Calculating the distance and yaw between ArUco marker and camera?

Question

I am trying to calculate the exact( 3 cm error rate is acceptable ) distance between aruco marker and camera. I use python, opencv and aruco. I can detect them ( marker side is 0.023 meters which is 2.3 cm ) but I can't interpret the distance because for 40 cm distance the norm of the translation vector gives 1 meter. I am so confused about this. Can anyone help? Full code ( sorry , not documented well ):

import numpy as np
import cv2
import cv2.aruco as aruco
import glob
import argparse
import math

# Marker id infos. Global to access everywhere. It is unnecessary to change it to local.
firstMarkerID = None
secondMarkerID = None

cap = cv2.VideoCapture(0)
image_width = 0
image_height = 0

#hyper parameters
distanceBetweenTwoMarkers = 0.0245  # in meters, 2.45 cm
oneSideOfTheMarker = 0.023 # in meters, 2.3 cm

# termination criteria
criteria = (cv2.TERM_CRITERIA_EPS + cv2.TERM_CRITERIA_MAX_ITER, 30, 0.001)


class Namespace:
    def __init__(self, **kwargs):
        self.__dict__.update(kwargs)

def calibrate(dirpath):
    """ Apply camera calibration operation for images in the given directory path. """
    # prepare object points, like (0,0,0), (1,0,0), (2,0,0) ....,(8,6,0)
    objp = np.zeros((6*9, 3), np.float32)
    objp[:, :2] = np.mgrid[0:9, 0:6].T.reshape(-1, 2)

    # Arrays to store object points and image points from all the images.
    objpoints = []  # 3d point in real world space
    imgpoints = []  # 2d points in image plane.

    images = glob.glob(dirpath+'/*.jpg')

    for fname in images:
        img = cv2.imread(fname)
        gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)

        # Find the chess board corners
        ret, corners = cv2.findChessboardCorners(gray, (9, 6), None)

        # If found, add object points, image points (after refining them)
        if ret:
            objpoints.append(objp)

            corners2 = cv2.cornerSubPix(gray, corners, (11, 11), (-1, -1), criteria)
            imgpoints.append(corners2)

            # Draw and display the corners
            img = cv2.drawChessboardCorners(img, (9, 6), corners2, ret)

    ret, mtx, dist, rvecs, tvecs = cv2.calibrateCamera(objpoints, imgpoints, gray.shape[::-1], None, None)

    return [ret, mtx, dist, rvecs, tvecs]


def saveCoefficients(mtx, dist, path):
    """ Save the camera matrix and the distortion coefficients to given path/file. """
    cv_file = cv2.FileStorage(path, cv2.FILE_STORAGE_WRITE)
    cv_file.write("camera_matrix", mtx)
    cv_file.write("dist_coeff", dist)
    # note you *release* you don't close() a FileStorage object
    cv_file.release()


def loadCoefficients(path):
    """ Loads camera matrix and distortion coefficients. """
    # FILE_STORAGE_READ
    cv_file = cv2.FileStorage(path, cv2.FILE_STORAGE_READ)

    # note we also have to specify the type to retrieve other wise we only get a
    # FileNode object back instead of a matrix
    camera_matrix = cv_file.getNode("camera_matrix").mat()
    dist_matrix = cv_file.getNode("dist_coeff").mat()

    # Debug: print the values
    # print("camera_matrix : ", camera_matrix.tolist())
    # print("dist_matrix : ", dist_matrix.tolist())

    cv_file.release()
    return [camera_matrix, dist_matrix]


def inversePerspective(rvec, tvec):
    """ Applies perspective transform for given rvec and tvec. """
    rvec, tvec = rvec.reshape((3, 1)), tvec.reshape((3, 1))
    R, _ = cv2.Rodrigues(rvec)
    R = np.matrix(R).T
    invTvec = np.dot(R, np.matrix(-tvec))
    invRvec, _ = cv2.Rodrigues(R)

    invTvec = invTvec.reshape((3, 1))
    invTvec = invTvec.reshape((3, 1))
    return invRvec, invTvec


def make_1080p():
    global image_width
    global image_height
    image_width = 1920
    image_height = 1080
    change_res(image_width, image_height)


def make_720p():
    global image_width
    global image_height
    image_width = 1280
    image_height = 720
    change_res(image_width, image_height)


def make_480p():
    global image_width
    global image_height
    image_width = 640
    image_height = 480
    change_res(image_width, image_height)


def change_res(width, height):
    cap.set(3, width)
    cap.set(4, height)


def relativePosition(rvec1, tvec1, rvec2, tvec2):
    """ Get relative position for rvec2 & tvec2. Compose the returned rvec & tvec to use composeRT with rvec2 & tvec2 """
    rvec1, tvec1 = rvec1.reshape((3, 1)), tvec1.reshape((3, 1))
    rvec2, tvec2 = rvec2.reshape((3, 1)), tvec2.reshape((3, 1))

    # Inverse the second marker, the right one in the image
    invRvec, invTvec = inversePerspective(rvec2, tvec2)

    info = cv2.composeRT(rvec1, tvec1, invRvec, invTvec)
    composedRvec, composedTvec = info[0], info[1]

    composedRvec = composedRvec.reshape((3, 1))
    composedTvec = composedTvec.reshape((3, 1))
    return composedRvec, composedTvec


def euclideanDistanceOfTvecs(tvec1, tvec2):
    return math.sqrt(math.pow(tvec1[0]-tvec2[0], 2) + math.pow(tvec1[1]-tvec2[1], 2) + math.pow(tvec1[2]-tvec2[2], 2))

def euclideanDistanceOfTvec(tvec):
    return euclideanDistanceOfTvecs(tvec, [0, 0, 0])

def draw(img, imgpts, color):
    """ draw a line between given two points. """
    imgpts = np.int32(imgpts).reshape(-1, 2)
    for pointf in range(len(imgpts)):
        for points in range(len(imgpts)):
            img = cv2.line(img, tuple(imgpts[pointf]), tuple(imgpts[points]), color, 3)
    return img


def track(matrix_coefficients, distortion_coefficients):
    global image_width
    global image_height
    """ Real time ArUco marker tracking.  """
    needleComposeRvec, needleComposeTvec = None, None  # Composed for needle
    ultraSoundComposeRvec, ultraSoundComposeTvec = None, None  # Composed for ultrasound
    savedNeedleRvec, savedNeedleTvec = None, None  # Pure Composed
    savedUltraSoundRvec, savedUltraSoundTvec = None, None  # Pure Composed
    TcomposedRvecNeedle, TcomposedTvecNeedle = None, None
    TcomposedRvecUltrasound, TcomposedTvecUltrasound = None, None

    make_480p()

    while True:
        isFirstMarkerDetected = False
        isSecondMarkerDetected = False
        ret, frame = cap.read()
        # operations on the frame come here
        gray = cv2.cvtColor(frame, cv2.COLOR_BGR2GRAY)  # Change grayscale
        aruco_dict = aruco.Dictionary_get(aruco.DICT_5X5_250)  # Use 5x5 dictionary to find markers
        parameters = aruco.DetectorParameters_create()  # Marker detection parameters

        # lists of ids and the corners beloning to each id
        corners, ids, rejected_img_points = aruco.detectMarkers(gray, aruco_dict,
                                                                parameters=parameters,
                                                                cameraMatrix=matrix_coefficients,
                                                                distCoeff=distortion_coefficients)


        if np.all(ids is not None):  # If there are markers found by detector
            zipped = zip(ids, corners)
            ids, corners = zip(*(sorted(zipped)))

            # print(ids)
            for i in range(0, len(ids)):  # Iterate in markers
                # Estimate pose of each marker and return the values rvec and tvec---different from camera coefficients
                rvec, tvec, markerPoints = aruco.estimatePoseSingleMarkers(corners[i], oneSideOfTheMarker, matrix_coefficients,
                                                                           distortion_coefficients)

                if ids[i] == firstMarkerID:
                    firstRvec = rvec
                    firstTvec = tvec
                    isFirstMarkerDetected = True
                    firstMarkerCorners = corners[i]
                elif ids[i] == secondMarkerID:
                    secondRvec = rvec
                    secondTvec = tvec
                    isSecondMarkerDetected = True
                    secondMarkerCorners = corners[i]

                (rvec - tvec).any()  # get rid of that nasty numpy value array error
                # aruco.drawAxis(frame, matrix_coefficients, distortion_coefficients, rvec, tvec, 0.01)  # Draw Axis
                aruco.drawDetectedMarkers(frame, corners)  # Draw A square around the markers

                ''' First try
                if isFirstMarkerDetected and isSecondMarkerDetected:
                    composedRvec, composedTvec = relativePosition(firstRvec, firstTvec, secondRvec, secondTvec)

                    info = cv2.composeRT(composedRvec, composedTvec, secondRvec.T, secondTvec.T)
                    composedRvec, composedTvec = info[0], info[1]

                    composedRvec, composedTvec = composedRvec.T, composedTvec.T

                    differenceRvec, differenceTvec = composedRvec-secondRvec, composedTvec-secondTvec

                    # print infos
                    print("composed Rvec: ", composedRvec)
                    print("composed Tvec: ", composedTvec)

                    print("Second marker Rvec: ", secondRvec)
                    print("Second marker Tvec: ", secondTvec)

                    print("differenceRvec: ", differenceRvec)
                    print("differenceTvec: ", differenceTvec)

                    print("real difference: ", euclideanDistanceOfTvecs(composedTvec[0], secondTvec[0][0]))

                    # draw axis to estimated location
                    aruco.drawAxis(frame, mtx, dist, composedRvec, composedTvec, 0.0115)

                    realDistanceInTvec = euclideanDistanceOfTvec(secondTvec[0][0])
                    difference = euclideanDistanceOfTvecs(composedTvec[0], secondTvec[0][0])
                    calculatedDistance = realDistanceInTvec * (distanceBetweenTwoMarkers / difference)
                    calculatedDistance = realDistanceInTvec * (distanceBetweenTwoMarkers / (secondTvec[0][0][2] - firstTvec[0][0][2]))

                    print(calculatedDistance)
                '''
                if isFirstMarkerDetected and isSecondMarkerDetected:
                    composedRvec, composedTvec = relativePosition(firstRvec, firstTvec, secondRvec, secondTvec)

                    camerafirstRvec, cameraFirstTvec = inversePerspective(firstRvec, firstTvec)
                    camerasecondRvec, camerasecondTvec = inversePerspective(secondRvec, secondTvec)

                    differenceRvec, differenceTvec = camerafirstRvec - camerasecondRvec, cameraFirstTvec - camerasecondTvec

                    # print infos
                    print("first Rvec: ", camerafirstRvec)
                    print("first Tvec: ", cameraFirstTvec)

                    print("Second marker Rvec: ", camerasecondRvec)
                    print("Second marker Tvec: ", camerasecondTvec)

                    # print("differenceRvec: ", differenceRvec)
                    # print("differenceTvec: ", differenceTvec)

                    realDistanceInTvec = euclideanDistanceOfTvec(secondTvec[0][0])
                    print(cv2.norm(secondTvec[0][0]))

                    difference = euclideanDistanceOfTvecs(composedTvec.T[0], secondTvec[0][0])
                    calculatedDistance = realDistanceInTvec * (distanceBetweenTwoMarkers / difference)

                    # print(calculatedDistance)


        # Display the resulting frame
        cv2.namedWindow('frame', cv2.WINDOW_NORMAL)
        cv2.resizeWindow('frame', image_width, image_height)
        cv2.imshow('frame', frame)
        # Wait 3 milisecoonds for an interaction. Check the key and do the corresponding job.
        key = cv2.waitKey(3) & 0xFF
        if key == ord('q'):  # Quit
            break
        elif key == ord('p'):  # print necessary information here
            pass  # Insert necessary print here


    # When everything done, release the capture
    cap.release()
    cv2.destroyAllWindows()


if __name__ == '__main__':
    parser = argparse.ArgumentParser(description='Aruco Marker Tracking')
    parser.add_argument('--coefficients', metavar='bool', required=True,
                        help='File name for matrix coefficients and distortion coefficients')
    parser.add_argument('--firstMarker', metavar='int', required=True,
                        help='first')
    parser.add_argument('--secondMarker', metavar='int', required=True,
                        help='second')

    # Parse the arguments and take action for that.
    args = parser.parse_args()
    firstMarkerID = int(args.firstMarker)
    secondMarkerID = int(args.secondMarker)

    if args.coefficients == '1':
        mtx, dist = loadCoefficients("test.yaml")
        ret = True
    else:
        ret, mtx, dist, rvecs, tvecs = calibrate("calib_images")
        saveCoefficients(mtx, dist, "calibrationCoefficients.yaml")
    print("Calibration is completed. Starting tracking sequence.")
    if ret:
        track(mtx, dist)

Answer 1

I got the answer. Problem is in the calibration. When calibration with chessboard, I gave the object points like this:

(0,0,0), (1,0,0) and so on.

The thing is when doing pose estimation, camera should be calibrated nicely. My chessboard square size was 1.5 centimeters which means 0.015 meters. I changed the object point matrix as:

(0,0,0), (0.015,0,0) and so on.

So I said to program that the calibration should be in meters. If you do the calibration with different object points matrix than it should be, the pose estimation fails. That was included in the opencv documentation but I couldn't see it. In the docs it was said like "you can pass them like that." and I didn't think that it fails at the pose estimation.