When discrete meets differential: Assessing the stability of structure from small motion
We provide a theoretical proof showing that under a proportional noise model, the discrete eight point algorithm behaves similarly to the differential eight point algorithm when the motion is small. This implies that the discrete algorithm can handle arbitrarily small motion for a general scene, as...
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sg-smu-ink.sis_research-58592020-01-23T07:09:08Z When discrete meets differential: Assessing the stability of structure from small motion LIN, Wen-yan TAN, Geok-Choo CHEONG, Loong-Fah We provide a theoretical proof showing that under a proportional noise model, the discrete eight point algorithm behaves similarly to the differential eight point algorithm when the motion is small. This implies that the discrete algorithm can handle arbitrarily small motion for a general scene, as long as the noise decreases proportionally with the amount of image motion and the proportionality constant is small enough. This stability result extends to all normalized variants of the eight point algorithm. Using simulations, we show that given arbitrarily small motions and proportional noise regime, the normalized eight point algorithms outperform their differential counterparts by a large margin. Using real data, we show that in practical small motion problems involving optical flow, these discrete structure from motion (SFM) algorithms also provide better estimates than their differential counterparts, even when the motion magnitudes reach sub-pixel level. The better performance of these normalized discrete variants means that there is much to recommend them as differential SFM algorithms that are linear and normalized. 2010-01-01T08:00:00Z text application/pdf https://ink.library.smu.edu.sg/sis_research/4856 info:doi/10.1007/s11263-009-0260-y https://ink.library.smu.edu.sg/context/sis_research/article/5859/viewcontent/When_Discrete_Meets_Differential.pdf http://creativecommons.org/licenses/by-nc-nd/4.0/ Research Collection School Of Computing and Information Systems eng Institutional Knowledge at Singapore Management University Structure from motion;Perturbation analysis Computer and Systems Architecture |
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Structure from motion;Perturbation analysis Computer and Systems Architecture LIN, Wen-yan TAN, Geok-Choo CHEONG, Loong-Fah When discrete meets differential: Assessing the stability of structure from small motion |
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We provide a theoretical proof showing that under a proportional noise model, the discrete eight point algorithm behaves similarly to the differential eight point algorithm when the motion is small. This implies that the discrete algorithm can handle arbitrarily small motion for a general scene, as long as the noise decreases proportionally with the amount of image motion and the proportionality constant is small enough. This stability result extends to all normalized variants of the eight point algorithm. Using simulations, we show that given arbitrarily small motions and proportional noise regime, the normalized eight point algorithms outperform their differential counterparts by a large margin. Using real data, we show that in practical small motion problems involving optical flow, these discrete structure from motion (SFM) algorithms also provide better estimates than their differential counterparts, even when the motion magnitudes reach sub-pixel level. The better performance of these normalized discrete variants means that there is much to recommend them as differential SFM algorithms that are linear and normalized. |
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text |
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LIN, Wen-yan TAN, Geok-Choo CHEONG, Loong-Fah |
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LIN, Wen-yan TAN, Geok-Choo CHEONG, Loong-Fah |
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LIN, Wen-yan |
title |
When discrete meets differential: Assessing the stability of structure from small motion |
title_short |
When discrete meets differential: Assessing the stability of structure from small motion |
title_full |
When discrete meets differential: Assessing the stability of structure from small motion |
title_fullStr |
When discrete meets differential: Assessing the stability of structure from small motion |
title_full_unstemmed |
When discrete meets differential: Assessing the stability of structure from small motion |
title_sort |
when discrete meets differential: assessing the stability of structure from small motion |
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Institutional Knowledge at Singapore Management University |
publishDate |
2010 |
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https://ink.library.smu.edu.sg/sis_research/4856 https://ink.library.smu.edu.sg/context/sis_research/article/5859/viewcontent/When_Discrete_Meets_Differential.pdf |
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