Timeline for Reconstructing set of points from one-dimensional images
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
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| Aug 13, 2014 at 21:32 | history | edited | user45183 | CC BY-SA 3.0 |
edited title
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| May 9, 2014 at 10:23 | vote | accept | CommunityBot | ||
| May 8, 2014 at 12:18 | vote | accept | CommunityBot | ||
| May 8, 2014 at 12:42 | |||||
| Apr 16, 2014 at 17:28 | answer | added | Liviu Nicolaescu | timeline score: 2 | |
| Apr 16, 2014 at 16:07 | comment | added | Aaron Meyerowitz | You might first consider the case that all the matrices are row vectors. Since the $M_j$ are known to us,we know the set of scalar values $r_{jk}x_i$ where $r_{jk}$ is row $k$ of $M_j$. | |
| Apr 16, 2014 at 11:58 | comment | added | Joseph O'Rourke | For points in $\mathbb{R}^3$, a version of the problem is called "shape from shadows," and is heavily studied. E.g., "The Episolar Constraint: Monocular Shape from Shadow Correspondence" PDF download link | |
| Apr 16, 2014 at 10:58 | comment | added | Camilo Sarmiento | Your question is addressed (for the complex case) in the paper arxiv.org/abs/1312.0158 by Conca, Edidin, Hering and Vinzant, and in the references it cites. Another keyword is "multiview- or epipolar geometry" | |
| Apr 16, 2014 at 10:52 | vote | accept | CommunityBot | ||
| Apr 16, 2014 at 10:52 | |||||
| Apr 16, 2014 at 10:45 | answer | added | Tommi | timeline score: 0 | |
| Apr 16, 2014 at 10:24 | comment | added | user45183 | Hello Tommi Brander: concerning your first question: for a fixed $j$, given a point $y$, you dont know whether it is generated by $M_j x_1$ or $M_j x_{100}$ If you had this orderning, then you could trivially solve the problem for each point $x_i$ separately. Hence the nessecary condition of trivial intersection of kernels. Concerning your second question: J is not apriori known and is part of the question. What I am looking for are conditions on $J$ and the set of projection matrices, such that the reconstruction is unique. | |
| Apr 16, 2014 at 10:01 | comment | added | Tommi | Some more questions: Is J known a priori? Can you select the matrices $M_j$ or are they arbitrary? | |
| S Apr 16, 2014 at 9:37 | history | suggested | Tommi | CC BY-SA 3.0 |
spelling and grammar
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| Apr 16, 2014 at 9:32 | review | Suggested edits | |||
| S Apr 16, 2014 at 9:37 | |||||
| Apr 16, 2014 at 9:22 | comment | added | Tommi | You write that the data includes no knowledge of ordering. What do you mean by this? Does it mean that we do not know if some y in the data is given as $y =M_1 x_4$ or $y=M_2 x_1$, for example? | |
| Apr 16, 2014 at 8:24 | history | asked | user45183 | CC BY-SA 3.0 |