calibration: DLT smaller error than solvePNP

asked 2015-12-14 03:29:29 -0500

cy gravatar image

I'm trying to calibrate the velodyne lidar to the camera. I picked corresponding points between the camera's image and the range image and then performed direct linear transformation, as well as using solvePNP(). Theoretically, solvePNP should produce the extrinsics that give better reproduction error, but looking at it, seems like that is not the case. Is there anything I'm doing wrong here?

 DEBUG:root:error:
    > DLT: 100.053025398
    > 
    > DEBUG:root:error: solvePNP: 163.847104258

Here is my code for calibration:

mport numpy as np
import cv2, logging    

def with_intrinsic(points2d, points3d):
    # tmp1 = []
    # for x,y,z in points3d:
    #     tmp1.append([x, -z, y])
    #
    # points3d = np.array(tmp1)

    scaleX = 1
    scaleY = .5
    centerX = 784.646528
    centerY = 312.174112
    focal = 402.206240

    # hardcoded camera intrinsics
    cam1_intrinsic = np.array([
        [focal * scaleX, 0, centerX],
        [0, focal * scaleY, centerY],
        [0, 0, 1]
    ])

    cam1_K_inverse = np.linalg.inv(cam1_intrinsic)

    # direct linear transformation calibration, assumes no intrinsic matrix
    assert points2d.shape[0] >= 3
    assert points3d.shape[0] == points2d.shape[0]

    A = []

    points2d_homo = []
    for u, v in points2d:
        points2d_homo.append([u, v, 1])

    points2d_homo = np.array(points2d_homo).T  # columns to be data points

    points2d_inv = np.dot(cam1_K_inverse, points2d_homo).T
    assert points2d_inv.shape == (points2d.shape[0], 3)
    assert points2d_inv[0, 2] == 1

    for idx in range(points2d.shape[0]):
        x3d, y3d, z3d = points3d[idx]
        u, v, _ = points2d_inv[idx]

        A.append([x3d, y3d, z3d, 1, 0, 0, 0, 0, -u * x3d, -u * y3d, -u * z3d, -u])
        A.append([0, 0, 0, 0, x3d, y3d, z3d, 1, -v * x3d, -v * y3d, -v * z3d, -v])

    A = np.array(A)

    U, D, VT = np.linalg.svd(A)
    M = VT.T[:, -1].reshape((3, 4))

    total = 0.

    for i in range(points2d.shape[0]):
        u, v = points2d[i]
        x, y, z = points3d[i]
        h3d = np.array([[x], [y], [z], [1]])
        h2d = np.dot(np.dot(cam1_intrinsic, M), h3d)
        predicted_u = h2d[0, 0] / h2d[2, 0]
        predicted_v = h2d[1, 0] / h2d[2, 0]
        logging.debug("actual u: %s vs %s", u, predicted_u)
        logging.debug("actual v: %s vs %s", v, predicted_v)
        total += ((u-predicted_u) **2 + (v-predicted_v) **2)**.5

    logging.debug("error: %s", total)
    return M


def opencv_calibrate(points2d, points3d):
    scaleX = 1
    scaleY = .5
    centerX = 784.646528
    centerY = 312.174112
    focal = 402.206240

    # hardcoded camera intrinsics
    cam1_intrinsic = np.array([
        [focal * scaleX, 0, centerX],
        [0, focal * scaleY, centerY],
        [0, 0, 1]
    ])

    _, rvec, tvec = cv2.solvePnP(points3d.astype("float32"), points2d.astype("float32"), cameraMatrix=cam1_intrinsic, distCoeffs=None)
    R, J = cv2.Rodrigues(rvec)

    total = 0.

    for i in range(points2d.shape[0]):
        u, v = points2d[i]
        x, y, z = points3d[i]
        h3d = np.array([[x], [y], [z]])
        h2d = np.dot(cam1_intrinsic, np.dot(R, h3d) + tvec)

        predicted_u = h2d[0, 0] / h2d[2, 0]
        predicted_v = h2d[1, 0] / h2d[2, 0]
        logging.debug("opencv actual u: %s vs %s", u, predicted_u)
        logging.debug("opencv actual v: %s vs %s", v, predicted_v)

        total += ((u-predicted_u) **2 + (v-predicted_v) **2)**.5

    logging.debug("error: %s", total)

    return rvec, tvec


if __name__ == '__main__':
    logging.basicConfig(level=logging.DEBUG)

    points2d = np.array([[157, 907 ...
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