Tech Report from CBCL at MIT

[Reza Shadmehr]

The following technical report from the Center for Biological
and Computational Learning at M.I.T. is now available via
anonymous ftp.

-------------
:CBCL Paper #78/AI Memo #1405
:author Amnon Shashua (amnon at ai.mit.edu)
:title On Geometric and Algebraic Aspects of 3D Affine and Projective
Structures from Perspective 2D Views
:date July 1993
:pages 14

Part I of this paper investigates the differences --- conceptually and
algorithmically --- between affine and projective frameworks for the
tasks of visual recognition and reconstruction from perspective views.
It is shown that an affine invariant exists between any view and a
fixed view chosen as a reference view. This implies that for tasks for
which a reference view can be chosen, such as in alignment schemes for
visual recognition, projective invariants are not really necessary.
The projective extension is then derived, showing that it is necessary
only for tasks for which a reference view is not available --- such as
happens when updating scene structure from a moving stereo rig. 
In part II we use the affine invariant to derive new algebraic
connections between perspective views. It is shown that three
perspective views of an object are connected by certain algebraic
functions of image coordinates alone (no structure or camera geometry
needs to be involved). In the general case, three views satisfy a
trilinear function of image coordinates. In case where two of the
views are orthographic and the third is perspective the function
reduces to a bilinear form. In case all three views are orthographic
the function reduces further to a linear form (the ``linear
combination of views'' of \cite{Ullman-Basri89}).  These functions are
shown to be useful for recognition, among other applications.

--------------

How to get a copy of this report:

The files are in compressed postscript format and are named by their 
AI memo number.  They are put in a directory named as the year
in which the paper was written.  

Here is the procedure for ftp-ing:

unix> ftp publications.ai.mit.edu (128.52.32.22, log-in as anonymous)
ftp>  cd ai-publications/1993
ftp>  binary
ftp>  get AIM-number.ps.Z
ftp>  quit
unix> zcat AIM-number.ps.Z | lpr


Best wishes,

Reza Shadmehr
Center for Biological and Computational Learning
M. I. T.
Cambridge, MA 02139