CameraCalibration and Image processing - image-processing

Question

I would like you to clarify me on these questions plz
1.If I calibrate my camera to a particular resolution say 640x360, can I use it for another resolution like 1024x768?
2.Also I want to know as to how many centimeters does 1 pixel contain in my image. It varies from system to system., How do I find that?. Also, it is not compulsorily square in shape. So I have to find the length and width of it. How do I do that?
I am using a logitech c170 which is a low speed cam. Is it okay to get an error around 8mm when I am trying to measure the distances in the image and compare them with real-time distances?
EDIT1:
Since the number of pixels in 1 mm is sensor_width/image_width , which is the inverse of density, I can calculate a_x/f and find the inverse right?
#marol
Intrinsic parameters of left camera:
Focal Length: fc_left = [ 1442.67707 1457.17435 ] ± [ 18.12442 19.46439 ]
Principal point: cc_left = [ 497.66112 291.77311 ] ± [ 42.37874 31.97065 ]
Skew: alpha_c_left = [ 0.00000 ] ± [ 0.00000 ] => angle of pixel axes = 90.00000 ± 0.00000 degrees
Distortion: kc_left = [ 0.02924 -0.65151 -0.01104 -0.01342 0.00000 ] ± [ 0.16553 1.57119 0.00913 0.01306 0.00000 ]
Intrinsic parameters of right camera:
Focal Length: fc_right = [ 1443.32678 1458.82558 ] ± [ 25.55850 26.08659 ]
Principal point: cc_right = [ 567.11672 258.09152 ] ± [ 20.46962 17.87495 ]
Skew: alpha_c_right = [ 0.00000 ] ± [ 0.00000 ] => angle of pixel axes = 90.00000 ± 0.00000 degrees
Distortion: kc_right = [ -0.58576 21.53289 -0.02278 0.00845 0.00000 ] ± [ 0.28148 9.37092 0.00787 0.00847 0.00000 ]
Extrinsic parameters (position of right camera wrt left camera):
Rotation vector: om = [ -0.04239 0.02401 -0.00677 ]
Translation vector: T = [ 71.66430 -0.79025 -8.76546 ]

Answer 1

If you mean: I have calibrated my camera using set of images with resolution X so I got calibration matrix K, can I use this matrix with images of different resolution Y? The direct answer is no, you cannot, since calibration matrix K has a form:
K = [a_x, 0, c_x;
0, a_y, c_y;
0, 0, 1;]
Where a_x = focal_length * density of pixels on mm in x direction, a_y = focal_length * density of pixels on mm in y direction (usually those densities are equal) and c_x = translation of image plane to principal point in x direction (similar c_y). When you ouput your calibration matrix K you will see something like:
K = [a_x, 0, 320;
0, a_y, 180;
0, 0, 1]
And yes, you can see that c_x = 320 = 640 / 2 and c_y = 180 = 360/2. So your calibration matrix is correlated with the image resolution, so you cannot use it directly with any other resolution without changing matrix K.
2.You have to divide sensor size by image size, ie
k_x = 1 / c_x = sensor_size_width / image_size_width.
k_y = 1 / c_y
Image sensor is that tiny plane made from photosensitive material which absorb light in your camera device. Usually you can find such information in camera manual, search for sensor size.
EDIT: And if you can't find sensor size in the camera manual, what is a normal behavior in case of webcameras, you can try to do the following: calibrate your camera given matrix K. Value a_x and a_y contains such information. Since we said a_x = f * density, so if you know focal length (and you know - it is 2.3mm - see here) so you can find out density = a_x / f. And we know that density is equal to image_width / sensor_width, so finally we have sensor_width = image_width / density = image_width * f / a_x. Similar thinking for sensor_height.
EDIT2: For example if you get:
Focal Length: fc_left = [ 1442.67707 1457.17435 ] ± [ 18.12442 19.46439 ]
So we have a_x = 1442.67707. From our conclusions and if we assume image size to 640 x 320, we have sensor width = 640 * 2.3 / 1442.67707 = 1,02 mm.