I know you can calculate homographies from image to camera plane using correspondence points between a "perfect model" and the image points.
I'm doing it for a football pitch/field, and have used edge detection to find the white lines in the pitch.
But the camera does not (always) cover all of the pitch, so I can't see all the corners... and I only the corners are 100% known points in the model (no other distinguished points).
So the problem is that unless the line intersects with another line and forms a corner, I only know the image points of the line, not it's corresponding "perfect/real-world" coordinates in the model.
Is there some way I can use the detected lines to calculate a homography, or even just a set of candidate homographies, even if the detected lines do not intersect with each other and create a corner?
Example image, showing the pitch, our field of view, and the points of the pitch where I can know the corresponding realworld/model coordinates(green circles), and an example of 2 lines that might be completely useless since in our field of view, I have no clue exactly at which point they start or stop in the corresponding realworld /model of the pitch:
The red lines are examples of lines which I would like to use, but I don't know their realworld coordinates, and it's kind of hard to estimate them because depending on the camera pose, the correspondent points could be "anywhere".