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When Discrete Meets Differential: Assessing The Stability Of Structure From Small Motion, Wen-Yan Lin, Geok-Choo Tan, Loong-Fah Cheong

Research Collection School Of Computing and Information Systems

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 …