Homotopy Continuation Resource Central
+Homotopy Continuation Resource Center
--This website is work in progress. -
- +Welcome to the HC Resource Center - HCRC, a selection of resources on efficient +solving of challenging systems of polynomial equations using the numerical technique of Homotopy Continuation.About
- Welcome to the HC Central, ia a list of resources for solving systems of - polynomial - equations using the numerical technique of Homotopy Continuation. This list is - hand-curated by us - an active team of researchers in - computational algebraic geometry with an experience in hard problems arising + This selection is + hand-curated by us -- an active team of researchers in + computational algebraic geometry with experience in hard problems arising from computer vision applications such as Augmented Reality and autonomous - cars. Any application can benefit from this information. - + cars. Many other compute-bound applications can benefit from this information. +
+It is not our intent to produce a comprehensive list of resources, but, rather - an opinionated selection that we personally recommend looking at. Our emphasis + an opinionated selection that we personally recommend looking at (including our own work). Our emphasis is on achieving real-time speed for online AR applications, rather than extreme precision, certification or robustness. All references are directly or indirectly aimed towards tackling the real-time scenario. @@ -67,40 +64,63 @@
About
Authors
- Benjamin Kimia: professor at Brown University -
- Timothy Duff: -
- Ricardo Fabbri: -
- Hongyi Fan: +
- Timothy Duff: professor at University of Misouri +
- Ricardo Fabbri: professor at IPRJ/UERJ, Rio de Janeiro State University +
- Hongyi Fan: Cognex corporation
- new! Code for 3D Curve Sketch now available! new!
- new! CVPR 2017 paper "The Surfacing of Multiview 3D Drawings via Lofting.." accepted! new!
- new! Analytic Multiview Curve Dataset now available! new!
- new! ArXiv preprint "Trifocal Relative Pose from Lines at Points and its Efficient Solution" new!
+Our collaboration began in 2018 at ICERM/Brown Univesity when we designed and optimized the first solver for the problem of reconstructing three images and the camera position from three oriented point correspondences, having algebraic degree of nonlinearity 312. The related paper is
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+Trifocal Relative Pose from Lines at Points, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2022, CVPR 2020 (online march 23 2019 4:29 UTC), Ricardo Fabbri, Timothy Duff, Hongyi Fan, Margaret Regan, David de Pinho (my former MSc. Student), Elias Tsigaridas, Charles Wampler, Jonathan Hauenstein, Peter Giblin, Benjamin Kimia, Anton Leykin and Tomas Pajdla (pdf |
+ code | datasets | bib)
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+ new! Line-point Macaulay2 tutorial in minus/tutorial/linepoint! new!
+ new! Metric Multiview Geometry -- A Catalogue in Low Dimensions by Duff and Rydel new!
Code
-Minus
+Minus C++ Fast Solver Framework
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- Source code is in the new VXD project we created - as part of the 3D Curve Drawing code release effort. The relevant code is in - the BMCSD (Brown Multiview Curve Sketch) library. We are preparing better - instructions, it is a fairly large multithreaded system, but we suggest you - start looking at bmcsd/cmd/mcs.cxx (multiview curve sketch command). Check out - the git log for news regarding this code base, or email us for news or - instructions. Only Linux or Mac OSX are supported. +
- A framework for square problems +
- Github +
- Highly optimized beyond Eigen +
- Fast CPU-oriented solver
Macaulay2 packagescoming soon!
+Macaulay2 packages coming soon!
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- MonodromySolver package +
GPU-based solvers
+ coming soon!Datasets
-This section lists datasets to evaluate HC. +This section lists datasets to evaluate HC. coming soon!
-HC for locating critical points of Dynamical Systems
+Books
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- , Numerically solving polynomial systems with BertiniNumerically solving polynomial systems with {B}ertini, +Bates, Hauenstein, Sommese, and Wampler (code) + +