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<w:wrap type="square" anchory="line"/> </v:shape><![endif]--><![if !vml]><img width=250 height=220 src=Pooran.png align=right alt="Description: Description: Description: Description: C:\Users\Pooran\Documents\Application\Pooran.png" v:shapes="Picture_x0020_2"><![endif]></p> <table class=MsoNormalTable border=1 cellpadding=0 width="31%" style='width:31.0%;mso-cellspacing:1.5pt;background:aquamarine;border:outset #FFDE5B 1.0pt; mso-border-alt:outset #FFDE5B .75pt;mso-yfti-tbllook:1184;mso-padding-alt: 5.25pt 5.25pt 5.25pt 5.25pt'> <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes;mso-yfti-lastrow:yes'> <td style='border:inset #FFDE5B 1.0pt;mso-border-alt:inset #FFDE5B .75pt; padding:5.25pt 5.25pt 5.25pt 5.25pt'> <table class=MsoNormalTable border=0 cellpadding=0 width="100%" style='width:100.0%;mso-cellspacing:1.5pt;mso-yfti-tbllook:1184;mso-padding-alt: 0in 5.4pt 0in 5.4pt'> <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes;mso-yfti-lastrow:yes'> <td style='padding:.75pt .75pt .75pt .75pt'> <p class=MsoNormal align=center style='text-align:center'><span style='font-size:10.0pt;mso-fareast-font-family:"Times New Roman"'><br> </span><b><i><span style='font-size:18.0pt;font-family:"Arial","sans-serif"; mso-fareast-font-family:"Times New Roman"'>Post-Doc Researcher</span></i></b><b><i><span style='font-size:14.0pt;mso-fareast-font-family:"Times New Roman"'> <br> <a href="http://www.geometry.caltech.edu/"><u>Applied Geometry Lab</u></a>, <a href="http://www.caltech.edu/"><u>Caltech</u></a></span></BR></i></b><span style='font-size:14.0pt;mso-fareast-font-family:"Times New Roman"'> <br> <b>Email:</b> <span class=SpellE>pmemari</span>(at)<span class=SpellE>caltech</span>(dot)<span class=SpellE>edu</span><br> <b>Phone:</b> (+1) 626 395 29 83 <br> <b>Address:</b> Mail Code 305-16 <br> California Institute of Technology <br> 1200 E. California Blvd. <br> Pasadena, CA 91125<o:p></o:p></span></p> </td> </tr> </table> </td> </tr> </table> <p class=MsoNormal align=center style='text-align:center'><span style='mso-fareast-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p> <p align=center style='margin-bottom:0in;margin-bottom:.0001pt;text-align:center'><span style='font-size:13.5pt'>[<a href="#interests"><u>Research Interests</u></a>] [<a href="CV-Pooran-Memari.pdf"><u>Curriculum vitae</u></a>][<a href="#Education"><u>Education</u></a>] [<a href="#Papers"><u>Papers</u></a>] </span><o:p></o:p></p> <div align=center> <table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0 width=703 style='width:527.25pt;mso-cellspacing:0in;mso-yfti-tbllook:1184;mso-padding-alt: 1.5pt 1.5pt 1.5pt 1.5pt'> <COL WIDTH=48><COL WIDTH=2><COL WIDTH=294><COL WIDTH=338><COL WIDTH=2> <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'> <td width=48 rowspan=2 style='width:.5in;padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td width=647 colspan=37 style='width:485.25pt;padding:1.5pt 1.5pt 1.5pt 1.5pt'> <div class=MsoNormal align=center style='text-align:center'><span style='mso-fareast-font-family:"Times New Roman"'> <hr size=3 width="100%" noshade style='color:#EEEE00' align=center> </span></div> <p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><a name=interests></a><b><span style='font-size:13.5pt'><o:p>&nbsp;</o:p></span></b></p> <p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><b><span style='font-size:13.5pt'>Research Interests</span></b><span style='font-size: 13.5pt'> <o:p></o:p></span></p> <p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><o:p>&nbsp;</o:p></p> <p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:13.5pt'>Computational Geometry: Shape Reconstruction, Surface Sampling <o:p></o:p></span></p> <p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><o:p>&nbsp;</o:p></p> <p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:13.5pt'>Discrete Geometry: Mesh Optimization <o:p></o:p></span></p> <p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><o:p>&nbsp;</o:p></p> <p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:13.5pt'>Geometric Modeling, Geometric Algorithms (cf. <a href="http://www.cgal.org/"><u>CGAL</u></a>) <o:p></o:p></span></p> <p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><o:p>&nbsp;</o:p></p> <div class=MsoNormal align=center style='text-align:center'><span style='mso-fareast-font-family:"Times New Roman"'> <hr size=3 width="100%" noshade style='color:#0AAAD0' align=center> </span></div> <p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><a name=Education></a><b><span style='font-size:13.5pt'><o:p>&nbsp;</o:p></span></b></p> <p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><b><span style='font-size:13.5pt'>Education <o:p></o:p></span></b></p> <p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><o:p>&nbsp;</o:p></p> <p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><b>January 2010-Now <br> </b><span style='font-size:13.5pt'>Post Doc at <a href="http://www.geometry.caltech.edu/"><u>Applied Geometry Lab</u></a>, California Institute of Technology (<a href="http://www.caltech.edu/"><u>Caltech</u></a>). <o:p></o:p></span></p> <p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><o:p>&nbsp;</o:p></p> <p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><b>September 2006- January 2010 <br> </b><span class=SpellE><span style='font-size:13.5pt'>Ph.D</span></span><span style='font-size:13.5pt'> at <a href="http://www.inria.fr/"><u>INRIA</u></a> Sophia-<span class=SpellE>Antipolis</span>, <a href="http://www-sop.inria.fr/geometrica/"><span class=SpellE><u>Geometrica</u></span><u> Project</u></a>. <o:p></o:p></span></p> <p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><o:p>&nbsp;</o:p></p> <p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><b>2005-2006 <br> </b><span style='font-size:13.5pt'><a href="http://www-sop.inria.fr/odyssee/lectures/Vision3D/Master-IGMMV/Vision3D.html"><u>Master</u></a> (Image and Geometry) at <a href="http://portail.unice.fr/jahia/jsp/index.jsp"><u>University of Nice-Sophia <span class=SpellE>Antipolis</span></u></a>. <o:p></o:p></span></p> <p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><o:p>&nbsp;</o:p></p> <p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><b>2002-2005 <br> </b><span style='font-size:13.5pt'>Engineering Studies at <a href="http://www.polytechnique.fr/"><span class=SpellE><u>Ecole</u></span><u> <span class=SpellE>Polytechnique</span></u></a> (<span class=SpellE>Palaiseau</span>). <o:p></o:p></span></p> <p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><o:p>&nbsp;</o:p></p> <p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><b>2000-2002 <br> </b><span style='font-size:13.5pt'>Bachelor in Mathematics at <a href="http://www.sharif.ir/en/"><u>Sharif University of Technology</u></a>. </span></p> <p class=MsoNormal style='mso-margin-top-alt:auto;margin-bottom:12.0pt'><o:p>&nbsp;</o:p></p> <div class=MsoNormal align=center style='text-align:center'><span style='mso-fareast-font-family:"Times New Roman"'> <hr size=3 width="100%" noshade style='color:#0000DD' align=center> </span></div> <p class=MsoNormal style='mso-margin-top-alt:auto;margin-bottom:12.0pt'><a name=Papers></a><b><span style='font-size:13.5pt'><o:p>&nbsp;</o:p></span></b></p> <p class=MsoNormal style='mso-margin-top-alt:auto;margin-bottom:12.0pt'><b><span style='font-size:13.5pt'>Selected Publications<o:p></o:p></span></b></p> <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p> <table class=MsoNormalTable border=1 cellpadding=0 width="100%" style='width:100.0%;mso-cellspacing:1.5pt;background:#FCFEBA;border:outset #FFDE5B 1.5pt; mso-yfti-tbllook:1184;mso-padding-alt:7.5pt 7.5pt 7.5pt 7.5pt'> <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes;mso-yfti-lastrow:yes'> <td style='border:inset #FFDE5B 1.0pt;mso-border-alt:inset #FFDE5B .75pt; padding:7.5pt 7.5pt 7.5pt 7.5pt'> <table class=MsoNormalTable border=0 cellpadding=0 width="100%" style='width:100.0%;mso-cellspacing:1.5pt;mso-yfti-tbllook:1184; mso-padding-alt:0in 5.4pt 0in 5.4pt'> <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'> <td style='padding:.75pt .75pt .75pt .75pt'></td> <td style='padding:.75pt .75pt .75pt .75pt'> <p class=MsoNormal><b><span style='mso-fareast-font-family:"Times New Roman"; color:#222288'>Hodge-Optimized Triangulations</span></b><span style='font-size:10.0pt;mso-fareast-font-family:"Times New Roman"'><o:p></o:p></span></p> </td> <td style='padding:.75pt .75pt .75pt .75pt'> <p class=MsoNormal align=right style='text-align:right'><span style='font-size:7.5pt;mso-fareast-font-family:"Times New Roman"; color:#A0A0A0'>2011</span><span style='font-size:10.0pt;mso-fareast-font-family: "Times New Roman"'><o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:1'> <td style='padding:.75pt .75pt .75pt .75pt'></td> <td colspan=2 style='padding:.75pt .75pt .75pt .75pt'> <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman"'> <a href="http://www.cs.caltech.edu/~patrickm/"><u>Patrick Mullen</u></a>, Pooran Memari, <a href="http://www.cs.caltech.edu/~fferrari/Home.html"><u>Fernando de Goes </u></a>, <a href="http://geometry.caltech.edu/~mathieu/"><u>Mathieu <span class=SpellE>Desbrun</span></u></a>.<br> SIGGRAPH 2011 / ACM Transactions on Graphics. <a href="http://www.geometry.caltech.edu/pubs/MMdGD11.pdf"> <u>Pdf</u> </a><o:p></o:p></span></p> <p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt: auto;text-align:justify'><!--[if gte vml 1]><v:shape id="Picture_x0020_4" o:spid="_x0000_s1030" type="#_x0000_t75" alt="Description: Description: Description: Description: C:\Users\Pooran\Documents\Application\CGF08.png" style='position:absolute;left:0;text-align:left;margin-left:189.55pt; margin-top:0;width:240.75pt;height:225pt;z-index:251657216;visibility:visible; mso-wrap-style:square;mso-width-percent:0;mso-height-percent:0; mso-wrap-distance-left:0;mso-wrap-distance-top:0; mso-wrap-distance-right:0;mso-wrap-distance-bottom:0; mso-position-horizontal:right;mso-position-horizontal-relative:text; mso-position-vertical:absolute;mso-position-vertical-relative:line; mso-width-percent:0;mso-height-percent:0;mso-width-relative:page; mso-height-relative:page' o:allowoverlap="f"> <v:imagedata src="BimbaFigure.png"/> <w:wrap type="square" anchory="line"/> </v:shape><![endif]--><![if !vml]><img width=321 height=300 src=BimbaFigure.png align=right alt="Description: Description: Description: Description: C:\Users\Pooran\Documents\Application\CGF08.png" v:shapes="Picture_x0020_4"><![endif]>We introduce Hodge-optimized triangulations, a family of <b>well-shaped primal-dual pairs of complexes</b> designed for fast and accurate computations in computer graphics. Previous work most commonly employs barycentric or circumcentric duals: while barycentric duals guarantee that the dual of each simplex lies within the simplex, circumcentric duals are often preferred due to the induced orthogonality between primal and dual complexes. We instead promote the use of weighted duals. They allow much greater flexibility in the location of dual vertices while keeping primal-dual orthogonality, thus providing a valuable extension to the usual choices of dual by only adding one additional scalar per primal vertex. Moreover, our work unveils an important connection between Hodge star accuracy and <i>optimal transport</i>. We introduce a family of functionals on pairs of complexes that we derive from bounds on the errors induced by diagonal Hodge stars, commonly used in discrete computations. The minimizers of these functionals are shown to be <i>generalizations of Centroidal Voronoi Tesselations (CVT) and Optimal Delaunay Triangulations (ODT)</i>, and to provide increased accuracy and flexibility for a variety of computational purposes.</p> </td> </tr> <tr style='mso-yfti-irow:2;mso-yfti-lastrow:yes'> <td style='padding:.75pt .75pt .75pt .75pt'></td> <td style='padding:.75pt .75pt .75pt .75pt'></td> <td style='padding:.75pt .75pt .75pt .75pt'></td> </tr> </table> </td> </tr> </table> <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p> <table class=MsoNormalTable border=1 cellpadding=0 width="100%" style='width:100.0%;mso-cellspacing:1.5pt;background:aquamarine;border:outset #FFDE5B 1.5pt; mso-yfti-tbllook:1184;mso-padding-alt:7.5pt 7.5pt 7.5pt 7.5pt'> <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes;mso-yfti-lastrow:yes'> <td style='border:inset #FFDE5B 1.0pt;mso-border-alt:inset #FFDE5B .75pt; padding:7.5pt 7.5pt 7.5pt 7.5pt'> <table class=MsoNormalTable border=0 cellpadding=0 width="100%" style='width:100.0%;mso-cellspacing:1.5pt;mso-yfti-tbllook:1184; mso-padding-alt:0in 5.4pt 0in 5.4pt'> <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'> <td style='padding:.75pt .75pt .75pt .75pt'></td> <td style='padding:.75pt .75pt .75pt .75pt'> <p class=MsoNormal><b><span style='mso-fareast-font-family:"Times New Roman"; color:#222288'>Parameterization of Generalized Primal-Dual Triangulations</span></b><span style='font-size:10.0pt;mso-fareast-font-family:"Times New Roman"'><o:p></o:p></span></p> </td> <td style='padding:.75pt .75pt .75pt .75pt'> <p class=MsoNormal align=right style='text-align:right'><span style='font-size:7.5pt;mso-fareast-font-family:"Times New Roman"; color:#A0A0A0'>2010</span><span style='font-size:10.0pt;mso-fareast-font-family: "Times New Roman"'><o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:1'> <td style='padding:.75pt .75pt .75pt .75pt'></td> <td colspan=2 style='padding:.75pt .75pt .75pt .75pt'> <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman"'> Pooran Memari, <a href="http://www.cs.caltech.edu/~patrickm/"><u>Patrick Mullen</u></a>, <a href="http://geometry.caltech.edu/~mathieu/"><u>Mathieu <span class=SpellE>Desbrun</span></u></a>. To appear in the proceedings of 20th International Meshing Roundtable <b>2011</b>.<o:p></o:p></span></p> <p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt: auto;text-align:justify'><!--[if gte vml 1]><v:shape id="Picture_x0020_5" o:spid="_x0000_s1029" type="#_x0000_t75" alt="Description: Description: Description: Description: C:\Users\Pooran\Documents\Application\PDT-Figure.png" style='position:absolute;left:0;text-align:left;margin-left:189.55pt; margin-top:0;width:240.75pt;height:165.75pt;z-index:251659264; visibility:visible;mso-wrap-style:square;mso-width-percent:0; mso-height-percent:0;mso-wrap-distance-left:0;mso-wrap-distance-top:0; mso-wrap-distance-right:0;mso-wrap-distance-bottom:0; mso-position-horizontal:right;mso-position-horizontal-relative:text; mso-position-vertical:absolute;mso-position-vertical-relative:line; mso-width-percent:0;mso-height-percent:0;mso-width-relative:page; mso-height-relative:page' o:allowoverlap="f"> <v:imagedata src="PDT-Figure.png"/> <w:wrap type="square" anchory="line"/> </v:shape><![endif]--><![if !vml]><img width=321 height=221 src=PDT-Figure.png align=right alt="Description: Description: Description: Description: C:\Users\Pooran\Documents\Application\PDT-Figure.png" v:shapes="Picture_x0020_5"><![endif]>In this paper, we introduce a convenient, geometric parameterization of the space of non-orthogonal primal-dual triangulations. Motivated by practical numerical issues in a number of modeling and simulation problems, we relax the conventional orthogonality of mesh duality and introduce the weaker notion of a <i style='mso-bidi-font-style: normal'>compatible dual complex </i>to a primal triangulation. We show that the existence of compatible dual complexes is guaranteed only for a particular type of triangulation known as weakly regular. We provide a simple parameterization of the entire space of compatible pairs of primal triangulations and dual complexes that extends the well known weighted Delaunay / power diagram duality, and allows us to easily explore a space of primal-dual structures much larger than the space of orthogonal primal-dual structures. This parameterization may play an important role in discrete optimization problems such as optimal mesh generation.</p> </td> </tr> <tr style='mso-yfti-irow:2;mso-yfti-lastrow:yes'> <td style='padding:.75pt .75pt .75pt .75pt'></td> <td style='padding:.75pt .75pt .75pt .75pt'></td> <td style='padding:.75pt .75pt .75pt .75pt'></td> </tr> </table> </td> </tr> </table> <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p> <table class=MsoNormalTable border=1 cellpadding=0 width="100%" style='width:100.0%;mso-cellspacing:1.5pt;background:#CFE8F3;border:outset #FFDE5B 1.5pt; mso-yfti-tbllook:1184;mso-padding-alt:7.5pt 7.5pt 7.5pt 7.5pt'> <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes;mso-yfti-lastrow:yes'> <td style='border:inset #FFDE5B 1.0pt;mso-border-alt:inset #FFDE5B .75pt; padding:7.5pt 7.5pt 7.5pt 7.5pt'> <table class=MsoNormalTable border=0 cellpadding=0 width="100%" style='width:100.0%;mso-cellspacing:1.5pt;mso-yfti-tbllook:1184; mso-padding-alt:0in 5.4pt 0in 5.4pt'> <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'> <td style='padding:.75pt .75pt .75pt .75pt'></td> <td style='padding:.75pt .75pt .75pt .75pt'> <p class=MsoNormal><b><span style='mso-fareast-font-family:"Times New Roman"; color:#222288'>Geometric Tomography With Topological Guarantees</span></b><span style='font-size:10.0pt;mso-fareast-font-family:"Times New Roman"'><o:p></o:p></span></p> </td> <td style='padding:.75pt .75pt .75pt .75pt'> <p class=MsoNormal align=right style='text-align:right'><span style='font-size:7.5pt;mso-fareast-font-family:"Times New Roman"; color:#A0A0A0'>2009</span><span style='font-size:10.0pt;mso-fareast-font-family: "Times New Roman"'><o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:1'> <td style='padding:.75pt .75pt .75pt .75pt'></td> <td colspan=2 style='padding:.75pt .75pt .75pt .75pt'> <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman"'><a href="http://www.math.ens.fr/~amini/"><span class=SpellE><u>Omid</u></span><u> <span class=SpellE>Amini</span></u></a>, <a href="http://www-sop.inria.fr/members/Jean-Daniel.Boissonnat/"><u>Jean-Daniel <span class=SpellE>Boissonnat</span></u></a>, Pooran Memari.<br> Proceedings of the 26th Symposium on Computational Geometry 2010. Journal version <a href="socg10.pdf"><span class=SpellE><u>Pdf</u></span></a>. <o:p></o:p></span></p> <p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt: auto;text-align:justify'><!--[if gte vml 1]><v:shape id="_x0000_s1028" type="#_x0000_t75" alt="Description: Description: Description: Description: C:\Users\Pooran\Documents\Application\socg10.png" style='position:absolute;left:0;text-align:left;margin-left:189.55pt; margin-top:0;width:240.75pt;height:165.75pt;z-index:251660288; visibility:visible;mso-wrap-style:square;mso-width-percent:0; mso-height-percent:0;mso-wrap-distance-left:0;mso-wrap-distance-top:0; mso-wrap-distance-right:0;mso-wrap-distance-bottom:0; mso-position-horizontal:right;mso-position-horizontal-relative:text; mso-position-vertical:absolute;mso-position-vertical-relative:line; mso-width-percent:0;mso-height-percent:0;mso-width-relative:page; mso-height-relative:page' o:allowoverlap="f"> <v:imagedata src="socg10.png"/> <w:wrap type="square" anchory="line"/> </v:shape><![endif]--><![if !vml]><img width=321 height=221 src=socg10.png align=right alt="Description: Description: Description: Description: C:\Users\Pooran\Documents\Application\socg10.png" v:shapes="_x0000_s1028"><![endif]>In this paper we consider the problem of <b>reconstructing a compact 3-manifold</b> (with boundary) embedded in R3 from its 2D cross-sections with a given set of cutting planes having arbitrary orientations. Under appropriate sampling conditions, we prove that a natural reconstruction method (presented by <a href="liu_et_al_08.doc"><u>Liu et al.</u></a> 2008), based on the distance to the cutting planes, preserves the <span class=SpellE><b>homotopy</b></span><b> type</b> of the original object. Moreover, the reconstructed object is <span class=SpellE><b>homeomorphic</b></span><b> (and isotopic)</b> to the original object. This is the <b>first time</b> that reconstruction from cross-sections comes with theoretical guarantees. </p> </td> </tr> <tr style='mso-yfti-irow:2;mso-yfti-lastrow:yes'> <td style='padding:.75pt .75pt .75pt .75pt'></td> <td style='padding:.75pt .75pt .75pt .75pt'></td> <td style='padding:.75pt .75pt .75pt .75pt'></td> </tr> </table> </td> </tr> </table> <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p> <table class=MsoNormalTable border=1 cellpadding=0 width="100%" style='width:100.0%;mso-cellspacing:1.5pt;background:#FCFEBA;border:outset #FFDE5B 1.5pt; mso-yfti-tbllook:1184;mso-padding-alt:7.5pt 7.5pt 7.5pt 7.5pt'> <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes;mso-yfti-lastrow:yes'> <td style='border:inset #FFDE5B 1.0pt;mso-border-alt:inset #FFDE5B .75pt; padding:7.5pt 7.5pt 7.5pt 7.5pt'> <table class=MsoNormalTable border=0 cellpadding=0 width="100%" style='width:100.0%;mso-cellspacing:1.5pt;mso-yfti-tbllook:1184; mso-padding-alt:0in 5.4pt 0in 5.4pt'> <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'> <td style='padding:.75pt .75pt .75pt .75pt'></td> <td style='padding:.75pt .75pt .75pt .75pt'> <p class=MsoNormal><b><span style='mso-fareast-font-family:"Times New Roman"; color:#222288'>Provably Good 2D Shape Reconstruction from Unorganized Cross Sections</span></b><span style='font-size:10.0pt;mso-fareast-font-family: "Times New Roman"'><o:p></o:p></span></p> </td> <td style='padding:.75pt .75pt .75pt .75pt'> <p class=MsoNormal align=right style='text-align:right'><span style='font-size:7.5pt;mso-fareast-font-family:"Times New Roman"; color:#A0A0A0'>2008</span><span style='font-size:10.0pt;mso-fareast-font-family: "Times New Roman"'><o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:1'> <td style='padding:.75pt .75pt .75pt .75pt'></td> <td colspan=2 style='padding:.75pt .75pt .75pt .75pt'> <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman"'> Pooran Memari, <a href="http://www-sop.inria.fr/members/Jean-Daniel.Boissonnat/"><u>Jean-Daniel <span class=SpellE>Boissonnat</span></u></a>.<br> Computer Graphics Forum, Vol.27, No. 5, 1403-1410, <b>2008</b>. <a href="CGF08.pdf"><span class=SpellE><u>Pdf</u></span></a>, <a href="CGF08.doc"><span class=SpellE><span class=GramE><u>BibTex</u></span></span><span class=GramE><u> </u></span></a>. <o:p></o:p></span></p> <p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt: auto;text-align:justify'><!--[if gte vml 1]><v:shape id="_x0000_s1027" type="#_x0000_t75" alt="Description: Description: Description: Description: C:\Users\Pooran\Documents\Application\CGF08.png" style='position:absolute;left:0;text-align:left;margin-left:189.55pt; margin-top:0;width:240.75pt;height:225pt;z-index:251658240;visibility:visible; mso-wrap-style:square;mso-width-percent:0;mso-height-percent:0; mso-wrap-distance-left:0;mso-wrap-distance-top:0; mso-wrap-distance-right:0;mso-wrap-distance-bottom:0; mso-position-horizontal:right;mso-position-horizontal-relative:text; mso-position-vertical:absolute;mso-position-vertical-relative:line; mso-width-percent:0;mso-height-percent:0;mso-width-relative:page; mso-height-relative:page' o:allowoverlap="f"> <v:imagedata src="CGF08.png"/> <w:wrap type="square" anchory="line"/> </v:shape><![endif]--><![if !vml]><img width=321 height=300 src=CGF08.png align=right alt="Description: Description: Description: Description: C:\Users\Pooran\Documents\Application\CGF08.png" v:shapes="_x0000_s1027"><![endif]>This paper deals with the reconstruction of <b>2-dimensional</b> geometric shapes from unorganized 1-dimensional cross-sections. We propose a variant of our 3D approach (<span class=SpellE>Boissonnat</span> and <span class=SpellE>Memari</span> 2007) adapted to the 2 dimensional <span class=GramE>structure</span>. The preliminary experimental results presented in this paper are quite promising regarding the practicality of the approach to reconstruct complex cross-sectional branching situations such as the coronary arterial tree. Moreover, we present <b>sampling conditions</b> to guarantee that the output of the algorithm has the same topology as the original object and is close to it (for the <span class=SpellE>Hausdorff</span> distance). </p> </td> </tr> <tr style='mso-yfti-irow:2;mso-yfti-lastrow:yes'> <td style='padding:.75pt .75pt .75pt .75pt'></td> <td style='padding:.75pt .75pt .75pt .75pt'></td> <td style='padding:.75pt .75pt .75pt .75pt'></td> </tr> </table> </td> </tr> </table> <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p> <table class=MsoNormalTable border=1 cellpadding=0 width="100%" style='width:100.0%;mso-cellspacing:1.5pt;background:blanchedalmond; border:outset #FFDE5B 1.5pt;mso-yfti-tbllook:1184;mso-padding-alt:7.5pt 7.5pt 7.5pt 7.5pt'> <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes;mso-yfti-lastrow:yes'> <td style='border:inset #FFDE5B 1.0pt;mso-border-alt:inset #FFDE5B .75pt; padding:7.5pt 7.5pt 7.5pt 7.5pt'> <table class=MsoNormalTable border=0 cellpadding=0 width="100%" style='width:100.0%;mso-cellspacing:1.5pt;mso-yfti-tbllook:1184; mso-padding-alt:0in 5.4pt 0in 5.4pt'> <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'> <td style='padding:.75pt .75pt .75pt .75pt'></td> <td style='padding:.75pt .75pt .75pt .75pt'> <p class=MsoNormal><b><span style='mso-fareast-font-family:"Times New Roman"; color:#222288'>Shape Reconstruction From Unorganized Cross Sections</span></b><span style='font-size:10.0pt;mso-fareast-font-family:"Times New Roman"'><o:p></o:p></span></p> </td> <td style='padding:.75pt .75pt .75pt .75pt'> <p class=MsoNormal align=right style='text-align:right'><span style='font-size:7.5pt;mso-fareast-font-family:"Times New Roman"; color:#A0A0A0'>2007</span><span style='font-size:10.0pt;mso-fareast-font-family: "Times New Roman"'><o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:1'> <td style='padding:.75pt .75pt .75pt .75pt'></td> <td colspan=2 style='padding:.75pt .75pt .75pt .75pt'> <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman"'><a href="http://www-sop.inria.fr/members/Jean-Daniel.Boissonnat/"><u>Jean-Daniel <span class=SpellE>Boissonnat</span></u></a>, Pooran Memari.<br> Symposium on Geometry Processing (SGP), 89-98, <b>2007</b>. <a href="SGP07.pdf"><span class=SpellE><u>Pdf</u></span></a>, <a href="SGP07.doc"><span class=SpellE><span class=GramE><u>BibTex</u></span></span><span class=GramE><u> </u></span></a>. <o:p></o:p></span></p> <p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt: auto;text-align:justify'><!--[if gte vml 1]><v:shape id="Picture_x0020_3" o:spid="_x0000_s1026" type="#_x0000_t75" alt="Description: Description: Description: Description: C:\Users\Pooran\Documents\Application\sgp07.png" style='position:absolute;left:0;text-align:left;margin-left:114.55pt; margin-top:0;width:165.75pt;height:290.25pt;z-index:251656192; visibility:visible;mso-wrap-style:square;mso-width-percent:0; mso-height-percent:0;mso-wrap-distance-left:0;mso-wrap-distance-top:0; mso-wrap-distance-right:0;mso-wrap-distance-bottom:0; mso-position-horizontal:right;mso-position-horizontal-relative:text; mso-position-vertical:absolute;mso-position-vertical-relative:line; mso-width-percent:0;mso-height-percent:0;mso-width-relative:page; mso-height-relative:page' o:allowoverlap="f"> <v:imagedata src="sgp07.png"/> <w:wrap type="square" anchory="line"/> </v:shape><![endif]--><![if !vml]><img width=221 height=387 src=sgp07.png align=right alt="Description: Description: Description: Description: C:\Users\Pooran\Documents\Application\sgp07.png" v:shapes="Picture_x0020_3"><![endif]>In this paper, we consider the problem of reconstructing a <b>3D shape</b> from unorganized cross-sections. The main motivation for this problem comes from medical imaging applications where cross-sections of human organs are obtained by means of a free hand ultrasound apparatus. The position and orientation of the cutting planes may be freely chosen which makes the problem substantially more difficult than in the case of parallel cross-sections, for which a rich literature exists. The input data consist of the cutting planes and (an approximation of) their intersection with the object. We first compute the arrangement of the cutting planes. Then, in each cell of the arrangement, we reconstruct an approximation of the object from its intersection with the boundary of the cell. Lastly, we glue the various pieces together. The method makes use of the Delaunay triangulation and generalizes the reconstruction method of <a href="http://spiedl.aip.org/getabs/servlet/GetabsServlet?prog=normal&amp;id=PSISDG001905000001000964000001&amp;idtype=cvips&amp;gifs=yes&amp;ref=no"><span class=SpellE><u>Boissonnat</u></span><u> and Geiger 1993</u></a> for the case of parallel planes. The analysis shows an interesting application of <a href="http://www.google.fr/url?sa=t&amp;source=web&amp;ct=res&amp;cd=7&amp;ved=0CBcQFjAG&amp;url=ftp%3A%2F%2Fftp-sop.inria.fr%2Fprisme%2FECG%2FReports%2FMonth24%2FECG-TR-241208-01.ps.gz&amp;rct=j&amp;q=mobius+diagram&amp;ei=xuPES8efD42wswPQ_rD_DA&amp;usg=AFQjCNH7k_hbpZFpYTthri13wwLHK-BjdA"><span class=SpellE><u>Moebius</u></span><u> diagrams</u></a> to compute the locus of the branching points. <b>Experimental results</b> (using the <a href="http://www.cgal.org/"><u>CGAL</u></a> library) show that the algorithm performs well and can handle complicated branching configurations. </p> </td> </tr> <tr style='mso-yfti-irow:2;mso-yfti-lastrow:yes'> <td style='padding:.75pt .75pt .75pt .75pt'></td> <td style='padding:.75pt .75pt .75pt .75pt'></td> <td style='padding:.75pt .75pt .75pt .75pt'></td> </tr> </table> </td> </tr> </table> <p class=MsoNormal align=center style='text-align:center'><span style='font-size:10.0pt;mso-fareast-font-family:"Times New Roman";color:windowtext; display:none;mso-hide:all'><o:p>&nbsp;</o:p></span></p> <div align=center> <table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0 width=703 style='width:527.25pt;mso-cellspacing:0in;mso-yfti-tbllook:1184;mso-padding-alt: 1.5pt 1.5pt 1.5pt 1.5pt'> <COL WIDTH=48><COL WIDTH=2><COL WIDTH=294><COL WIDTH=338><COL WIDTH=2> <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'> <td width=48 rowspan=2 style='width:.5in;padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td width=647 style='width:485.25pt;padding:1.5pt 1.5pt 1.5pt 1.5pt'> <div class=MsoNormal align=center style='text-align:center'><span style='mso-fareast-font-family:"Times New Roman"'> <hr size=3 width="100%" noshade style='color:#EEEE00' align=center> </span></div> </td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 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1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> </tr> <tr style='mso-yfti-irow:1;mso-yfti-lastrow:yes'> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> </tr> </table> </div> <p class=MsoNormal align=center style='text-align:center'><span style='font-size:10.0pt;mso-fareast-font-family:"Times New Roman";color:windowtext; display:none;mso-hide:all'><o:p>&nbsp;</o:p></span></p> <div align=center> <table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0 width=703 style='width:527.25pt;mso-cellspacing:0in;mso-yfti-tbllook:1184;mso-padding-alt: 1.5pt 1.5pt 1.5pt 1.5pt'> <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes;mso-yfti-lastrow:yes'> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 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1.5pt 1.5pt 1.5pt'></td> </tr> </table> </div> <p align=center style='margin-bottom:12.0pt;text-align:center'><o:p></o:p></p> </td> </tr> <tr style='mso-yfti-irow:1;mso-yfti-lastrow:yes'> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> <td style='padding:1.5pt 1.5pt 1.5pt 1.5pt'></td> </tr> </table> </div> <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman"; color:windowtext'><o:p>&nbsp;</o:p></span></p> </div> </body> </html>