Single and Multiple View Geometry

Our group has worked on the study and exploitation of the geometric properties of single and multiple uncalibrated images in the context of both Euclidean and Projective Geometry. In the field of single image geometry, new mathematical models and alternative approaches have been proposed and evaluated concerning camera calibration (from single or multi-single views) and 3D metric or affine reconstruction, mainly based on the utilization of va­nishing points and their properties.

SMVG_1

Regarding the geometry of an uncalibrated stereopair the 2D epipolar geometry, embedded in the Fundamental matrix, has been studied in the Euclidean 3D space. Specifically, a ma­the­matical expression is formulated to encompass the infinite, compatible with the fundamental matrix, combinations of relative and interior orientation of the two images and, conse­quently, the corresponding projective reconstruction of imaged space. Additionally, with a still Euclidean approach equations are formulated to express in a new form the constraints posed by the fundamental matrix upon the parameters of interior orientation.

SMVG_2

SMVG_3

2007 An automatic approach for camera calibration from vanishing points. L. Grammatiko­poulos, G. Karras, E. Petsa. ISPRS Journal of Photogrammetry and Remote Sensing, vol. 62, pp. 64-78.

2006 A unified approach for automatic camera calibration from vanishing points. L. Gram­mati­kopoulos, G. Karras, E. Petsa, I. Kalisperakis. International Archives of the Photogrammetry, Remote Sensing & Spatial Information Sciences, Vol. XXXVI, Part 5 (in CD).

2006 3D aspects of 2D epipolar geometry. I. Kalisperakis, G. Karras, L. Grammatikopoulos. Inter­national Archives of the Photogrammetry, Remote Sensing & Spatial Information Sciences, Vol. XXXVI, Part 3, pp.255-259.

2004 Camera calibration combining images with two vanishing points. L. Grammatikopoulos, G. Karras, E. Petsa. International Archives of the Photogrammetry, Remote Sensing & Spatial Information Sciences, 35(5), pp. 99-104.

2003 Camera calibration approaches using single images of man-made objects. L. Gramma­ti­kopoulos, G. E. Karras, E. Petsa. XIX CIPA International Symposium, Antalya, Turkey, 30 September – 4 October, pp. 328-332