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Journal for Geometry and Graphics 13 (2009), No. 1, 113--120
Copyright Heldermann Verlag 2009

3D-Images in Photography?

Georg Glaeser
Dept. of Geometry, University of Applied Arts, Oskar-Kokoschka-Platz 2, 1010 Vienna, Austria

Photography is geometrically considered a typical example of a perspective, i.e., a central projection of 3-space onto a plane. Although in principle true, this cannot explain some quite common facts that each photographer is confronted with: depth of field (and the fact that it varies with the size of the scene), circles of confusion, etc. A much more correct explanation is that the real 3-space in front of the lens is converted via the lens system into a collinear virtual 3-space behind the lens (more precisely, the transformation is an elation). The photographer depicts an ideal cross section of this virtual space by optimizing the distance of the focus plane which corresponds to the sensor plane in virtual space. In this paper, we will illuminate artifacts of photography that cannot be explained by means of the simplified projection.

Keywords: Projective Geometry, collineation, geometrical optics, diffraction blur, depth of field.

MSC: 51N05; 65D18

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