CN112330556B - Spherical screen projection geometric correction method based on rational Bessel curved surface - Google Patents

Spherical screen projection geometric correction method based on rational Bessel curved surface Download PDF

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CN112330556B
CN112330556B CN202011207309.XA CN202011207309A CN112330556B CN 112330556 B CN112330556 B CN 112330556B CN 202011207309 A CN202011207309 A CN 202011207309A CN 112330556 B CN112330556 B CN 112330556B
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curved surface
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侯培国
张铮
宋涛
祁继辉
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Yanshan University
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Abstract

The invention discloses a spherical screen projection geometric correction method based on a rational Bessel curved surface, which belongs to the field of virtual reality projection image processing, and provides a scheme for distortion correction of an original image by a rational Bessel curved surface optimization algorithm aiming at the problem that factors such as the model of a projector, the position of the projector, the projection angle of the projector and the like change influence the projection image, the invention ensures the flexibility of geometric correction, and experimental results show that compared with the projection image after the geometric correction of the Bessel curved surface, after the geometric correction of the rational Bessel curved surface, the difference between the actual value and the theoretical value of the coordinate of the mark point of the projection picture is reduced, the ideal geometric shape of the projection picture of the spherical screen is more trend, the method is suitable for the condition that the model, the position and the angle of the projector are changed, the feasibility of the weight optimization method in realizing the geometric correction of the spherical screen projection system is proved.

Description

Spherical screen projection geometric correction method based on rational Bessel curved surface
Technical Field
The invention relates to the field of virtual reality projection image processing, in particular to a spherical screen projection geometric correction method based on rational Bessel curved surfaces.
Background
Virtual reality technology is an important development subject in the twenty-first century and is also one of important technologies affecting people's lives. The virtual reality technology research content relates to a plurality of fields, uses the computer as the basis, uses high-tech means to promote vision, sense of hearing, touch effect by a wide margin with the mode of imitating, makes the user produce the sensation of immersing in virtual environment. In recent years, as computer technology has advanced, virtual reality technology has also advanced rapidly. The dome screen projection system is a completely immersive VR display system, and because the system can enlarge the visual angle of a user, provide all-around observation, bring a better visual field range and a stronger sense of presence, the system has become one of the popular directions of research in the technical field of home and abroad virtual reality. A good ball curtain projection virtual reality system should have good resolution ratio, high sense of immersing, but because a series of problems such as projection screen geometry, projecting apparatus model or projecting apparatus put skew, the projection picture on the ball curtain can take place the geometric distortion, leads to presenting the picture unreal, influences user experience.
At present, some geometric correction methods for spherical screen projection mostly adopt a Bezier curved surface to carry out geometric correction, but only the Bezier curved surface is used to carry out geometric correction, and the influence of factors such as the type of a projector, the position of the projector, the projection angle of the projector and the like on a projection picture cannot be solved.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a spherical screen projection geometric correction method based on a rational Bessel curved surface, and each control point is given a weight on the basis of obtaining control points of the Bessel curved surface, and the rational Bessel curved surface is adopted to optimize geometric correction.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows: a spherical screen projection geometric correction method based on rational Bessel curved surfaces comprises the following steps:
step 1) fixing a projector and installing a fisheye camera;
step 2) generating a uniform mark by using OpenCVRecording a rectangular picture of points, projecting the rectangular picture to a spherical screen, and obtaining a coordinate value set P of an actual mark point in a projection picture in a shooting space by using a findContours function and an ellipse function of OpenCV (open computing environment)C；
Step 3) marking theoretical marking points of the dome screen at the intersection points of the longitude and the latitude of the dome screen by a laser array, shooting by a fish-eye camera, extracting the positions of the theoretical marking points in the shooting space, and obtaining a set P of coordinate values of the theoretical marking points in the dome screen in the shooting space by using a findContours function and an ellipse function of OpenCV (open computer vision system)I；
Step 4) collecting P according to coordinate values of actual mark points in the projection pictureCAnd a set P of theoretical mark point coordinate values in the dome in the camera shooting spaceIFinding a set of control points p for the coordinate space transformationC→I；
Step 5) obtaining the coordinates of 4 multiplied by 4 control points according to the step 4) and constructing a bicubic Bessel curved surface model;
step 6) projecting the original image to a spherical screen after geometric correction according to the step 5);
step 7), if the model, the position and the angle of the projector are not changed, the correction process is finished;
step 8) if any one of the model, the position and the angle of the projector changes, giving a weight to each control point through comparison between the set of the mark point coordinate values of the projection picture obtained after the geometric correction of the original image in the shooting space in the step 6) and the set of the theoretical mark point coordinate values obtained in the step 3);
step 9) constructing a rational Bessel curved surface model through the control points obtained in the step 5) and the control point weights obtained in the step 8), and improving the precision of geometric correction;
and step 10) performing geometric correction on the original image according to the step 9) and then projecting the original image to the spherical screen, and finishing the correction process.
The technical scheme of the invention is further improved as follows: in step 2), shooting the dome screen projection picture without geometric correction through a fish-eye camera, and converting the shot dome screen projection picture from an RGB color space to a YCbCr color space.
The inventionThe technical proposal is further improved in that: in the step 2), the mark points in the spherical screen space are circular, and a coordinate set P of the center of the actual circular mark point in the projection picture before geometric correction in the shooting space is obtained by using an OpenCV profile to extract a findContours function and an ellipse fitting ellise functionC。
The technical scheme of the invention is further improved as follows: in the step 4), a coordinate value set P is set according to the actual mark points in the projection pictureCAnd a set P of theoretical mark point coordinate values in the dome in the camera shooting spaceIFinding a set of control points p for the coordinate space transformationC→IThe expression of the geometrical transformation relationship is as follows:
PI＝C(PC)·pC→I，
wherein, C (P)C) Represents PCThe corresponding set of Bessel basis functions.
The technical scheme of the invention is further improved as follows: the coordinates of 4 × 4 control points are obtained in step 5), as shown in the following formula:
Figure BDA0002757451150000031
Figure BDA0002757451150000032
Figure BDA0002757451150000033
wherein u represents the abscissa of the position of the actual mark point in the projection picture in the shooting space; v represents the vertical coordinate of the position of the actual mark point in the projection picture in the shooting space; n and M represent the times of the horizontal and vertical coordinates of the Bessel curved surface, and the specific numerical values of the N and M are determined according to the number of the control points; i belongs to [0, N ]]；j∈[0，M]；pijRepresents the (i +1) × (j +1) th control point; p (u, v) represents the coordinate value of the theoretical mark point in the shooting space after the pixel point of the actual mark point (u, v) is transformed;
Figure BDA0002757451150000034
and
Figure BDA0002757451150000035
is a Bessel basis function;
n, M is all taken as 3, a bicubic rational Bessel curved surface is constructed, the coordinate set of the actual mark points in the shooting space is taken as the value before transformation of the Bessel curved surface, the coordinate set of the theoretical mark points in the shooting space is taken as the value after transformation of the Bessel curved surface, and the coordinate set can be substituted into the bicubic Bessel curved surface and expanded into a matrix as shown in the following formula:
Figure BDA0002757451150000041
the technical scheme of the invention is further improved as follows: in step 6), a set of coordinates of the mark points of the projection picture after geometric correction in the imaging space is obtained by using a findContours function and an ellipse function of OpenCV.
The technical scheme of the invention is further improved as follows: giving a weight to each control point in step 8), as shown in the following equation:
Figure BDA0002757451150000042
wherein, wijFor corresponding control point pijThe weight of (2).
The technical scheme of the invention is further improved as follows: in step 9), there is a rational bezier surface model, as shown in the following equation:
P＝CR(P0)·W·pC→I,
wherein, P0Projecting each pixel point of the original image; w is the control point pC→ISet of weights, CR() For the set of rational Bessel basis functions, P is each pixel point after the geometric pre-distortion of the projection image.
Due to the adoption of the technical scheme, the invention has the technical progress that:
1. the invention ensures the flexibility of geometric correction, and experimental results show that after rational Bezier curved surface geometric correction, the difference between the actual value and the theoretical value of the mark point coordinates of the projection picture is reduced, so that the projection picture tends to be in an ideal geometric shape of a spherical screen projection picture, and the method is suitable for the condition that the model, the position and the angle of a projector are changed, and proves the feasibility of the weight optimization method in realizing the geometric correction of a spherical screen projection system.
Drawings
FIG. 1 is an overall flow diagram of the present invention;
FIG. 2 is a projected image of actual marker points in the projection image before geometric correction in the imaging space according to the present invention;
FIG. 3 is a projection image of the coordinate values of the theoretical marking points in the dome before geometric correction in the camera space according to the present invention;
fig. 4 is a schematic diagram of a bicubic bezier surface.
Detailed Description
The present invention will be described in further detail with reference to the following examples:
as shown in fig. 1 to 4, a spherical screen projection geometric correction method based on a rational bezier surface utilizes OpenCV recognition images and OpenGL distorted images on a Windows operating system, and specifically includes the following steps:
step 1) fixing a projector and installing a fisheye camera;
step 2) generating a rectangular picture with uniform mark points by using OpenCV, projecting the rectangular picture to a dome screen, shooting a dome screen projection picture without geometric correction by using a fish-eye camera because the brightness of the mark points in the projection picture is overlarge than that of the background, converting the shot dome screen projection picture from an RGB color space to a YCbCr color space so as to enhance the brightness of the mark points, so that the mark points in a shooting space can be accurately extracted, and in order to avoid the influence of environmental factors to cause that Hough circle detection Hough curves function cannot be accurately identified, obtaining a coordinate value set P of actual mark points in the projection picture in the shooting space by using a findContours function and an ellipse function of OpenCVC；
Step 3) marking theoretical marking points of the dome screen at the intersection points of the longitude and the latitude of the dome screen by a laser array, shooting by a fish-eye camera, extracting the positions of the theoretical marking points in the shooting space, and obtaining a set P of coordinate values of the theoretical marking points in the dome screen in the shooting space by using a findContours function and an ellipse function of OpenCV (open computer vision system)I；
Step 4) collecting P according to coordinate values of actual mark points in the projection pictureCAnd a set P of theoretical mark point coordinate values in the dome in the camera shooting spaceIFinding a set of control points p for the coordinate space transformationC→ISet of control points pC→IThe expression of the geometrical transformation relationship is as follows:
PI＝C(PC)·pC→I
wherein, C (P)C) Represents PCThe corresponding set of Bessel basis functions.
And 5) obtaining the coordinates of 4 multiplied by 4 control points according to the step 4), as shown in the following formula:
Figure BDA0002757451150000061
Figure BDA0002757451150000062
Figure BDA0002757451150000063
wherein u represents the abscissa of the position of the actual mark point in the projection picture in the shooting space; v represents the vertical coordinate of the position of the actual mark point in the projection picture in the shooting space; n and M represent the times of the horizontal and vertical coordinates of the Bessel curved surface, and the specific numerical values of the N and M are determined according to the number of the control points; i belongs to [0, N ]]；j∈[0，M]；pijRepresents the (i +1) × (j +1) th control point; p (u, v) represents the coordinate value of the theoretical mark point in the shooting space after the pixel point of the actual mark point (u, v) is transformed;
Figure BDA0002757451150000064
and
Figure BDA0002757451150000065
is a Bessel basis function;
n, M is all taken as 3, a bicubic rational Bessel curved surface is constructed, the coordinate set of the actual mark points in the shooting space is taken as the value before transformation of the Bessel curved surface, the coordinate set of the theoretical mark points in the shooting space is taken as the value after transformation of the Bessel curved surface, and the coordinate set can be substituted into the bicubic Bessel curved surface and expanded into a matrix as shown in the following formula:
Figure BDA0002757451150000071
step 6) obtaining a set of projection picture mark point coordinate values after geometric correction in the shooting space by using a findContours function and an ellise function of OpenCV, and projecting the original image to a spherical screen after geometric correction according to the step 5);
step 7), if the model, the position and the angle of the projector are not changed, the correction process is finished;
step 8) if any one of the model, the position and the angle of the projector changes, giving a weight to each control point by comparing the set of the mark point coordinate values of the projection picture obtained by geometrically correcting the original image in the shooting space in the step 6) with the set of the theoretical mark point coordinate values obtained in the step 3), as shown in the following formula:
Figure BDA0002757451150000072
wherein, wijFor corresponding control point pijThe weight of (2).
Step 9) constructing a rational Bessel curved surface model through the control points obtained in the step 5) and the control point weights obtained in the step 8), as shown in the following formula:
P＝CR(P0)·W·pC→I,
wherein, P0Projecting each pixel point of the original image; w is the control point pC→ISet of weights, CR() For the set of rational Bessel basis functions, P is each pixel point after the geometric pre-distortion of the projection image;
and giving a weight to each control point, optimizing by adopting a rational Bessel curved surface to improve the geometric correction precision in different projection environments, and warping the original image by using the obtained rational Bessel curved surface to project the original image to the spherical screen.
And step 10) performing geometric correction on the original image according to the step 9) and then projecting the original image to the spherical screen, and finishing the correction process.
The specific embodiment is as follows:
the experimental result shows that when the projection environment of the spherical screen changes, the projection image which is subjected to Bezier curve geometric pre-distortion is projected to the spherical screen again, the projection picture is collected through a fisheye camera, the actual value and the theoretical value of the coordinate of the mark point are compared in the shooting space, the average absolute error (namely MAE) is obtained, then a rational Bezier curve model is constructed, the weight value is obtained, the projection image is subjected to rational Bezier curve geometric pre-distortion and then projected to the spherical screen, the actual value and the theoretical value of the coordinate of the mark point are compared in the shooting space, the average absolute error is obtained, and the comparison result is shown in the following table:
number of experiments Experiment one Experiment two Experiment three Experiment four
MAE for bezier surface geometric correction 3.13 2.42 2.36 2.84
MAE for rational Bessel surface geometric correction 1.52 1.34 1.43 1.66
Compared with the projection picture after the Bezier surface geometric correction, the MAE (namely the difference between the actual value and the theoretical value of the mark point coordinate) of the mark point coordinate value of the projection picture after the rational Bezier surface geometric correction is reduced, the MAE tends to the ideal geometric shape of the spherical screen projection picture, and the method is suitable for the condition that the model, the position and the angle of a projector are changed, and proves the feasibility of the weight optimization method in realizing the geometric correction of the spherical screen projection system.

Claims (8)

1. A spherical screen projection geometric correction method based on rational Bessel curved surfaces is characterized by comprising the following steps: the method comprises the following steps:
step 1) fixing a projector and installing a fisheye camera;
step 2) generating a rectangular picture with uniform mark points by using OpenCV, projecting the rectangular picture to a spherical screen, and obtaining a coordinate value set P of actual mark points in a projection picture in a shooting space by using a findContours function and an ellipse function of OpenCVC；
Step 3) marking theoretical marking points of the dome screen at the intersection points of the longitude and the latitude of the dome screen through a laser array, shooting through a fish-eye camera, extracting the positions of the theoretical marking points in a shooting space, and obtaining shooting through a findContours function and an ellipse function of OpenCV (open computer vision library)Set P of theoretical marking point coordinate values in dome in image spaceI；
Step 4) collecting P according to coordinate values of actual mark points in the projection pictureCAnd a set P of theoretical mark point coordinate values in the dome in the camera shooting spaceIFinding a set of control points p for the coordinate space transformationC→I；
Step 5) obtaining the coordinates of 4 multiplied by 4 control points according to the step 4) and constructing a bicubic Bessel curved surface model;
step 6) projecting the original image to a spherical screen after geometric correction according to the step 5);
step 7), if the model, the position and the angle of the projector are not changed, the correction process is finished;
step 8) if any one of the model, the position and the angle of the projector changes, giving a weight to each control point through comparison between the set of the mark point coordinate values of the projection picture obtained after the geometric correction of the original image in the image pick-up space in the step 6) and the set of the theoretical mark point coordinate obtained in the step 3) to construct a rational Bessel curved surface model;
step 9) constructing a rational Bessel curved surface model through the control points obtained in the step 5) and the control point weights obtained in the step 8), and improving the precision of geometric correction;
and step 10) performing geometric correction on the original image according to the step 9) and then projecting the original image to the spherical screen, and finishing the correction process.
2. The spherical screen projection geometric correction method based on the rational B-Bessel curved surface according to claim 1, characterized in that: in step 2), shooting the dome screen projection picture without geometric correction through a fish-eye camera, and converting the shot dome screen projection picture from an RGB color space to a YCbCr color space.
3. The spherical screen projection geometric correction method based on the rational B-Bessel curved surface according to claim 2, characterized in that: in the step 2), the mark points in the spherical screen space are circular, and a few camera shooting spaces are obtained by using the outline extraction findContours function of OpenCV and the ellipse fitting ellise functionWhich corrects the coordinate set P of the center of the actual circular mark point in the front projection pictureC。
4. The spherical screen projection geometric correction method based on the rational B-Bessel curved surface according to claim 3, characterized in that: in the step 4), a coordinate value set P is set according to the actual mark points in the projection pictureCAnd a set P of theoretical mark point coordinate values in the dome in the camera shooting spaceIFinding a set of control points p for the coordinate space transformationC→IThe expression of the geometrical transformation relationship is as follows:
PI＝C(PC)·pC→I，
wherein, C (P)C) Represents PCThe corresponding set of Bessel basis functions.
5. The spherical screen projection geometric correction method based on the rational B-Bessel curved surface according to claim 4, characterized in that: the coordinates of 4 × 4 control points are obtained in step 5), as shown in the following formula:
Figure FDA0002757451140000021
Figure FDA0002757451140000022
Figure FDA0002757451140000023
wherein u represents the abscissa of the position of the actual mark point in the projection picture in the shooting space; v represents the vertical coordinate of the position of the actual mark point in the projection picture in the shooting space; n and M represent the times of the horizontal and vertical coordinates of the Bessel curved surface, and the specific numerical values of the N and M are determined according to the number of the control points; i belongs to [0, N ]]；j∈[0，M]；pijRepresents the (i +1) × (j +1) th control point; p (u, v) represents an image with an actual marker point of (u, v)The coordinate values of the theoretical mark points in the camera space after the prime point transformation;
Figure FDA0002757451140000031
and
Figure FDA0002757451140000032
is a Bessel basis function;
n, M is all taken as 3, a bicubic rational Bessel curved surface is constructed, the coordinate set of the actual mark points in the shooting space is taken as the value before transformation of the Bessel curved surface, the coordinate set of the theoretical mark points in the shooting space is taken as the value after transformation of the Bessel curved surface, and the coordinate set can be substituted into the bicubic Bessel curved surface and expanded into a matrix as shown in the following formula:
Figure FDA0002757451140000033
6. the spherical screen projection geometric correction method based on the rational B-Bessel curved surface according to claim 5, characterized in that: in step 6), a set of coordinates of the mark points of the projection picture after geometric correction in the imaging space is obtained by using a findContours function and an ellipse function of OpenCV.
7. The spherical screen projection geometric correction method based on the rational B-Bessel curved surface according to claim 6, characterized in that: giving a weight to each control point in step 8), as shown in the following equation:
Figure FDA0002757451140000034
wherein, wijFor corresponding control point pijThe weight of (2).
8. The spherical screen projection geometric correction method based on the rational B-Bessel curved surface according to claim 7, characterized in that: in step 9), there is a rational bezier surface model, as shown in the following equation:
P＝CR(P0)·W·pC→I,
wherein, P0Projecting each pixel point of the original image; w is the control point pC→ISet of weights, CR() For the set of rational Bessel basis functions, P is each pixel point after the geometric pre-distortion of the projection image.
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