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daniyar-niantic avatar daniyar-niantic commented on September 7, 2024 2

@aj96 I think you are more-or-less on the right track with the reprojection equation. You just need to take it a step further and look at the projection of 3D point into the 2D view and look at the pixel coordinates of relatively static pixels.

Another way to look at this is with an extreme situation, where ego car is following another car that is moving at the same speed as ego car. Let's assume there is no rotation for now, i.e. rotation matrix is identity. If you consider a point on a car that is moving with the ego car, then that point will have exactly the same pixel coordinate in both view. So, if you were to rectify these two views using ground truth poses, then the relatively static pixel will have 0 disparity. Finally, 0 disparity is equivalent to infinite depth.

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larsme avatar larsme commented on September 7, 2024

From what I understand, infinite depth only makes sense if there is no rotation.
The matrix product becomes an identity matrix,
the translation is negligible because its so much smaller
1/z gets applied because of homogeneaus coordinates
and you get p'=p.

If there is a (small) rotation, i assume infinity might still be a possible solution for low texture regions.

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aj96 avatar aj96 commented on September 7, 2024

But for translation to be small and for rotation matrix to be identity matrix that would mean that all the pixels didn't move. That doesn't explain the case for one of relatively static pixels like a car that moves with the ego-car.

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larsme avatar larsme commented on September 7, 2024

Its not that translation is small, just smaller than the "competing" term scaled by near infinite depth

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