OpenCV - Tilted camera and triangulation landmark for stereo vision

Question

I am using a stereo system and so I am trying to get world coordinates of some points by triangulation.

My cameras present an angle, the Z axis direction (direction of the depth) is not normal to my surface. That is why when I observe flat surface, I get no constant depth but a "linear" variation, correct? And I want the depth from the baseline direction... How I can re-project?

A piece of my code with my projective arrays and triangulate function :

#C1 and C2 are the cameras matrix (left and rig)
#R_0 and T_0 are the transformation between cameras
#Coord1 and Coord2 are the correspondant coordinates of left and right respectively
P1 = np.dot(C1,np.hstack((np.identity(3),np.zeros((3,1))))) 

P2 =np.dot(C2,np.hstack(((R_0),T_0)))

for i in range(Coord1.shape[0])
    z = cv2.triangulatePoints(P1, P2, Coord1[i,],Coord2[i,])

-------- EDIT LATER -----------

Thanks scribbleink, so i tried to apply your proposal. But i think i have a mistake because it doesnt work well as you can see below. And the point clouds seems to be warped and curved towards the edges of the image.

U, S, Vt = linalg.svd(F)
V = Vt.T

#Right epipol
U[:,2]/U[2,2]

# The expected X-direction with C1 camera matri and C1[0,0] the focal length
vecteurX = np.array([(U[:,2]/U[2,2])[0],(U[:,2]/U[2,2])[1],C1[0,0]])
vecteurX_unit = vecteurX/np.sqrt(vecteurX[0]**2 + vecteurX[1]**2 + vecteurX[2]**2)


# The expected Y axis :
height = 2048
vecteurY = np.array([0, height -1, 0])
vecteurY_unit = vecteurY/np.sqrt(vecteurY[0]**2 + vecteurY[1]**2 + vecteurY[2]**2)


# The expected Z direction :
vecteurZ = np.cross(vecteurX,vecteurY)
vecteurZ_unit = vecteurZ/np.sqrt(vecteurZ[0]**2 + vecteurZ[1]**2 + vecteurZ[2]**2)

#Normal of the Z optical (the current Z direction)
Zopitcal = np.array([0,0,1])

cos_theta = np.arccos(np.dot(vecteurZ_unit, Zopitcal)/np.sqrt(vecteurZ_unit[0]**2 + vecteurZ_unit[1]**2 + vecteurZ_unit[2]**2)*np.sqrt(Zopitcal[0]**2 + Zopitcal[1]**2 + Zopitcal[2]**2))

sin_theta = (np.cross(vecteurZ_unit, Zopitcal))[1]

#Definition of the Rodrigues vector and use of cv2.Rodrigues to get rotation matrix
v1 = Zopitcal  
v2 = vecteurZ_unit 

v_rodrigues = v1*cos_theta + (np.cross(v2,v1))*sin_theta + v2*(np.cross(v2,v1))*(1. - cos_theta)
R = cv2.Rodrigues(v_rodrigues)[0]

Answer 1

Your expected z direction is arbitrary to the reconstruction method. In general, you have a rotation matrix that rotates the left camera from your desired direction. You can easily build that matrix, R. Then all you need to do is to multiply your reconstructed points by the transpose of R.