Relative Camera Pose Estimation using OpenCV

Question

I'm trying to estimate the relative camera pose using OpenCV. Cameras in my case are calibrated (i know the intrinsic parameters of the camera).

Given the images captured at two positions, i need to find out the relative rotation and translation between two cameras. Typical translation is about 5 to 15 meters and yaw angle rotation between cameras range between 0 - 20 degrees.

For achieving this, following steps are adopted.

• a. Finding point corresponding using SIFT/SURF
• b. Fundamental Matrix Identification
• c. Estimation of Essential Matrix by E = K'FK and modifying E for singularity constraint
• d. Decomposition Essential Matrix to get the rotation, R = UWVt or R = UW'Vt (U and Vt are obtained SVD of E)
• e. Obtaining the real rotation angles from rotation matrix

Experiment 1: Real Data

For real data experiment, I captured images by mounting a camera on a tripod. Images captured at Position 1, then moved to another aligned Position and changed yaw angles in steps of 5 degrees and captured images for Position 2.

Problems/Issues:

1. Sign of the estimated yaw angles are not matching with ground truth yaw angles. Sometimes 5 deg is estimated as 5deg, but 10 deg as -10 deg and again 15 deg as 15 deg.
2. In experiment only yaw angle is changed, however estimated Roll and Pitch angles are having nonzero values close to 180/-180 degrees.
3. Precision is very poor in some cases the error in estimated and ground truth angles are around 2-5 degrees.
4. How to find out the scale factor to get the translation in real world measurement units?

The behavior is same on simulated data also.

Have anybody experienced similar problems as me? Have any clue on how to resolve them. Any help from anybody would be highly appreciated.

(I know there are already so many posts on similar problems, going trough all of them has not saved me. Hence posting one more time.)

Answer 1

In chapter 9.6 of Hartley and Zisserman, they point out that, for a particular essential matrix, if one camera is held in the canonical position/orientation, there are four possible solutions for the second camera matrix: [UWV' | u3], [UWV' | -u3], [UW'V' | u3], and [UW'V' | -u3].

The difference between the first and third (and second and fourth) solutions is that the orientation is rotated by 180 degrees about the line joining the two cameras, called a "twisted pair", which sounds like what you are describing.

The book says that in order to choose the correct combination of translation and orientation from the four options, you need to test a point in the scene and make sure that the point is in front of both cameras.

Answer 2

For problems 1 and 2, Look for "Euler angles" in wikipedia or any good math site like Wolfram Mathworld. You would find out the different possibilities of Euler angles. I am sure you can figure out why you are getting sign changes in your results based on literature reading.

For problem 3, It should mostly have to do with the accuracy of our individual camera calibration.

For problem 4, Not sure. How about, measuring a point from camera using a tape and comparing it with the translation norm to get the scale factor.

Possible reasons for bad accuracy:

1) There is a difference between getting reasonable and precise accuracy in camera calibration. See this thread. 2) The accuracy with which you are moving the tripod. How are you ensuring that there is no rotation of tripod around an axis perpendicular to surface during change in position.

I did not get your simulation concept. But, I would suggest the below test.

Take images without moving the camera or object. Now if you calculate relative camera pose, rotation should be identity matrix and translation should be null vector. Due to numerical inaccuracies and noise, you might see rotation deviation in arc minutes.