use A4 paper, by camera calibration image printing out, and be pasted onto on a surface plate, form scaling board;
Step 2, in a computer, produce a width projector uncalibrated image, and store in a computer; The rgb value of projector's uncalibrated image background color is all 0; Projector's uncalibrated image comprises the identical white circle of 48 radiuses, and radius is 9mm, and arrange arrangement by 8 row 6, the distance between adjacent two centers of circle is 23.5mm;
Step 3, video camera and projector fixedly to be put in scaling board front, ensure that scaling board is positioned at the field range of video camera and projector;
Step 4, absorb scaling board by video camera, obtain camera calibration plate image;
Step 5, maintenance scaling board are motionless, are all projected on scaling board by projector's uncalibrated image by projector, use video camera shooting scaling board, obtain projector's scaling board image;
Step 6, under ensureing that scaling board is positioned at the prerequisite of the field range of video camera and projector, change the position of scaling board or angle, repeat step 4 and step 5 obtains several camera calibration plate images and projector's scaling board image;
Step 7, the cvThreshold function used in OpenCV1.0, carry out binaryzation to camera calibration plate image and projector's scaling board image successively; Use the cvFindContours function in OpenCV1.0, in camera calibration plate image after binarization and projector's scaling board image, find out the point set of the profile of each figure successively; Use the cvCvtSeqToArray function in OpenCV1.0, successively the point set of the profile of each figure is converted to one-dimension array, in one-dimension array, the type of element is all CvPoint; Finally, use the cvFitEllipse function in OpenCV1.0, ellipse fitting is carried out to each one-dimension array, obtains the center of circle of each ellipse;
Step 8, the camera calibration function CalibrateCamera2 three-dimensional coordinate in the oval center of circle corresponding on the two-dimensional coordinate in the center of circle of circle each in camera calibration image and every width camera calibration plate image passed in OpenCV1.0, Z axis coordinate figure in the world coordinate system in wherein corresponding on the every width camera calibration plate image oval center of circle gets 1.0, be set to WorldZ, just can calculate 3 × 3 rank video camera internal reference matrixes, 3 rank video camera rotating vectors and 3 rank camera translation vectors;
Step 9, the cvRodrigues2 function used in OpenCV1.0, convert 3 × 3 rank video camera rotation matrixs to by video camera rotating vector; Structure 3 × 4 rank video cameras join matrix outward, and wherein first three column vector is three column vectors that video camera rotation matrix is corresponding, and the 4th column vector is camera translation vector; Use the cvGEMM function in OpenCV1.0, video camera internal reference matrix and video camera are joined the video camera homography matrix that matrix conversion becomes 3 × 4 rank outward, is designated as CameraMatrix;
Step 10, according to following formulae discovery temporary variable tmp1 and tmp2
tmp1?=?(FeatureV?*?CameraMatrix[2][1]?–?CameraMatrix[1][1]);
tmp2?=?(FeatureU?*?CameraMatrix[2][1]?–?CameraMatrix[0][1]);
Wherein FeatureV is the V axial coordinate of the oval center of circle under projector's coordinate system in projector's scaling board image, and FeatureU is the U axial coordinate of the oval center of circle under projector's coordinate system in projector's scaling board image;
According to the X-axis coordinate figure WorldX in the world coordinate system in the oval center of circle in projection on following formulae discovery scaling board and Y-axis coordinate figure WorldY;
WorldX?=?(tmp2?*?WorldZ?*?CameraMatrix[1][2]?+?tmp2?*?CameraMatrix[1][3]?-?tmp2?*?FeatureV?*?WorldZ?*?CameraMatrix[2][2]?-?tmp2?*?FeatureV?*?CameraMatrix[2][3]?-?tmp1?*?WorldZ?*?CameraMatrix[0][2]?-?tmp1?*?CameraMatrix[0][3]?+?tmp1?*?FeatureU?*?WorldZ?*?CameraMatrix[2][2]?+?tmp1?*?FeatureU?*?CameraMatrix[2][3])?/?(tmp1?*?CameraMatrix[0][0]?-?tmp1?*?FeatureU?*?CameraMatrix[2][0]?-?tmp2?*?CameraMatrix[1][0]?+?tmp2?*?FeatureV?*?CameraMatrix[2][0]);
WorldY?=?(WorldX?*?CameraMatrix[2][0]?+?WorldZ?*?CameraMatrix[1][2]?+?CameraMatrix[1][3]?-?FeatureV?*?WorldX?*?CameraMatrix[2][0]?-?FeatureV?*?WorldZ?*?CameraMatrix[2][2]?-?FeatureV?*?CameraMatrix[2][3])?/?(FeatureV?*?CameraMatrix[2][1]?–?CameraMatrix[1][1]);
Step 11, the camera calibration function CalibrateCamera2 three-dimensional coordinate in the oval center of circle corresponding on the two-dimensional coordinate in the center of circle of circle each in projector's uncalibrated image and Mei Fu projector scaling board image passed in OpenCV1.0, Z axis coordinate figure in the world coordinate system in wherein corresponding on the Mei Fu projector scaling board image oval center of circle also gets WorldZ, calculates 3 × 3 rank projector internal reference matrixes, 3 rank projector rotating vectors and 3 rank projector translation vectors;
Step 12, the cvRodrigues2 function used in OpenCV1.0, convert 3 × 3 rank projector rotation matrixs to by projector's rotating vector; Join matrix outside structure projector, wherein first three column vector is three column vectors that projector's rotation matrix is corresponding, and the 4th column vector is projector's translation vector; Use the cvGEMM function in OpenCV1.0, projector's internal reference matrix is become projector's homography matrix on 3 × 4 rank with outer ginseng matrix conversion, be designated as ProjectorMatrix;
The homography matrix of video camera and the homography matrix of projector is obtained successively by above step.
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