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} } } } </script> <!--[if gte mso 9]><xml> <o:shapedefaults v:ext="edit" spidmax="45058"/> </xml><![endif]--><!--[if gte mso 9]><xml> <o:shapelayout v:ext="edit"> <o:idmap v:ext="edit" data="2"/> </o:shapelayout></xml><![endif]--> </head> <body lang=ZH-TW link=blue vlink=purple style='tab-interval:24.0pt' onload="MM_CheckFlashVersion('7,0,0,0',',gu??Q?[???O(u???e?v Macromedia Flash Player Hr,g0/f&amp;T?s(W&#11;N}??[?;"> <div class=Section1> <p class=MsoNormal><span lang=EN-US style='font-family:Arial'><o:p>&nbsp;</o:p></span></p> <div align=center> <table class=hhgQe border=0 cellpadding=0 width=978 style='width:733.5pt; mso-cellspacing:1.5pt;mso-yfti-tbllook:1184;mso-padding-alt:0pt 5.4pt 0pt 5.4pt'> <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes;height:88.5pt'> <td colspan=2 style='padding:.75pt .75pt .75pt .75pt;height:88.5pt'> <p class=MsoNormal align=center style='margin-bottom:12.0pt;text-align:center'><span class=style91><span lang=EN-US style='font-size:18.0pt'>Skeleton Extraction by Mesh Contraction</span></span><span lang=EN-US style='font-family:Arial'><o:p></o:p></span></p> <p class=style7 align=center style='text-align:center'><span lang=EN-US><a href="http://www.cse.ust.hk/~oscarau/" target="_blank">Oscar Kin-Chung Au</a><sup>1</sup>&nbsp; <a href="http://www.cse.ust.hk/~taicl" target="_blank">Chiew-Lan Tai</a><sup>1</sup> </span><span lang=EN-US style='mso-fareast-font-family:°e0}fÔš'>,</span><span lang=EN-US>&nbsp;&nbsp;&nbsp;<a href="http://vision.csie.ncku.edu.tw/~hkchu/">Hung-Kuo Chu</a><sup>2</sup> </span><span lang=EN-US style='mso-fareast-font-family: °e0}fÔš'>, </span><span lang=EN-US><a href="http://www.cs.tau.ac.il/~dcor/" target="_blank">Daniel Cohen-Or</a><sup>3</sup></span><span lang=EN-US style='mso-fareast-font-family:°e0}fÔš'>,</span><span lang=EN-US> <a href="http://graphics.csie.ncku.edu.tw/Tony/tony.htm">Tong-Yee Lee</a><sup>2</sup></span></p> <p align=center style='text-align:center'><span class=style71><span lang=EN-US>ACM Transaction on Graphics (Proceedings of </span></span><span class=style71><span lang=EN-US style='font-weight:normal;mso-bidi-font-weight: bold'><a href="http://www.siggraph.org/s2008/"><b style='mso-bidi-font-weight: normal'>SIGGRAPH 2008</b></a></span><span lang=EN-US>) <o:p></o:p></span></span></p> <p align=center style='text-align:center'><b style='mso-bidi-font-weight: normal'><sup><span lang=EN-US style='font-family:Arial'>1</span></sup></b><b style='mso-bidi-font-weight:normal'><span lang=EN-US style='font-family:Arial'><a href="http://www.cse.ust.hk/">Hong Kong University of Science &amp; Technology</a></span></b></p> <p align=center style='text-align:center'><b style='mso-bidi-font-weight: normal'><sup><span lang=EN-US style='font-family:Arial'>2</span></sup></b><b style='mso-bidi-font-weight:normal'><span lang=EN-US style='font-family:Arial'><a href="http://graphics.csie.ncku.edu.tw/">National Cheng Kung University</a><o:p></o:p></span></b></p> <p align=center style='text-align:center'><b style='mso-bidi-font-weight: normal'><sup><span lang=EN-US style='font-family:Arial'>3</span></sup></b><b style='mso-bidi-font-weight:normal'><span lang=EN-US style='font-family:Arial'><a href="http://www.tau.ac.il/" target="_blank">Tel Aviv University</a><o:p></o:p></span></b></p> </td> </tr> <tr style='mso-yfti-irow:1;height:211.5pt'> <td colspan=2 style='padding:.75pt .75pt .75pt .75pt;height:211.5pt'> <div> <p align=center style='text-align:center'><span lang=EN-US style='font-family: Arial'><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> <v:stroke joinstyle="miter"/> <v:formulas> <v:f eqn="if lineDrawn pixelLineWidth 0"/> <v:f eqn="sum @0 1 0"/> <v:f eqn="sum 0 0 @1"/> <v:f eqn="prod @2 1 2"/> <v:f eqn="prod @3 21600 pixelWidth"/> <v:f eqn="prod @3 21600 pixelHeight"/> <v:f eqn="sum @0 0 1"/> <v:f eqn="prod @6 1 2"/> <v:f eqn="prod @7 21600 pixelWidth"/> <v:f eqn="sum @8 21600 0"/> <v:f eqn="prod @7 21600 pixelHeight"/> <v:f eqn="sum @10 21600 0"/> </v:formulas> <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/> <o:lock v:ext="edit" aspectratio="t"/> </v:shapetype><v:shape id="_x0000_i1025" type="#_x0000_t75" style='width:999.75pt; height:164.25pt'> <v:imagedata src="index.files/image001.emz" o:title=""/> </v:shape><![endif]--><![if !vml]><img border=0 width=1333 height=219 src="index.files/image002.gif" v:shapes="_x0000_i1025"><![endif]></span><span lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:Arial'><o:p></o:p></span></p> <p><i><span lang=EN-US style='mso-bidi-font-family:"Times New Roman"'>Teaser: Our method extracts a 1D skeletal shape by performing geometry contraction using constrained <span class=SpellE>Laplacian</span> <span class=GramE>smoothing.?</span> Left to right are the original mesh and the results of the contraction after 1, 2 and 3 iterations. Faces with zero area are drawn in red. The ray-traced image shows the final skeleton after performing connectivity surgery and embedding refinement.<o:p></o:p></span></i></p> </div> </td> </tr> <tr style='mso-yfti-irow:2;height:141.35pt'> <td width=110 style='width:82.6pt;background:#CEE3F2;padding:.75pt .75pt .75pt .75pt; height:141.35pt'> <p class=MsoNormal align=right style='text-align:right'><span class=style71><span lang=EN-US>Abstract</span></span><span lang=EN-US style='font-family:Arial'><o:p></o:p></span></p> </td> <td width=862 style='width:646.4pt;padding:.75pt .75pt .75pt .75pt; height:141.35pt'> <div> <p class=MsoNormal><span lang=EN-US style='mso-bidi-font-family:"Times New Roman"'>Extraction of curve-skeletons is a fundamental problem with many applications in computer graphics and visualization. In this paper, we present a simple and robust skeleton extraction method based on mesh contraction. The method works directly on the mesh domain, without pre-sampling the mesh model into a volumetric representation. The method first contracts the mesh geometry into a zero-volume skeletal shape by applying implicit <span class=SpellE>Laplacian</span> smoothing with global positional constraints. The contraction does not alter the mesh connectivity and retains the key features of the original mesh. The contracted mesh is then converted into a 1D curve-skeleton through a connectivity surgery process to remove all the collapsed faces while preserving the shape of the contracted mesh and the original topology. The centeredness of the skeleton is refined by exploiting the induced skeleton-mesh mapping. The contraction process generates valuable information about the object's geometry, in particular, the skeleton-vertex correspondence and the local thickness, which are useful for various applications. We demonstrate its effectiveness in mesh segmentation and skinning animation.<o:p></o:p></span></p> </div> </td> </tr> <tr style='mso-yfti-irow:3;height:24.75pt'> <td width=110 style='width:82.6pt;background:#CEE3F2;padding:.75pt .75pt .75pt .75pt; height:24.75pt'> <p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US style='font-family:Arial'>Paper<o:p></o:p></span></b></p> </td> <td width=862 style='width:646.4pt;padding:.75pt .75pt .75pt .75pt; height:24.75pt'> <p class=MsoNormal align=center style='margin-bottom:12.0pt;text-align:center'><b style='mso-bidi-font-weight:normal'><span lang=EN-US style='font-size:10.0pt; mso-bidi-font-family:"Times New Roman";color:red'><span style='mso-spacerun:yes'> </span></span></b><span class=style91><span lang=EN-US style='font-size:14.0pt'><a href="skeleton-paperfinal.pdf"><span style='font-weight:normal'>Skeleton Extraction by Mesh Contraction</span></a></span></span><span lang=EN-US style='font-size:14.0pt;font-family:Arial'><o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:4;height:24.75pt'> <td width=110 style='width:82.6pt;background:#CEE3F2;padding:.75pt .75pt .75pt .75pt; height:24.75pt'> <p class=MsoNormal align=right style='text-align:right;word-break:break-all'><b><span lang=EN-US style='font-family:Arial'>Talk Slide<o:p></o:p></span></b></p> </td> <td width=862 style='width:646.4pt;padding:.75pt .75pt .75pt .75pt; height:24.75pt'> <p class=MsoNormal align=center style='margin-bottom:12.0pt;text-align:center'><b style='mso-bidi-font-weight:normal'><span lang=EN-US style='font-size:14.0pt; mso-bidi-font-family:"Times New Roman"'><a href="skeleton-talk.zip">Our SIGGRAPH Talk Slides</a><o:p></o:p></span></b></p> </td> </tr> <tr style='mso-yfti-irow:5;height:24.75pt'> <td width=110 style='width:82.6pt;background:#CEE3F2;padding:.75pt .75pt .75pt .75pt; height:24.75pt'> <p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US style='font-family:Arial'>Video<o:p></o:p></span></b></p> </td> <td width=862 style='width:646.4pt;padding:.75pt .75pt .75pt .75pt; height:24.75pt'> <p><span class=style111><span lang=EN-US style='font-size:14.0pt;mso-bidi-font-family: "Times New Roman"'><a href="skeleton_extraction.mp4"><span style='font-weight: normal'>&nbsp;Skeleton Extraction (~46MB)</span></a></span></span><span class=style111><span lang=EN-US style='font-size:14.0pt;color:black'><o:p></o:p></span></span></p> </td> </tr> <tr style='mso-yfti-irow:6;height:24.75pt'> <td width=110 style='width:82.6pt;background:#CEE3F2;padding:.75pt .75pt .75pt .75pt; height:24.75pt'> <p class=MsoNormal align=right style='text-align:right'><span class=msonormalstyle3><b><span lang=EN-US>Demo Program </span></b></span><span lang=EN-US style='mso-bidi-font-family:"Times New Roman"'><o:p></o:p></span></p> </td> <td width=862 style='width:646.4pt;padding:.75pt .75pt .75pt .75pt; height:24.75pt'> <p class=MsoNormal><span class=style41><span lang=EN-US style='font-size: 14.0pt'><a href="skeleton-demo.zip">zipped executable code with models </a></span></span><span lang=EN-US style='font-size:14.0pt;mso-bidi-font-family:"Times New Roman"'><o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:7;height:147.75pt'> <td width=110 style='width:82.6pt;background:#CEE3F2;padding:.75pt .75pt .75pt .75pt; height:147.75pt'> <p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US style='font-family:Arial'>Examples<o:p></o:p></span></b></p> </td> <td width=862 style='width:646.4pt;padding:.75pt .75pt .75pt .75pt; height:147.75pt'> <p class=MsoNormal align=center style='text-align:center'><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-family:"Times New Roman"'><!--[if gte vml 1]><v:shape id="_x0000_i1026" type="#_x0000_t75" style='width:885pt;height:444pt'> <v:imagedata src="index.files/image003.emz" o:title=""/> </v:shape><![endif]--><![if !vml]><img border=0 width=1180 height=592 src="index.files/image004.gif" v:shapes="_x0000_i1026"><![endif]><o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:8;mso-yfti-lastrow:yes;height:133.3pt'> <td width=110 style='width:82.6pt;background:#CEE3F2;padding:.75pt .75pt .75pt .75pt; height:133.3pt'> <p class=MsoNormal align=right style='text-align:right'><span class=SpellE><b><span lang=EN-US style='font-family:Arial'>BibTeX</span></b></span><b><span lang=EN-US style='font-family:Arial'><o:p></o:p></span></b></p> </td> <td width=862 style='width:646.4pt;padding:.75pt .75pt .75pt .75pt; height:133.3pt'> <p class=MsoNormal><span lang=EN-US style='font-size:14.0pt;mso-bidi-font-family: "Times New Roman"'>@ARTICLE{Au:2008,<br> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;author = {Oscar Kin-Chung Au and <span class=SpellE>Chiew-Lan</span> Tai and Hung-<span class=SpellE>Kuo</span> <span class=SpellE>Chu</span> and Daniel Cohen-Or and Tong-Yee Lee},<br> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;title = { Skeleton Extraction by Mesh Contraction },<br> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;journal = {ACM Transactions on Graphics},<br> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;year = {2008},<o:p></o:p></span></p> <p class=MsoNormal style='text-indent:21.0pt;mso-char-indent-count:1.5'><span lang=EN-US style='font-size:14.0pt;mso-bidi-font-family:"Times New Roman"'>volume = {27},<o:p></o:p></span></p> <p class=MsoNormal style='text-indent:21.0pt;mso-char-indent-count:1.5'><span lang=EN-US style='font-size:14.0pt;mso-bidi-font-family:"Times New Roman"'>number = {3},<br> }</span><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-family:"Times New Roman"'><o:p></o:p></span></p> </td> </tr> </table> </div> <p class=style1 align=center style='text-align:center'><span lang=EN-US style='font-family:Arial'><o:p>&nbsp;</o:p></span></p> </div> </body> </html>