Reconstruction of Some Segmented and Dynamic Scenes: Trifocal Tensors in P4 Theoretical Set Up for Critical Loci, and Instability

Authors:
Marina Bertolini;Gianmario Besana;Cristina Turrini
Affiliations:
Dipartimento di Matematica, Universita' degli Studi di Milano, Milano, Italy I20133;College of Computing and Digital Media, DePaul University, Chicago, USA;Dipartimento di Matematica, Universita' degli Studi di Milano, Milano, Italy I20133
Venue:
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing, Part II
Year:
2008

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Abstract

The context of this work is projective reconstruction ofsegmented or dynamic scenes from multiple views. More explicitly,the following two cases are considered: 3D points lying ontwo bodies moving relatively to each other by pure translation and3D points moving independently along parallel straightlines with constant velocities. These situations are interpreted asstatic scenes in ℙ4 following Shashua and Wolf,(IJCV 48, 2002). Algorithms to determine suitable tensors used toreconstruct a scene in ℙ4 from three views areimplemented in MATLAB®. From the theoretical pointof view, a detailed description, with proof, of critical loci inthe general context of projections ℙ4 →ℙ2 is given. A number of simulated experiments areperformed to prove instability of reconstruction near critical lociin both cases described above. Algorithms for tensor reconstructionallow us to bypass the stratification approach followed in ourprevious work (ICCV, 2007), thus offering more comprehensiveevidence of instability in higher dimension.