WIDE FOV CAMERA IMAGE CALIBRATION AND DE-WARPING
A system and method for providing calibration and de-warping for ultra-wide FOV cameras. The method includes estimating intrinsic parameters such as the focal length of the camera and an image center of the camera using multiple measurements of the near optical axis object points and a pinhole camera model. The method further includes estimating distortion parameters of the camera using an angular distortion model that defines an angular relationship between an incident optical ray passing an object point in an object space and an image point on an image plane that is an image of the object point on the incident optical ray. The method can include a parameter optimization process to refine the parameter estimation.
1 . A method for calibrating and de-warping a camera, said method comprising:
estimating a focal length of the camera;
estimating an image center of an image plane of the camera;
providing an angular distortion model that defines an angular relationship between an incident optical ray passing an object point in an object space and an image point on the image plane that is an image of the object point on the incident optical ray; and
estimating distortion parameters in the distortion model.
2 . The method according to claim 1 further comprising optimizing the estimated parameters to refine the parameter estimation.
3 . The method according to claim 2 wherein optimizing the estimated parameters includes using initial estimates of the focal length and the image center of the camera and the distortion parameters for multiple points on a target to refine the estimate of the focal length and the image center and a camera position estimation, and using the refined focal length and image center estimation to refine the estimation of the distortion parameters, and wherein the refinement of the estimates of the focal length, the image center, the camera position and the distortion parameters are performed iteratively until a predetermined value is reached.
4 . The method according to claim 1 wherein estimating a focal length and an image center of an image plane of the camera includes mounting the camera to a translational stage and moving the camera along the stage to different locations, mounting a checkerboard target to a target stage positioned relative to the translational stage, defining a target region on the target around an optical axis of the camera that includes squares in the checkerboard target and using the pinhole camera model and positions of corners of the squares in images acquired at the different locations along the stage to determine the focal length and the image center.
5 . The method according to claim 4 further comprising determining camera extrinsic parameters.
6 . The method according to claim 5 wherein the camera extrinsic parameters include a rotational matrix of the camera and a translational vector of the camera in terms of object space coordinates.
7 . The method according to claim 6 wherein the translational vector is determined using a vector from a camera aperture point to an object space center point.
8 . The method according to claim 6 wherein the rotational matrix and the translational vector are determined by the pinhole camera model.
9 . The method according to claim 4 wherein the target region satisfies the pinhole camera model and a perspective rectilinear projection condition.
10 . The method according to claim 1 wherein estimating distortion parameters includes mounting the camera to a two-axis rotational stage that rotates the camera in two perpendicular rotational directions and calculating a combined angle based on the combination of the two rotational angles.
11 . The method according to claim 10 wherein determining angular distortion parameters includes determining a combined incident angle for a plurality of two rotational angles.
12 . The method according to claim 1 wherein providing an angular distortion model includes using the equation:
= g (θ)= p 1 ·θ+p 2 ·θ 2 +p 3 ·θ 5 + . . .
where is the distortion angle, θ is an incident angle of the object point and p is the angular distortion parameters.
13 . The method according to claim 1 wherein the camera is a wide view or ultra-wide view camera.
14 . The method according to claim 13 wherein the camera has a 180° or greater field-of-view.
15 . The method according to claim 13 wherein the camera is a vehicle camera.
16 . A method for calibrating and de-warping a wide view or ultra-wide view vehicle camera, said method comprising:
estimating a focal length and an image center of an image plane of the camera, wherein estimating a focal length and an image center of an image plane of the camera includes mounting the camera to a translational stage and moving the camera along the stage to different locations, mounting a checkerboard target to a target stage positioned relative to the translational stage, defining a target region on the target around an optical axis of the camera that includes squares in the checkerboard target and using the pinhole camera model and positions of corners of the squares in images acquired at the different locations along the stage to determine the focal length and the image center;
providing an angular distortion model that defines an angular relationship between an incident optical ray passing an object point in an object space and an image point on the image plane that is an image of the object point on the incident optical ray; and
estimating distortion parameters in the distortion model, wherein estimating distortion parameters includes mounting the camera to a two-axis rotational stage that rotates the camera in two perpendicular rotational directions and calculating a combined angle based on the combination of the two rotational angles.
17 . The method according to claim 16 further comprising determining camera extrinsic parameters, wherein the camera extrinsic parameters include a rotational matrix of the camera and a translational vector of the camera in terms of object space coordinates, and wherein the translational vector is determined using a vector from a camera aperture point to an object space center point, and wherein the rotational matrix and the translational vector are determined by the pinhole camera model.
18 . The method according to claim 16 wherein determining angular distortion parameters includes determining a combined incident angle for a plurality of two rotational angles.
19 . The method according to claim 16 wherein providing an angular distortion model includes using the equation:
=g(θ)= p 1 ·θ+p 2 ·θ 2 +p 3 ·θ 5 + . . .
where σ is the distortion angle, θ is an incident angle of the object point and p is the angular distortion parameters.
20 . A system for calibrating and a de-warping a camera, said system comprising:
means for estimating a focal length of the camera;
means for estimating an image center of an image plane of the camera;
means for providing an angular distortion model that defines an angular relationship between an incident optical ray passing an object point in an object space and an image point on the image plane that is an image of the object point on the incident optical ray; and
means for estimating distortion parameters in the distortion model.