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attraction for the bounding volume.  This is the formula we settled with,
and the cosine term does provide us with a smooth deformation.  A sample
of this muscle model is shown below:

<p><center>
<!WA8><!WA8><!WA8><!WA8><!WA8><!WA8><!WA8><!WA8><img src="http://www.tc.cornell.edu/Visualization/Education/cs718/fall1995/ddhung/linear.gif">
<p></center>

Not all muscles on the face apply force linearly.  Sphincter muscles around
the lips, for example, do not work well with this formula unmodified.  We
thus defined a special case of the formula to deal with these muscles:

<pre>
                       |<em>Po</em> - <em>P</em>|  
             1 + <strong>cos</strong>( ---------- <strong>pi</strong> )
<em>P'</em> = <em>P</em> + <em>K</em> (               <em>R</em>          ) (<em>P</em> - <em>Pd</em>) <em>t</em>
             ------------------------
                        2
</pre>

There are two important differences.  The <em>K</em> term was introduced
to allow the muscle to contract in one axis and expand in another, instead
of a uniform contraction or expansion.  The direction of motion is now
defined by <em>P</em> - <em>Pd</em>, which is in the direction of the
point of attraction (similar to formula 1).  The reason we inverted the
sign of this formula was because we felt that a positive <em>K</em> should
denote contraction and a negative <em>K</em> should denote expansion, in
order to be consistent with formula 2.  The example on the left below
shows a contracting sphincter muscle and the one on the right shows an
expanding sphincter muscle:

<p><center>
<!WA9><!WA9><!WA9><!WA9><!WA9><!WA9><!WA9><!WA9><img src="http://www.tc.cornell.edu/Visualization/Education/cs718/fall1995/ddhung/sphinc2.gif">
<!WA10><!WA10><!WA10><!WA10><!WA10><!WA10><!WA10><!WA10><img src="http://www.tc.cornell.edu/Visualization/Education/cs718/fall1995/ddhung/sphinc.gif">
<p></center>

<h2>Putting it all together</h2>

Armed with the face mesh and the muscles, what remains is the definition
of parameters, which is largely a tedious trial-and-error task.  We
present a few expressions generated by <strong>IBM DataExplorer</strong>
below (for mpeg demos click on the links below the images):

<p><center>
<!WA11><!WA11><!WA11><!WA11><!WA11><!WA11><!WA11><!WA11><img src="http://www.tc.cornell.edu/Visualization/Education/cs718/fall1995/ddhung/smile1.gif">
<!WA12><!WA12><!WA12><!WA12><!WA12><!WA12><!WA12><!WA12><img src="http://www.tc.cornell.edu/Visualization/Education/cs718/fall1995/ddhung/smile2.gif">
<!WA13><!WA13><!WA13><!WA13><!WA13><!WA13><!WA13><!WA13><img src="http://www.tc.cornell.edu/Visualization/Education/cs718/fall1995/ddhung/smile3.gif">
<!WA14><!WA14><!WA14><!WA14><!WA14><!WA14><!WA14><!WA14><img src="http://www.tc.cornell.edu/Visualization/Education/cs718/fall1995/ddhung/smile4.gif">
<p>
<!WA15><!WA15><!WA15><!WA15><!WA15><!WA15><!WA15><!WA15><img src="http://www.tc.cornell.edu/Visualization/Education/cs718/fall1995/ddhung/kiss1.gif">
<!WA16><!WA16><!WA16><!WA16><!WA16><!WA16><!WA16><!WA16><img src="http://www.tc.cornell.edu/Visualization/Education/cs718/fall1995/ddhung/kiss2.gif">
<!WA17><!WA17><!WA17><!WA17><!WA17><!WA17><!WA17><!WA17><img src="http://www.tc.cornell.edu/Visualization/Education/cs718/fall1995/ddhung/kiss3.gif">
<!WA18><!WA18><!WA18><!WA18><!WA18><!WA18><!WA18><!WA18><img src="http://www.tc.cornell.edu/Visualization/Education/cs718/fall1995/ddhung/kiss4.gif">
<p></center>

<strong> MPEG demos of our work </strong><p>
<!WA19><!WA19><!WA19><!WA19><!WA19><!WA19><!WA19><!WA19><a href="http://www.tc.cornell.edu/Visualization/Education/cs718/fall1995/ddhung/smile.mpg"> Click Here </a> to see the smile animation.<p>
<!WA20><!WA20><!WA20><!WA20><!WA20><!WA20><!WA20><!WA20><a href="http://www.tc.cornell.edu/Visualization/Education/cs718/fall1995/ddhung/kiss.mpg"> Click Here </a> to see the kiss animation.<p>

<strong> Data Explorer files of our work </strong><p>
<ul>
<li><!WA21><!WA21><!WA21><!WA21><!WA21><!WA21><!WA21><!WA21><a href="http://www.tc.cornell.edu/Visualization/Education/cs718/fall1995/ddhung/deidre-pts.dx>Click here</a> for the vertex list of the mesh.
<li><a href="deidre-con.dx>Click here</a> for the connections 
list of the mesh.
<li><!WA22><!WA22><!WA22><!WA22><!WA22><!WA22><!WA22><!WA22><a href="http://www.tc.cornell.edu/Visualization/Education/cs718/fall1995/ddhung/deidre-lip.dx>Click here</a> for the lip connections 
list of the mesh.
<li><a href="LinMuscle.net>Click here</a> for the DX macro which models a
linear contract/relax muscle on the face.
<li><!WA23><!WA23><!WA23><!WA23><!WA23><!WA23><!WA23><!WA23><a href="http://www.tc.cornell.edu/Visualization/Education/cs718/fall1995/ddhung/SpcMuscle.net>Click here</a> for the DX macro which models a 
sphincter squeez/expand muscle on the face.
<li><a href="Face.net>Click here</a> for the DX macro which models the
facial mesh.  Note that this requires a vertex list, connections, and lip
connections file (similar to the ones above) in order to work.
</ul>
<h2>Ahead</h2>

The effects we have achieved are far from realistic.  The complexities
of facial animation have not yet been fully explored, but we believe we
have come up with a reasonable model for manipulating data (less than
500 vertices) versus the much larger data set acquired by machines with
good quality.  Other areas may be explored, and those we feel are
interesting are listed below:

<ul>
<li> Texture-mapped skin [Nahas90]
<li> Coordination of lip muscles with speech [<!WA24><!WA24><!WA24><!WA24><!WA24><!WA24><!WA24><!WA24><a 
href="http://www.tc.cornell.edu/Visualization/Education/cs718/fall1995/ddhung/thalmann88.html>Thalmann88</a>, <a href="nahas88.html>Nahas88</a>]
<li> Motion of other facial elements such as eyeball or jaw
<li> Modelling of the interior of the mouth such as teeth and gums
<li> Modelling of hair features such as hair, moustache, beard, or
eyebrows
</ul>

<h2>References</h2>

Arad N., Dyn N., Reisfeld D., and Yeshurun Y., <em>Image Warping by
Radial Basis Functions - Application to Facial Expressions</em>,
CVGIP-Graphical Models and Image Processing, 1994

<p>

Badler N. and Platt S., <!WA25><!WA25><!WA25><!WA25><!WA25><!WA25><!WA25><!WA25><a href="http://www.tc.cornell.edu/Visualization/Education/cs718/fall1995/ddhung/platt81.html><em>Animating Facial
Expressions</em></a>, Computer Graphics, August 1981

<p>

Bergeron P. and Lachappelle P., <em>Control of Facial Expressions and Body
Movements in the Computer-generated Animated Short Tony de Peltrie</em>,
1985

<p>

Fahlander O., <em>Moving Picture Synthesis at Linkoping
University</em><br> Kalra P., Mangili A., Thalmann N., and Thalmann D., <a
href="kalra92.html> <em>Simulation of Facial Muscle Actions Based on
Rational Free-form Deformations</em></a>, Computer Graphics, September
1992

<p>

Kang C., Chen Y., and Hsu W., <em>Automatic Approach to Mapping a Lifelike
2.5D Human Face</em>, Image and Vision Computing, 1994

<p>

Magnenat-Thalmann N., Minh H., de Angelis, M., and Thalmann D., <!WA26><!WA26><!WA26><!WA26><!WA26><!WA26><!WA26><!WA26><a
href="http://www.tc.cornell.edu/Visualization/Education/cs718/fall1995/ddhung/thalmann89.html"><em>Design, Transformation, and Animation of Human
Faces</em></a>, Visual Computer

<p>

Magnenat-Thalmann N., Primeau E., and Thalmann D., <!WA27><!WA27><!WA27><!WA27><!WA27><!WA27><!WA27><!WA27><a
href="http://www.tc.cornell.edu/Visualization/Education/cs718/fall1995/ddhung/thalmann88.html"><em>Abstract Muscle Action Procedures for Human
Face Animation</em></a>, Visual Computer, 1988

<p>

Nahas M., Huitric H., Rioux M., and Domey J., <em>Facial Image Synthesis
Using Skin Texture Recording</em>, Visual Computer, December 1990

<p>

Nahas M., Huitric H., and Saintourens M., <!WA28><!WA28><!WA28><!WA28><!WA28><!WA28><!WA28><!WA28><a href="http://www.tc.cornell.edu/Visualization/Education/cs718/fall1995/ddhung/nahas88.html>
<em>Animation of a B-Spline Figure</em></a>, Visual Computer, 1988

<p>

Parke F., <em>A Model for Human Faces that Allowed Speech Synchronized
Animation</em>, Computer Graphics, 1975

<p>

Parke F., <em>Animation of Faces</em>, Proceedings of the ACM
(Annual Conference), 1972

<p>

Parke F., <em>Parametric Models for Facial Animation</em>, Computer
Graphics and Applications, November 1982

<p>

Thalmann D. and Magnenat-Thalman N., <em>Artificial Intelligence in
Three-dimensional Computer Animation</em>, Computer Graphics Forum, 1986

<p>

Thalmann N. and Thalmann D., <a href="thalmann95.html><em>Digital Actors
for Interactive Television</em></a>, Proceedings of the IEEE, 1995

<p>

Tost D. and Pueyo X., <em>Human Body Animation:  A Survey</em>, Visual
Computer, March 1988

<p>

Waters K., <!WA29><!WA29><!WA29><!WA29><!WA29><!WA29><!WA29><!WA29><a href="http://www.tc.cornell.edu/Visualization/Education/cs718/fall1995/ddhung/waters87.html"><em>A Muscle Model for Animating
Three-dimensional Facial Expressions</em></a>, Computer Graphics, July
1987

<p>
<hr>
<address>
Maintained by: <!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><a href="mailto:[e-mail]">Steven Huang</a>
and <!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><a href="mailto:[e-mail]">Dan Hung</a><br>
Last Modified: December 11, 1995
</address>