Image projection device for 3D measurement and calibration method for calibration of camera and projector

1. An image projection device, comprising:

a camera;

a projector configured to:

project a first image; and

project structural light on a checker pattern; and

circuitry configured to:

calibrate the camera;

ray trace the checker pattern;

determine first distortion parameters of the projector based on evaluation of a distortion amount, wherein the distortion amount is based on a group of lattice points of the checker pattern, wherein the group of lattice points of the checker pattern constitutes a straight line on projector coordinates;

determine a first correspondence relation between a first lattice point of the group of lattice points of the checker pattern and the projector coordinates, and a second correspondence relation between a second lattice point of the group of lattice points on a second image of the checker pattern after distortion correction and world coordinates;

determine internal parameters of the projector and external parameters of the projector, based on the first correspondence relation; and

determine a first perspective projection matrix that includes the internal parameters and the external parameters of the projector by first nonlinear optimization, based on the second correspondence relation; and

generate a corrected image based on correction of the first image projected from the projector, wherein the first image projected from the projector is corrected based on at least one of the determined internal parameters, the determined external parameters, or the determined first distortion parameters.

2. The image projection device according to claim 1 ,

wherein the circuitry is further configured to determine the internal parameters of the projector and the external parameters of the projector based on lens distortion of the projector, and

wherein the determination of the internal parameters of the projector and the external parameters of the projector is independent of a calibration result of the camera.

3. The image projection device according to claim 1 ,

wherein the circuitry is further configured to determine the first distortion parameters of the projector by a Levenberg-Marquardt (LM) method, with an inclination difference between two candidates of straight lines as the distortion amount, and

wherein the group of lattice points constitutes the straight line on each of the two candidates of straight lines.

4. The image projection device according to claim 1 ,

wherein the circuitry is further configured to determine the first perspective projection matrix based on the first nonlinear optimization of a re-projection error between detection image coordinates of the camera and re-projection image coordinates by a Levenberg-Marquardt (LM) method.

5. The image projection device according to claim 1 ,

wherein the circuitry is further configured to determine the first correspondence relation with sub-pixel accuracy.

6. The image projection device according to claim 1 ,

wherein the circuitry is further configured to determine LocalHomography of calibration of a plurality of projector pixels limited to surroundings of the first lattice point of the checker pattern.

7. The image projection device according to claim 6 ,

wherein the circuitry is further configured to determine the LocalHomography of calibration of the plurality of projector pixels with a limit to a surrounding area of the first lattice point, and wherein the surrounding area of the first lattice point excludes influences of lens distortion of the projector.

8. The image projection device according to claim 7 ,

wherein the circuitry is further configured to determine the LocalHomography of calibration of the plurality of projector pixels based on a decoding error of the structural light.

9. The image projection device according to claim 1 ,

wherein the circuitry is further configured to:

detect the first lattice point from a third image obtained based on photography of the checker pattern with the camera,

determine second distortion parameters of the camera based on the evaluation of the distortion amount based on the group of lattice points, and

determine internal parameters of the camera and external parameters of the camera based on the second correspondence relation.

10. The image projection device according to claim 9 ,

wherein the circuitry is further configured to determine the second distortion parameters of the camera by a Levenberg-Marquardt (LM) method, with an inclination difference between two candidates of straight lines as the distortion amount, and wherein the group of lattice points constitutes the straight line on each of the two candidates of straight lines.

11. The image projection device according to claim 9 ,

wherein the circuitry is further configured to determine a second perspective projection matrix including the internal parameters of the camera and the external parameters of the camera by second nonlinear optimization, based on the second correspondence relation.

12. The image projection device according to claim 11 ,

wherein the circuitry is further configured to determine the second perspective projection matrix based on the second nonlinear optimization of a re-projection error between detection image coordinates of the camera and re-projection image coordinates by a Levenberg-Marquardt (LM) method.

13. The image projection device according to claim 1 , wherein the circuitry is further configured to ray trace the world coordinates obtained by projection of a pixel on the projector coordinates with ray influenced by lens distortion.

14. The image projection device according to claim 1 , wherein the circuitry is further configured to reverse ray trace a pixel on the projector coordinates, irradiated with ray, to project the world coordinates based on lens distortion.

15. The image projection device according to claim 14 ,

wherein the circuitry is further configured to:

ray trace a gray code projected by the projector on the checker pattern with the world coordinates,

calculate a corresponding point of the world coordinates and the projector coordinates in a state with projector distortion,

determine a distortion correction function,

determine a third correspondence relation between the world coordinates and distortionless projection coordinates, and

formulate a reverse ray tracing process.

16. The image projection device according to claim 15 ,

wherein the circuitry is further configured to:

determine a reverse distortion correction function D′ to correct distortionless projector coordinates to the projector coordinates in the state with projector distortion; and

formulate a ray tracing process to ray trace the world coordinates projected on a projector pixel.

17. The image projection device according to claim 1 ,

wherein the circuitry is further configured to determine at least one of the first distortion parameters, the internal parameters of the projector, the external parameters of the projector, internal parameter of the camera, or external parameter of the camera, with high accuracy based on a number of photographed images and depth information of a depth from the camera to a checker board, and

wherein the check pattern in on the checker board.

18. A calibration method, comprising:

in an image projection device including a camera and a projector:

projecting structural light on a checker pattern:

ray tracing the checker pattern;

determining distortion parameters of the projector by evaluating a distortion amount, wherein the distortion amount is based on a group of lattice points of the checker pattern, wherein the group of lattice points of the checker pattern constitutes a straight line on projector coordinates;

determining a first correspondence relation between a first lattice point of the group of lattice points of the checker pattern and the projector coordinates and a second correspondence relation between a second lattice point of the group of lattice points on an image of the checker pattern after distortion correction and world coordinates;

determining internal parameters of the projector and external parameters of the projector based on the first correspondence relation,

wherein the determination of the internal parameters and the external parameters of the projector is independent of camera calibration parameters; and

determining a perspective projection matrix that includes the internal parameters and the external parameters of the projector by nonlinear optimization, based on the second correspondence relation.