Shape tensors for efficient and learnable indexing

Daphna Weinshall*, Michael Werman, Ammon Shashua

*Corresponding author for this work

Research output: Contribution to conferencePaperpeer-review

11 Scopus citations


The geometry of 1 point in N images under perspective projection is thoroughly investigated, identifying bilinear, trilinear, and quadrilinear relations between the projections of 1 point, 2, 3, and 4 frames respectively. A complete description of the problem is provided. A formalism is employed in which multiframe and multi-point geometries appear in symmetry. The bilinear equations for 6 points, trilinear equations for 7 points, and quadrilinear equations for 8 points are derived. It is shown that the quadrilinear equations are dependent on the bilinear and trilinear equations and that adding more points will not generate any new equation. The new equations are used to design new algorithms for the reconstruction of shape from many frames, and for learning invariant relations for indexing into a data-base.

Original languageAmerican English
Number of pages8
StatePublished - 1995
EventProceedings of the 1995 IEEE Workshop on Representation of Visual Scenes - Cambridge, MA, USA
Duration: 24 Jun 199524 Jun 1995


ConferenceProceedings of the 1995 IEEE Workshop on Representation of Visual Scenes
CityCambridge, MA, USA


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