Y X Z R3R3 Y X R3R3 Perspective view R x, R y, P rz Perspective Transformations (VPy)i = 0 (VPx)j=(VPz)j X VPxVPz VPy

The principal point is the intersection of the three heights in the triangle of the V.P.

Determination of the orientation parameters of the camera, from image space R 2 to object space R 3   zczc For the theory see: G.Fangi,G.Gagliardini,E.S.Malionverni: Photointerpretation and small scale Stereoplotting with digitally rectified photographs with geometrical constraints, Cipa, Potsdam2000,

Case 1. ONE Vanishing Point S. Miniato al Monte S. Miniato al Monte (Florence).  The vertical lines are vertical in the image also, the horizontal lines converge into a V.P.  The rectified image, where the ratio base/height is not correct (see the two circles aside the central window).

Florence – S.Miniato al monte – The original image taken from a book and the rectified one with one V.P. In the books of architecture the images have the vertical edges of the buildings, vertical in the images too.

Case 2: TWO Vanishing Points S.Francesco in Assisi Here two convergent photographs of the façade of S.Francesco in Assisi. Below, the corresponding rectified images, adjusted to fit the rose window in a circumference.

Assisi S.Francesco – The original photographs and the rectified ones with two V.P.

Assisi S.Francesco – Window rose -Anaglyph with the rectified images

Case 3: THREE Vanishing PointsCase 3: THREE Vanishing Points S. Miniato al MonteAgain S. Miniato al Monte (Florence).The original image taken with a digital camera Fuji Finepix resolution 2400x1800 pixel-. Three V.P. are detected. The orientation parameters are estimated by V.P. procedure.

S. Miniato al Monte – The original and the rectified images with three V.P.