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3D Reconstruction by Fitting Low-rank Matrices with Missing Data

Daniel Martinec, Tomáš Pajdla, Jana Kostková, and Radim Šára

Given a set of unorganized images taken from unknown viewpoints and directions, the proposed method [1] estimates camera positions. Such automatic calibration makes it possible to compute an accurate 3D model of the object. The only assumption is a sufficient overlap between some image pairs.

Animations will be seen, e.g.,
in Cortona VRML Client
under Windows and freewrl
under Linux.
Dinosaur (Oxford)

36 images [720×576]
Harris operator
90.84% occlusions

10 images [1391×1043]
distinguished regions (DR)
73% occlusions

64 images [811×1219]
94% occlusions
St. George rotunda

60 images [1100×1650]
92% occlusions
St. Martin rotunda

24 images [984×1312]
89% occlusions

Reconstructions of the sparse correspondences were obtained using method [1] and the dense reconstructions using methods [2], [3] and [4].

Fully automatic data processing pipeline [4]: Highly discriminative features are first detected in all images. Correspondences are then found in all image pairs by wide-baseline stereo matching and used in a scene structure and camera reconstruction step that can cope with occlusions and outliers [1]. Image pairs suitable for dense matching are automatically selected, rectified and used in dense binocular matching [2]. The dense point cloud obtained as the union of all pairwise reconstructions is fused by a local approximation using oriented geometric primitives [3]. For texturing, every primitive is mapped on the image with the best resolution.


This research was supported by The Czech Academy of Sciences under project 1ET101210406 and by the EU project IST-2001-39184. Andrew Zisserman from the University of Oxford kindly provided the Dinosaur data, Tomáš Werner from the Czech Technical University provided the routine for the bundle adjustment.


[1] D. Martinec and T. Pajdla. 3D Reconstruction by Fitting Low-rank Matrices with Missing Data. CVPR 2005, vol. I, pp. 198-205, IEEE, San Diego, CA, USA, June 2005. (poster, presentation)

[2] J. Kostková and R. Šára. Stratified Dense Matching for Stereopsis in Complex Scenes. In BMVC 2003: Proceedings of the 14th British Machine Vision Conference, volume 1, pages 339-348, Norwich, UK, September 2003.

[3] R. Šára and R. Bajcsy. Fish-Scales: Representing Fuzzy Manifolds. Proc. IEEE Conf. ICCV ’98, pp. 811-817, Bombay, India, January 1998.

[4] H. Cornelius, R. Šára, D. Martinec, T. Pajdla, O. Chum, J. Matas. Towards Complete Free-Form Reconstruction of Complex 3D Scenes from an Unordered Set of Uncalibrated Images. SMVP/ECCV 2004, vol. LNCS 3247, pp. 1-12, Prague, Czech Republic, May 2004. (presentation)

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