I\'m working with a homography calculated by OpenCV. I currently use this homography to transform points using the function below. This function performs the task I require
cvFindHomography()
returns a matrix using homogenous coordinates:
Homogeneous coordinates are ubiquitous in computer graphics because they allow common operations such as translation, rotation, scaling and perspective projection to be implemented as matrix operations
What's happening in the code:
The cartesian point p_origin_cartesian(x,y)
is transformed to homogenous coordinates, then the 3x3 perspective transformation matrix h
is applied and the result is converted back to cartesian coordinates p_transformed_cartesian(px,py)
.
UPDATE
In detail:
Convert p_origin_cartesian
to p_origin_homogenous
:
(x,y) => (x,y,1)
Do perspective transformation:
p_transformed_homogenous = h * p_origin_homogenous =
(h0,h1,h2) (x) (h0*x + h1*y + h2) (tx)
(h3,h4,h5) * (y) = (h3*x + h4*y + h5) = (ty)
(h6,h7,h8) (1) (h6*x + h7*y + h8) (tz)
Convert p_transformed_homogenous
to p_transformed_cartesian
:
(tx,ty,tz) => (tx/tz, ty/tz)
Your code translated:
px = tx/tz;
py = ty/tz;
Z = 1/tz;
OpenCV Python implementation following @Ben answer
p = np.array((x,y,1)).reshape((3,1))
temp_p = M.dot(p)
sum = np.sum(temp_p ,1)
px = int(round(sum[0]/sum[2]))
py = int(round(sum[1]/sum[2]))