Question

I have a project which applies SURF(Speeded Up Robust Features) in order to detected a given picture within another set of pictures or within a live stream video from my Web Camera.

It works similar to what is illustrated within this video :

http://www.youtube.com/watch?NR=1&v=uKI9qyi1wMg&feature=fvwrel

The thing is that the rectangle which frames the reference picture is in 2D, and I want to obtain its position with respect to 3D. Basically this is the normal of the image.

Is there a way of obtaining the normal of the image based on the determined rectangle?

The rectangle is something like :

Top Left = (x1, y1) 
Top Right = (x2, y1)
Bottom Left = (x3, y3)
Bottom Right = (x4, y4)

Is there a way of obtaining the normal of the image with respect to the frame based on this coordinates?

Answer 1

You can obtain the 3D transform that matches your set of input points to your detected rectangle:

cv::Mat in = 0, 0
             w, 0
             0, h
cv::Mat ou = x1, y1
             x2, y2
             x3, y3
cv::Mat mat = cv::getAffineTransform(in, ou);

And then use this matrix to transform the normal of the input image:

[row, col] = mat * [0, 0, 1]