User:Moderately Sized Greg/sandbox: Difference between revisions

Revision as of 23:30, 27 December 2024

Revision as of 04:49, 30 December 2024

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The simplest parametric model is the [[Lucas-Kanade method]]. This uses rectangular regions and parameterises the motion as purely translational. The Lucas-Kanade method uses the original brightness constancy constrain as the data cost term and selects <math>g(x, y) = 1</math>.

This yields the local loss function,

This yields the local loss function, <ref>{{cite conference |last=Lucas |first=Bruce D. |last2=Kanade |first2=Takeo |date=1981-08-24 |title=An iterative image registration technique with an application to stereo vision |url=https://dl.acm.org/doi/10.5555/1623264.1623280 |journal=Proceedings of the 7th International Joint Conference on Artificial intelligence - Volume 2 |series=IJCAI'81 |___location=San Francisco, CA, USA |publisher=Morgan Kaufmann Publishers Inc. |pages=674–679}}</ref>

:<math>

\hat{\boldsymbol{\alpha}} = \arg \min_{\boldsymbol{\alpha}} \sum_{(x, y) \in \mathcal{R}} [| I(x + u_{\boldsymbol{\alpha}}, y + v_{\boldsymbol{\alpha}}, t + 1) - I(x, y, t)]^2| .

</math>

ThisOther yields thepossible local loss function,functions include the negative normalized [[cross-correlation]] between the two frames. <ref>{{cite conference |last=Lucas |first=Bruce D. |last2=Kanade |first2=Takeo |date=1981-08-24 |title=An iterative image registration technique with an application to stereo vision |url=https://dl.acm.org/doi/10.5555/1623264.1623280 |journal=Proceedings of the 7th International Joint Conference on Artificial intelligence - Volume 2 |series=IJCAI'81 |___location=San Francisco, CA, USA |publisher=Morgan Kaufmann Publishers Inc. |pages=674–679}}</ref>

===Learning Based Models===