AprilTag Pose Calculation Example C

AprilTag Pose Calculator

Enter camera intrinsics and the four AprilTag corners. Use the order top left, top right, bottom right, and bottom left.

Example Data Table

Formula Used

The calculator models the tag as a square on the Z = 0 plane. The four tag corners create a planar homography:

s [u, v, 1]^T = K [r1 r2 t] [X, Y, 1]^T

Here, K is the camera intrinsic matrix. The homography H is first solved from four point pairs. Then K^-1H gives scaled pose columns.

λ = 2 / (||b1|| + ||b2||)

Rotation columns are normalized as r1 and r2. The normal axis is computed as r3 = r1 × r2. Translation is t = λb3. Reprojection error is the pixel distance between measured corners and projected corners.

C Style Pose Example

double tag_size = 0.162;
double fx = 820.0, fy = 820.0, cx = 640.0, cy = 360.0;

/* Corner order:
   top-left, top-right, bottom-right, bottom-left */

solve_homography(tag_corners_world, tag_corners_image, H);
multiply_inverse_intrinsics(K, H, B);
lambda = 2.0 / (norm(col(B,0)) + norm(col(B,1)));

r1 = normalize(lambda * col(B,0));
r2 = orthogonalize(lambda * col(B,1), r1);
r3 = cross(r1, r2);
t  = lambda * col(B,2);

How To Use This Calculator

1. Measure the printed AprilTag edge size.
2. Enter fx, fy, cx, and cy from camera calibration.
3. Enter corner pixels in clockwise order.
4. Enable distortion correction only when calibrated coefficients are known.
5. Press Calculate Pose.
6. Review distance, translation, rotation, and reprojection error.
7. Export CSV or PDF for reporting.

AprilTag Pose Calculation Guide

AprilTag Pose Basics

An AprilTag gives a camera a known square target. The four detected corners define a planar marker. The calculator uses those corners, the real tag size, and camera intrinsics. It estimates where the tag sits relative to the camera. This is the same idea used by robots, drones, augmented reality tools, and lab measurement systems.

Why Corner Order Matters

Corner order controls the pose direction. Use top left, top right, bottom right, and bottom left. The image origin is normally the top left of the frame. A swapped corner can flip axes or produce a poor reprojection error. Good detections should form a clean quadrilateral with visible edges.

Camera Intrinsics

Focal length values fx and fy convert normalized camera rays to pixels. The principal point values cx and cy define the optical center. A calibrated camera gives the best result. Approximate values can work for demos, but they reduce accuracy. Lens distortion should be removed before pose estimation when precise range matters.

How The Estimate Works

The calculator first builds a homography from the tag plane to the image plane. It then removes the camera intrinsic matrix. The remaining columns contain scaled rotation and translation terms. The rotation vectors are normalized and corrected so they remain perpendicular. Translation gives left right offset, vertical offset, and forward range in tag units.

Reading The Results

X translation is sideways motion. Y translation is vertical motion in the camera frame. Z translation is depth. Yaw, pitch, and roll describe marker orientation. Distance is the direct three dimensional range from camera origin to tag center. Reprojection error compares measured corners against projected corners. Lower error usually means better geometry.

Practical Tips

Use a sharp image. Keep the whole border visible. Measure tag size carefully. Use the same printed marker size in every test. Avoid strong glare and motion blur. Increase image resolution for distant tags. Run calibration for each lens. When the tag is tilted steeply, small corner noise can cause larger angle changes.

For C style examples, pass the same values to your pose solver. The method remains identical. Only memory layout and matrix calls change across most camera projects.

FAQs