Frobenius Integration Theorem for Mirror Design

Start: 10/13/2010 - 4:15pm
End  : 10/13/2010 - 5:15pm


Emek Kose Can Loyola Marymount University


Imaging devices that combine cameras and mirrors are called catadioptric sensors. The
main problem of catadioptric sensor design is to fi nd a mirror surface such that the sensor
realizes a certain projection, which generally does not have a solution. In this talk, I will
present my work on overcoming the limitations of single-mirror catadioptric sensors by de-
signing the camera projection as well as the mirror surface. This novel construction allows
one to exactly achieve any desired projection, not only orthographic or perspective. The
key in finding the mirror surface and the camera projection is constructing a vector field
normal to the sought-after mirror surface. The integrability of the normal vector fi eld is
provided by the Frobenius Integration Theorem for di fferential forms, which yields a system
of quasilinear PDEs. The camera projection is obtained by numerical solution of this system
and the mirror surface is computed by numerical integration of the vector fi eld. I present
my results for di fferent system designs.

Millikan 134, Pomona College

Misc. Information

Refreshments served at 3:45 p.m.
Harry Mullikin Room, Millikan 209
The dinner will be hosted by Prof. Stephan Garcia
If interested in attending, email

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