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I was reading the following paper on how you can incorporate variable time offset for a camera in VIO:

https://openaccess.thecvf.com/content_ECCV_2018/papers/Yonggen_Ling_Modeling_Varying_Camera-IMU_ECCV_2018_paper.pdf

As far as I understand the paper is optimizing camera-image time offset and not IMU time offset.

What I am confused on is how the jacobian of the image residual is computed with respect to time.

I'm clearly missing something as normally the image jacobian should be time-independent(IE SFM does not consider time as a variable as there isn't a motion model associated with it).

So what's going on? I guess I don't understand what they are doing.

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