April Tag / Algorithms for translation and rotation from the camera

CAPKE · August 9, 2021, 10:53am

Hi all,

I plan to use the April Tag for localization purposes, therefor I found the following methods:

apriltag.rotation()

apriltag.x_translation()
apriltag.y_translation()

apriltag.x_rotation()
apriltag.y_rotation()

Where can I find the algorithms for these methods?
To the best of my knowledge, these methods are not part of the standard April Tag library?

Are there sample projects to determine the exact camera position over an April Tag?

Thank you for your answers.

Best regards,

Christoph

kwagyeman · August 9, 2021, 5:19pm

github.com

openmv/openmv/blob/v4.1.0/src/omv/imlib/apriltag.c#L12083


      
              }
          
          
    lnk_data.hamming = det->hamming;
              lnk_data.centroid.x = fast_roundf(det->c[0]) + roi->x;
              lnk_data.centroid.y = fast_roundf(det->c[1]) + roi->y;
              lnk_data.goodness = det->goodness / 255.0; // scale to [0:1]
              lnk_data.decision_margin = det->decision_margin / 255.0; // scale to [0:1]
          
          
    matd_t *pose = homography_to_pose(det->H, -fx, fy, cx, cy);
          
          
    lnk_data.x_translation = MATD_EL(pose, 0, 3);
              lnk_data.y_translation = MATD_EL(pose, 1, 3);
              lnk_data.z_translation = MATD_EL(pose, 2, 3);
              lnk_data.x_rotation = fast_atan2f(MATD_EL(pose, 2, 1), MATD_EL(pose, 2, 2));
              lnk_data.y_rotation = fast_atan2f(-MATD_EL(pose, 2, 0), fast_sqrtf(sq(MATD_EL(pose, 2, 1)) + sq(MATD_EL(pose, 2, 2))));
              lnk_data.z_rotation = fast_atan2f(MATD_EL(pose, 1, 0), MATD_EL(pose, 0, 0));
          
          
    matd_destroy(pose);
          
          
    list_push_back(out, &lnk_data);
          }

gaurav · March 15, 2022, 1:16pm

To calculate x_rotation(), y_rotation() and z_rotation() some formula are used here from where these are taken from? or using which sequence it is derived xyz or zyx or anything else.

kwagyeman · March 15, 2022, 1:54pm

I don’t remember.