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<h2>Open Problems in Digital Geometry an Topology</h2>
<p>
This list of open problems was first initiated during the winter school
<a href="http://citr.auckland.ac.nz/~rklette/Announcements/DIG2000.html">DIG'2000</a> at Dagstuhl/Germany.
New problems were introduced during an open problems session oragnized during DGCI 2016.
If you want to add new problems, feel free to send a pdf or simple html file
</p>
<p>
Responses or partial new results to the published problems are inserted into the table, next to the related problem. A response should also be in pdf format
(about 2 pages) and may include links to further material.
</p>
<center>
<table width="95%" border="0" cellspacing="1" cellpadding="3">
<tbody><tr align="left"> <th class="header"> Date </th> <th class="header"> Problem/Response </th> <th class="header"> (First) Author </th> <th class="header"> Links </th> </tr>
<tr>
<td class="odd">9, May 2001</td>
<td class="odd">1 <a class="list" href="openProblems/SurfaceArea.pdf">Surface Area Estimation</a></td>
<td class="odd"><a class="list" href="mailto:r.klette@auckland.ac.nz">Reinhard Klette</a></td>
<td class="odd"> <a class="list" href="http://www.citr.auckland.ac.nz/techreports/show.php?id=87">CITR-TR-87</a></td>
</tr>
<tr>
<td class="odd">11, September 2001</td>
<td class="odd">1.1 <a class="list" href="openProblems/Coeurjolly.pdf">Estimation algorithm and multigrid convergence proof</a></td>
<td class="odd"><a class="list" href="mailto:dcoeurjo@eric.univ-lyon2.fr">David Coeurjolly</a></td>
<td class="odd"><a class="list" href="openProblems/Coeurjolly_Tetaud.pdf">Technical Report</a> </td>
</tr>
<tr> <td class="even">10, May 2001</td>
<td class="even">2 <a class="list" href="openProblems/CurveLength.pdf">Superlinear Convergence for Length Estimation</a></td>
<td class="even"><a class="list" href="mailto:r.klette@auckland.ac.nz">Reinhard Klette</a></td>
<td class="even"><a class="list" href="http://www.citr.auckland.ac.nz/techreports/show.php?id=87">Citr-TR-87</a></td>
</tr>
<tr>
<td class="odd">22, June 2001</td>
<td class="odd">3 <a class="list" href="openProblems/GoodPairs.pdf">Axiomatic 3-D Digital Topology</a></td>
<td class="odd"><a class="list" href="mailto:ykong@euler.cs.qc.edu">T. Yung Kong</a></td>
<td class="odd"> </td>
</tr>
<tr>
<td class="even">21, August 2001</td>
<td class="even">4 <a class="list" href="openProblems/DigTopologies.pdf">Binary Codes for Counting Digital Topologies</a></td>
<td class="even"><a class="list" href="mailto:imiya@media.imit.chiba-u.ac.jp">Atsushi Imiya</a></td>
<td class="even"></td>
</tr>
<tr>
<td class="odd">11, September 2001</td>
<td class="odd">5 <a class="list" href="openProblems/NumberDSSs.pdf">Minimal-Number DSS and DPS Segmentations</a></td>
<td class="odd">Azriel Rosenfeld</td>
<td class="odd"> <a class="list" href="http://www.citr.auckland.ac.nz/techreports/show.php?id=93">CITR-TR-93</a></td>
</tr>
<tr>
<td class="odd">27, January 2005</td>
<td class="odd">5.1 <a class="list" href="openProblems/RRFeschetTougne.pdf">On the min DSS problem of closed discrete curves</a></td>
<td class="odd"><a class="list" href="mailto:feschet@llaic3.u-clermont1.fr">Fabien Feschet</a></td>
<td class="odd"></td>
</tr>
<tr>
<td class="odd">4, May 2009</td>
<td class="odd">5.2 <a class="list" href="openProblems/DC_2009.pdf">Minimum decomposition of a digital surface into digital plane segments is NP-hard</a></td>
<td class="odd"><a class="list" href="mailto:david.coeurjolly@liris.cnrs.fr">Isabelle Sivignon</a></td>
<td class="odd"></td>
</tr>
<tr>
<td class="even">16, April 2002</td>
<td class="even">6 <a class="list" href="openProblems/CurveLength3D.pdf">MLP Linear-time 3D Length Estimation</a></td>
<td class="even"><a class="list" href="mailto:thomasbl@cs.berkeley.edu">Thomas Buelow</a></td>
<td class="even"><a class="list" href="http://www.citr.auckland.ac.nz/techreports/1999/CITR-TR-55.html">CITR-TR-55</a></td>
</tr>
<tr>
<td class="odd">17, February 2003</td>
<td class="odd">7 <a class="list" href="openProblems/Brimkov_OpenProblem.pdf">Connectivity Number</a></td>
<td class="odd"><a class="list" href="mailto:brimkov@cs.fredonia.edu">Valentin Brimkov</a></td>
<td class="odd"> <a class="list" href="http://www.citr.auckland.ac.nz/techreports/show.php?id=125">CITR-TR-125</a></td>
</tr>
<tr>
<td class="even">23, April 2004</td>
<td class="even">8 <a class="list" href="openProblems/Dagstuhl_2004.pdf">List collected on a 2004 Dagstuhl seminar</a></td>
<td class="even"><a class="list" href="mailto:r.klette@auckland.ac.nz">Reinhard Klette</a></td>
<td class="even"></td>
</tr>
<tr>
<td class="even">01, November 2004</td>
<td class="even">8.1 <a class="list" href="openProblems/08_q14.pdf">Vertices of the digital line/(hyper)plane segment polytope</a></td>
<td class="even"><a class="list" href="mailto:valentin_brimkov@yahoo.com">Valentin E. Brimkov</a></td>
<td class="even"></td>
</tr>
<tr>
<td class="odd">01, November 2004</td>
<td class="odd">9 <a class="list" href="openProblems/BrimkovSegmentation.pdf">Convex digital curve segmentation</a></td>
<td class="odd"><a class="list" href="mailto:valentin_brimkov@yahoo.com">Valentin E. Brimkov</a></td>
<td class="odd"></td>
</tr>
<tr>
<td class="even">13, December 2004</td>
<td class="even">10 <a class="list" href="openProblems/convex_skull.pdf">The convex skull problem</a></td>
<td class="even"><a class="list" href="mailto:Jean-marc.Chassery@lis.inpg.fr">Jean-Marc Chassery</a></td>
<td class="even"></td>
</tr>
<tr>
<td class="even">4, May 2016</td>
<td class="even">10.1 <a class="list" href="openProblems/BorgeforsConvexSkull.php">A good approximation of the convex skull (updated but still open)</a></td>
<td class="even"><a class="list" href="mailto:gunilla.borgefors@it.uu.se">Gunilla Borgefors</a></td>
<td class="even"></td>
</tr>
<tr>
<td class="odd">15, January 2005</td>
<td class="odd">11 <a class="list" href="openProblems/NAKAM_animal.pdf">Animal and B-Problems</a></td>
<td class="odd">Akira Nakamura</td>
<td class="odd"></td>
</tr>
<tr>
<td class="even">17, September 2007</td>
<td class="even">12 <a class="list" href="openProblems/Nahum07.pdf">Surface Area Estimation with Non-Cubic Voxels</a></td>
<td class="even"><a class="list" href="mailto:nk@eng.tau.ac.il">Nahum Kiryati</a></td>
<td class="even"></td>
</tr>
<tr>
<td class="odd">19, April 2016</td>
<td class="odd">13 <a class="list" href="openProblems/LachaudCountCells.pdf">Counting the number of k-dimensional grid cells of Zd that intersect a polytope</a></td>
<td class="odd"><a class="list" href="mailto:jacques-olivier.lachaud@univ-savoie.fr">J.-O. Lachaud</a></td>
<td class="odd"></td>
</tr>
<tr>
<td class="even">19, April 2016</td>
<td class="even">14 <a class="list" href="https://matheuscmss.wordpress.com/2013/01/27/nivats-conjecture-after-cyr-kra/">Nivat-Vuillon Conjecture</a></td>
<td class="even"><a class="list" href="mailto:yan.gerard@udamail.fr">Yan Gérard</a></td>
<td class="even"></td>
</tr>
<tr>
<td class="odd">19, April 2016</td>
<td class="odd">15 <a class="list" href="openProblems/SivignonLonelyRunner.pdf">Lonely runner and view obstruction</a></td>
<td class="odd"><a class="list" href="mailto:isabelle.sivignon@gipsa-lab.grenoble-inp.fr">I. Sivignon</a></td>
<td class="odd"></td>
</tr>
<tr>
<td class="even">13, May 2016</td>
<td class="even">16 <a class="list" href="openProblems/SivignonDSSLowerBounds.pdf">Complexity lower bounds for DSS problems</a></td>
<td class="even"><a class="list" href="mailto:isabelle.sivignon@gipsa-lab.grenoble-inp.fr">I. Sivignon</a></td>
<td class="even"></td>
</tr>
<tr>
<td class="odd">19, April 2016</td>
<td class="odd">17 <a class="list" href="openProblems/">Thickness diagram: complexity of the arrangement of balls of a digital set medial axis</a></td>
<td class="odd"><a class="list" href="mailto:david.coeurjolly@liris.cnrs.fr">D. Coeurjolly</a></td>
<td class="odd"></td>
</tr>
<tr>
<td class="even">19, April 2016</td>
<td class="even">18 <a class="list" href="openProblems/">Number of cuts of a hypervoxel by a hyperplane</a></td>
<td class="even"><a class="list" href="mailto:eric.andres@univ-poitiers.fr">E. Andres</a></td>
<td class="even"></td>
</tr>
<tr>
<td class="odd">19, April 2016</td>
<td class="odd">19 <a class="list" href="http://www.tc18.org/openProblems/LachaudCountCells.pdf">3D Digital Straight Segment embedded in a given Digital Plane</a></td>
<td class="odd"><a class="list" href="mailto:jacques-olivier.lachaud@univ-savoie.fr">J.-O. Lachaud</a></td>
<td class="odd"></td>
</tr>
<tr>
<td class="even">20, September 2017</td>
<td class="even">20 Analytical characterization of the 3D bijective digitized rotations</td>
<td class="even"><a class="list" href="mailto:kacper.pluta@esiee.fr">Kacper Pluta</a></td>
<td class="even"><a class="list" href="https://perso.esiee.fr/~plutak/projects/2017-06-06-3d-bij">link</a></td>
</tr>
<tr>
<td class="odd">20, September 2017</td>
<td class="odd">21 <a class="list" href="http://www.tc18.org/openProblems/OpenProblem1_Andres.pdf">New digital plane thickness with unknown properties</a></td>
<td class="odd"><a class="list" href="mailto:eric.andres@univ-poitiers.fr">Eric Andres</a></td>
<td class="odd"></td>
</tr>
<tr>
<td class="odd">20, September 2017</td>
<td class="odd">22 <a class="list" href="http://www.tc18.org/openProblems/OpenProblem2_Andres.pdf">Does an unfolding of Menger1 pave space?</a></td>
<td class="odd"><a class="list" href="mailto:eric.andres@univ-poitiers.fr">Eric Andres</a></td>
<td class="odd"></td>
</tr>
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