Calibration of an Interactive Whiteboard

[Etherian]

I am trying to create an interactive whiteboard with an IR camera (wiimote actually), IR pen, and an arbitrary surface. For simplicity I'll assume the surface is a screen. To know how an IR dot from the camera's point of view relates to a point on the screen's surface, I must calibrate it with a series of points.

I have a matrix [A] that represents the location of a series of points on the screen's surface S and a matrix that represents the location of those points as projected on to the camera's viewing plane C. From those points I am trying to figure out the transformation that must be applied to all subsequent points. If S is thought of as a plane in an ideal position relative to the camera (i.e. z=1, S_x,y=C_x,y), I know the situation can almost be modeled by:

[P][T]=[A]​

where [T] is a 3D transformation matrix, [P] is a 2D-3D projection matrix, [A] is a set of three 3D vectors, and is a set of three 2D vectors. If that was correct, I could simply perform ^-1[A] to obtain the transformation/projection matrix for subsequent points. Unfortunately, I don't know the Z of the points in and don't know how to compensate. Also, I want to use more than three calibration points, but that would make non-square.

I have found many different materials on the topic, but none of them where exactly what I am looking for. Any help would be greatly appreciated. This problem is driving me nuts.

 

[lofgran]

Hello,

It sounds like you are on the right track with your approach to calibrating the IR camera and IR pen for your interactive whiteboard. It is important to have a solid understanding of the transformation and projection matrices in order to accurately map the points from the screen's surface to the camera's viewing plane.

One way to approach the issue of non-square matrices is to use a technique called "least squares estimation." This involves finding the best-fit transformation matrix that minimizes the error between the projected points on the camera's viewing plane and the actual points on the screen's surface. You can find more information on this technique and how to apply it to your calibration process in resources such as "Computer Vision: Algorithms and Applications" by Richard Szeliski.

Another helpful resource for your project may be the "Wiimote Whiteboard" project on the Instructables website. This project provides step-by-step instructions for building an interactive whiteboard using a wiimote and IR pen, and includes information on how to calibrate the setup.

I hope this information helps you in your project. Good luck!