Abstract
The reconstruction of 3D objects from photographs is well-known and several methods are implemented in various software. The vast majority of reconstruction software uses statistical methods and rather less geometric knowledge. At hand of an example, we shall illustrate that the reconstruction of a 3D object from a single edgy photo can be done with a small portion of geometric knowledge about conics. We first collect the basic facts about central projections, perspective images, and their rectification. Subsequently, we use some basic properties of conics in order to rectify an image and to reconstruct an object without previously undistorting or deskewing the image itself. The constructive approach is preferred because of its simplicity and shall also be understood as a plea for Descriptive Geometry and Constructive Geometry.
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Notes
- 1.
This ambiguity occurs only in English texts. In German, Verschwindungspunkte are those who are mapped to infinity, while Fluchtpunkte are the images of ideal points.
In connection with (perspective) collineations, the image and pre-image of ideal points interchange their meaning if we change from the collineation to its inverse.
- 2.
Here, the German language tends to wipe away the differences between projection and image. Both, the map** and the image are frequently called Perspektive.
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The authors are greatful to Toni Neagu for his permission to use the photograph of the installation.
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Odehnal, B., Porsch, J. (2023). Rectification of an Edgy Photograph. In: Cheng, LY. (eds) ICGG 2022 - Proceedings of the 20th International Conference on Geometry and Graphics. ICGG 2022. Lecture Notes on Data Engineering and Communications Technologies, vol 146. Springer, Cham. https://doi.org/10.1007/978-3-031-13588-0_22
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