1. R3 R3 Y Y X X Z VPx VPz X VPy Perspective Transformations Perspective view Rx, Ry, Prz (VPy)i = 0 (VPx)j=(VPz)j

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

3. Determination of the orientation parameters of the camera, from image space R2 to object space R3 zc  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, www.icomos.org/papers 

4. Case 1. ONE Vanishing Point • 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).

5. 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.

6. Case 2: TWO Vanishing Points 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.

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

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

9. Case 3: THREE Vanishing Points • Again S. Miniato al Monte (Florence).The original image taken with a digital camera Fuji Finepix 4900 - resolution 2400x1800 pixel-. Three V.P. are detected. • The orientation parameters are estimated by V.P. procedure.

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