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.

Y

X

Z

R3 Y

X

R3Perspective view

Rx, Ry, Prz

Perspective Transformations

(VPy)i = 0

(VPx)j=(VPz)j

X

VPx VPz

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 R2 to object space R3

costan

1VP

c

x

za

C

VP

z

ya 1tan

21. VPVPC yyz

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

Case 1. Case 1. ONE Vanishing PointONE Vanishing PointS. Miniato al MonteS. 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 PointsCase 2: TWO Vanishing Points Here two convergent photographs of the façade of

S.Francesco in AssisiS.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

• Again S. Miniato al MonteS. 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.

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