projective-geometry

Hey math geeks, I've got a problem that's been stumping me for a while now. It's for a personal project. I've got three dots: red, green, and blue. They're positioned on a cardboard slip such that the red dot is in the lower left (0,0), the blue dot is in the lower right (1,0), and the green dot is in the upper left. Imagine stepping back and taking a picture of the card from an angle. If you were to find the center of each dot in the picture (let's say the units are pixels), how would you find the normal vector of the card's face in the picture (relative to the camera)? Now a few things I've

The issue we are trying to solve the issue of locating a point in two different representations of a plane. The first plane we have is rotated to create perspective; the second is a 2d view of that same plane. We have 4 points on each of the plans that we know to be equivalent. The question is if we have an arbitrary point in plane 1, how do we find the corresponding point in plane 2? It is best probably to illustrate the use case in order to best clarify the question. We have an image illustrated on the left. Projective plane 2D layout diagram of space So the givens that we have are the red

I want to convert an image using control points according to this scheme extracted from here : A and B contains the coordinates of the source an target vertices. I am computing the transformation matrix as: A = [51 228; 51 127; 191 127; 191 228]; B = [152 57; 219 191; 62 240; 92 109]; X = imread('rectangle.png'); info = imfinfo('rectangle.png'); T = cp2tform(A,B,'projective'); Up to here it seems to properly work, because (using normalized coordinates) a source vertex produces its target vertex: H = T.tdata.T; > [51 228 1]*H ans = -248.2186 -93.0820 -1.6330 > [51 228 1]*H/ -1.6330 ans = 152

Given a 2d picture of a rectangle distorted by perspective: I know that the shape was originally a rectangle, but I do not know its original size. If I know the pixel coordinates of the corners in this picture, how can I calculate the original proportions, i.e. the quotient ( width / height ) of the rectangle? (background: the goal is to automatically undistort photos of rectangular documents, edge detection will probably be done with hough transform) UPDATE: There has been some discussion on whether it is possible at all to determine the width:height ratio with the information given. My naive