I am attempting to calibrate and find the location and rotation of a single virtual camera in Blender 3d using homography. I am using Blender so that I can double check my results before I move on to the real world where that is more difficult.

I rendered ten pictures of a chess board in various locations and rotations in the view of my stationary camera. With OpenCV's Python, I used `cv2.calibrateCamera`

to find the intrinsic matrix from the detected corners of the chess board in the ten images and then used that in `cv2.solvePnP`

to find the extrinsic parameters(translation and rotation).

However, though the estimated parameters were close to the actual ones, there is something fishy going on. My initial estimation of the translation was `(-0.11205481,-0.0490256,8.13892491)`

. The actual location was `(0,0,8.07105)`

. Pretty close right?

But, when I moved and rotated the camera slightly and rerendered the images, the estimated translation became farther off. Estimated: `(-0.15933154,0.13367286,9.34058867)`

. Actual: `(-1.7918,-1.51073,9.76597)`

. The Z value is close, but the X and the Y are not.

I am utterly confused. If anybody can help me sort through this, I would be highly grateful. Here is the code (it's based off of the Python2 calibrate example supplied with OpenCV):

```
#imports left out
USAGE = '''
USAGE: calib.py [--save <filename>] [--debug <output path>] [--square_size] [<image mask>]
'''
args, img_mask = getopt.getopt(sys.argv[1:], '', ['save=', 'debug=', 'square_size='])
args = dict(args)
try: img_mask = img_mask[0]
except: img_mask = '../cpp/0*.png'
img_names = glob(img_mask)
debug_dir = args.get('--debug')
square_size = float(args.get('--square_size', 1.0))
pattern_size = (5, 8)
pattern_points = np.zeros( (np.prod(pattern_size), 3), np.float32 )
pattern_points[:,:2] = np.indices(pattern_size).T.reshape(-1, 2)
pattern_points *= square_size
obj_points = []
img_points = []
h, w = 0, 0
count = 0
for fn in img_names:
print 'processing %s...' % fn,
img = cv2.imread(fn, 0)
h, w = img.shape[:2]
found, corners = cv2.findChessboardCorners(img, pattern_size)
if found:
if count == 0:
#corners first is a list of the image points for just the first image.
#This is the image I know the object points for and use in solvePnP
corners_first = []
for val in corners:
corners_first.append(val[0])
np_corners_first = np.asarray(corners_first,np.float64)
count+=1
term = ( cv2.TERM_CRITERIA_EPS + cv2.TERM_CRITERIA_COUNT, 30, 0.1 )
cv2.cornerSubPix(img, corners, (5, 5), (-1, -1), term)
if debug_dir:
vis = cv2.cvtColor(img, cv2.COLOR_GRAY2BGR)
cv2.drawChessboardCorners(vis, pattern_size, corners, found)
path, name, ext = splitfn(fn)
cv2.imwrite('%s/%s_chess.bmp' % (debug_dir, name), vis)
if not found:
print 'chessboard not found'
continue
img_points.append(corners.reshape(-1, 2))
obj_points.append(pattern_points)
print 'ok'
rms, camera_matrix, dist_coefs, rvecs, tvecs = cv2.calibrateCamera(obj_points, img_points, (w, h))
print "RMS:", rms
print "camera matrix:\n", camera_matrix
print "distortion coefficients: ", dist_coefs.ravel()
cv2.destroyAllWindows()
np_xyz = np.array(xyz,np.float64).T #xyz list is from file. Not shown here for brevity
camera_matrix2 = np.asarray(camera_matrix,np.float64)
np_dist_coefs = np.asarray(dist_coefs[:,:],np.float64)
found,rvecs_new,tvecs_new = cv2.solvePnP(np_xyz, np_corners_first,camera_matrix2,np_dist_coefs)
np_rodrigues = np.asarray(rvecs_new[:,:],np.float64)
print np_rodrigues.shape
rot_matrix = cv2.Rodrigues(np_rodrigues)[0]
def rot_matrix_to_euler(R):
y_rot = asin(R[2][0])
x_rot = acos(R[2][2]/cos(y_rot))
z_rot = acos(R[0][0]/cos(y_rot))
y_rot_angle = y_rot *(180/pi)
x_rot_angle = x_rot *(180/pi)
z_rot_angle = z_rot *(180/pi)
return x_rot_angle,y_rot_angle,z_rot_angle
print "Euler_rotation = ",rot_matrix_to_euler(rot_matrix)
print "Translation_Matrix = ", tvecs_new
```

I think you may be thinking of `tvecs_new`

as the camera position. Slightly confusingly that is not the case! In fact its the position of the world origin in camera co-ords. To get the camera pose in the object/world co-ords, I believe you need to do:

```
-np.matrix(rotation_matrix).T * np.matrix(tvecs_new)
```

And you can get the Euler angles using `cv2.decomposeProjectionMatrix(P)[-1]`

where `P`

is the `[r|t]`

3 by 4 extrinsic matrix.

I found this to be a pretty good article about the intrinsics and extrinsics...

Licensed under: CC-BY-SA with attribution

Not affiliated with: Stack Overflow