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. [1], 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.

Impact and interest:

Citation counts are sourced monthly from Scopus and Web of Science® citation databases.

These databases contain citations from different subsets of available publications and different time periods and thus the citation count from each is usually different. Some works are not in either database and no count is displayed. Scopus includes citations from articles published in 1996 onwards, and Web of Science® generally from 1980 onwards.

Citations counts from the Google Scholar™ indexing service can be viewed at the linked Google Scholar™ search.

Full-text downloads:

43 since deposited on 26 Nov 2015
43 in the past twelve months

Full-text downloads displays the total number of times this work’s files (e.g., a PDF) have been downloaded from QUT ePrints as well as the number of downloads in the previous 365 days. The count includes downloads for all files if a work has more than one.

ID Code: 90804
Item Type: Conference Paper
Refereed: Yes
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

Export: EndNote | Dublin Core | BibTeX

Repository Staff Only: item control page