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Affine Reconstruction from Translational Motion under Various Autocalibration Constraints

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Abstract

In this paper algorithms for affine reconstruction from translational motion under various auto calibration constraints are presented. A general geometric constraint, expressed using the camera matrices, is derived and this constraint is used in a least square solution to the problem. Necessary and sufficient conditions for critical motions are derived and shown to depend on the knowledge of the intrinsic parameters of the camera. Experiments on simulated data are performed to evaluate the noise sensitivity of the algorithms and the reconstruction quality for motions close to being critical. An experiment is performed on real data to illustrate that the method works in practice.

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Authors and Affiliations

  1. School of Technology and Society, Malmo University, Sweden

    Pär Hammarstedt & Anders Heyden

  2. Centre for Mathematical Sciences (LTH), Lund University, Sweden

    Fredrik Kahl

Authors
  1. Pär Hammarstedt
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  2. Fredrik Kahl
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  3. Anders Heyden
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Corresponding author

Correspondence to Pär Hammarstedt.

Additional information

Pär Hammarstedt received his MSc degree in Engineering Physics in 2002 and is currently a PhD student in Applied Mathematics at Lund Institute of Technology. His main research area is computer vision, in particular, geometric reconstruction problems and auto-calibration.

Fredrik Kahl received his MSc degree in computer science and technology in 1995 and his PhD in mathematics in 2001. His thesis was awarded the Best Nordic Thesis Award in pattern recognition and image analysis 2001–2002 at the Scandinavian Conference on Image Analysis 2003. He has been a postdoctoral research fellow at the Australian National University (ANU) and at the University of California, San Diego (UCSD). He is currently a Research Fellow at the Centre for Mathematical Sciences, Lund University, Sweden. His main research area is computer vision, in particular, geometric reconstruction problems, photometric stereo, geometry of curves & surfaces and machine learning.

Anders Heyden received the MSc degree in Engineering Physics, in 1989, and the PhD degree in Applied Mathematics, in 1995, all from Lund Institute of Technology, Lund University. He became reader in 1999 and was promoted to professor in mathematics in 2002, also at Lund Unviersity. In 2001 he obtained a full professorship position in applied mathematics at Malmo University and is currently leading a research in applied mathematics and Malmo University.

He has made significant contributions within the fields of multiple view geometry, auto-calibration and reconstruction methods. His current research interests are mainly computer vision and image analysis, especially surface reconstruction and image segmentation based on variational methods, dynamic vision and auto-calibration, but also within mathematical biology.

He has authored or co-authored more than 100 papers published in international journals and conference proceedings and is the inventor of 12 patents. He has been involved in the start-up of several companies within the area of image analysis; CellaVision AB, Precise Biometrics AB, WeSpot AB and Ludesi AB. He is currently member of the editorial board of the Int. Journal of Computer Vision and member of the conference board of the European Conference on Computer Vision. He has received an honorable mention for the Marr Prize, been invited speaker at the Asian Conf. on Computer Vision and received the best paper award at Int. Conf. on Automation Robotics and Vision.

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Hammarstedt, P., Kahl, F. & Heyden, A. Affine Reconstruction from Translational Motion under Various Autocalibration Constraints. J Math Imaging Vis 24, 245–257 (2006). https://doi.org/10.1007/s10851-005-3626-y

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