Question about derivation of disparity vertical case

[Jarrome]

Hi authors,

Excellent work. I find your paper useful and read carefully.

However, I find there's some confusing derivation in paper. Maybe I'm wrong. (I'm only interested in the vertical case)

Q1. In eq.2, the partial derivative of theta on y, the sin should be on the denominator instead of numerator. Maybe I miss something? A typo?

Q2. For the disparity vertical case, I find it make a different derivation comparing to the Law of sine. Shouldn't it follow the Law of sine? since the disparity is the difference of latitude.

[zuru]

Hi Jarrome,

sorry for the late reply, just found some time to be able to provide a useful answer.

Regarding Q1, in Spherical_Vertical_Disparity.pdf provides the full derivation for you to verify. The only difference is the use of z as the vertical axis (as the online figure I quickly found online was this way).

Regarding Q2, a quick formulation using the law of sines can be found in the Law_of_Sines.pdf, which results into the Equation (1) of 360SD-Net: 360° Stereo Depth Estimation with Learnable Cost Volume. Perhaps the ambiguity comes from considering a different radius? (i.e. the top, not bottom)

Let me know if this was helpful and suffices or please continue the discussion otherwise.

[Jarrome]

Thank you, zuru, for the detailed reply.
I really appreciate it.

Actually, in Spherical View Synthesis for Self-Supervised 360o Depth Estimation, the vertical disparity formula

I find it fancy but I personally cannot relate it to the Law of sines.
In addition, I find lines of code using the formula but have no idea why the disparity looks like this.

The work is nice, I just want to better understand it.