On Projection Matrices $P^k->P^2$, $k=3,…, 6$, and their Applications in Computer Vision

Lior Wolf and Amnon Shashua

School of Computer Science and Engineering,

The Hebrew University,

Jerusalem 91904, Israel

Projection matrices from projective spaces $P^3$ to $P^2$ have long been

used in multiple-view geometry to model the perspective projection

created by the pin-hole camera. In this work we introduce

higher-dimensional mappings $P^k -> P^2$,

$k=3,4,5,6$ for the representation of various applications in which

the world we view is no longer rigid. We also describe the

multi-view constraints

from these new projection matrices (where $k>3$) and methods for extracting the

non-rigid structure and motion for each application.

Keywords: Dynamic structure from motion, Multiple view geometry, Multi-linear constraints.