Tracking Rectangles

[Greg McKaskle]

Originally Posted by mikegrundvig

The whitepaper is extremely useful ...

Except it stops there. Have any other reading or direction you can send us to take this the rest of the way? I'd really like our bot to be able to find it's location on the floor with the vision targets and unless we are straight-on, this is going to require handling the angle. Thanks!

-Mike

There are a number of approaches, but I'll show the one that I would use -- not in code, but as an example. I'm also making a few simplifications to get things started -- notably, I'm often assuming that the camera and target are in the same vertical plane.

1. I open up the image shown in the paper into Vision Assistant (the one with the perspective distortion).
2. Use the third tool, the Measure tool to determine the lengths of the left and right vertical edges of the reflective strip. I measure 100 pixels and 134 pixels.

First image shows the measurements in red and green.

Since the edges are different pixel sizes, they are clearly different distances from the camera, but in the real-world, both are 18" long. The image is 320x240 pixels in size.

The FOV height where the red and green lines are drawn are found using ...

240 / 100 x 18" -> 43.2" for green,
and
240 / 134 x 18" -> 32.2" for red.

These may seem odd at first, but it is stating that if a tape measure were in the photo where the green line is drawn, taped to the backboard, you would see that from top to bottom in the camera photo, 43.2 inches would be visible on the left/green side, and since the red is closer, only 32.2 inches would be visible.

Next find the distance to the lines using theta of 47 degrees for the M1011...
(43.2 / 2) / tan( theta / 2) -> 49.7"
and
(32.2 / 2 ) / tan( theta / 2) -> 37.0"

This says that if you were to stretch a tape measure from the camera lens to to green line, it would read 49.7 inches, and to the red line would read 37 inches.

These measurements form two edges of a triangle from the camera to the red line and from the camera to the green line, and the third is the width of the retro-reflective rectangle, or 24". Note that this is not typically a right triangle.

I think the next step would depend on how you intend to shoot. One team may want to solve for the center of the hoop, another may want to solve for the center of the rectangle.

If you would like to measure the angles of the rectangle described above, you may want to look up the law of cosines. It will allow you to solve for any of the unknown angles.

I'd encourage you to place yardsticks or tape measures on your backboard and walk to different locations on the field and capture photos through your camera. You can then do similar calculations by hand or with your program. You can then calculate many of the different unknown values and determine which are useful for determining a shooting solution.

As with the white paper, this is not intended to be a final solution, but a starting point. Feel free to ask followup questions or pose other approaches.

Greg McKaskle