Closed-form solutions for low-rank non-rigid reconstruction
Valmadre, Jack, Sridharan, Sridha, Denman, Simon, Fookes, Clinton B., & Lucey, Simon (2015) Closed-form solutions for low-rank non-rigid reconstruction. In International Conference on Digital Image Computing: Techniques and Applications (DICTA 2015), 23-25 November 2015, Adelaide Town Hall, Adelaide, S.A.
Recovering the motion of a non-rigid body from a set of monocular images permits the analysis of dynamic scenes in uncontrolled environments. However, the extension of factorisation algorithms for rigid structure from motion to the low-rank non-rigid case has proved challenging. This stems from the comparatively hard problem of finding a linear “corrective transform” which recovers the projection and structure matrices from an ambiguous factorisation.
We elucidate that this greater difficulty is due to the need to find multiple solutions to a non-trivial problem, casting a number of previous approaches as alleviating this issue by either a) introducing constraints on the basis, making the problems nonidentical, or b) incorporating heuristics to encourage a diverse set of solutions, making the problems inter-dependent. While it has previously been recognised that finding a single solution to this problem is sufficient to estimate cameras, we show that it is possible to bootstrap this partial solution to find the complete transform in closed-form. However, we acknowledge that our method minimises an algebraic error and is thus inherently sensitive to deviation from the low-rank model.
We compare our closed-form solution for non-rigid structure with known cameras to the closed-form solution of Dai et al. , which we find to produce only coplanar reconstructions. We therefore make the recommendation that 3D reconstruction error always be measured relative to a trivial reconstruction such as a planar one.
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|Item Type:||Conference Paper|
|Keywords:||Non-Rigid Structure from Motion, 3D reconstruction, Structure from Motion|
|Subjects:||Australian and New Zealand Standard Research Classification > INFORMATION AND COMPUTING SCIENCES (080000) > ARTIFICIAL INTELLIGENCE AND IMAGE PROCESSING (080100) > Computer Vision (080104)|
|Divisions:||Current > Schools > School of Electrical Engineering & Computer Science
Current > QUT Faculties and Divisions > Science & Engineering Faculty
|Copyright Owner:||Copyright 2015 [Please consult the author]|
|Deposited On:||26 Nov 2015 22:46|
|Last Modified:||15 Feb 2016 09:05|
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