I've had a lot of these problems where everything is correct but nothing works as intended. Turns out, numerical mathematics excels at making programming more about validation than verification.
Breaking the continuum into pieces breaks your symmetries. For example on a finite rectangular grid, a sphere is not rotationally invariant. Even if your maths is valid in the continuum, for the implementation, you still need to prove that it is valid (i.e. fulfills all desired properties) on a discrete grid.
I have zero experience with video compression, however, the author states that the issues get less severe when the video is rotated by 90˚. I guess the compression algorithm is designed to work irrespective of orientation. Therefore, my humble guess is that they failed to implement the desired symmetry of the continuum in the compression algorithm that acts upon discrete spatial coordinates. Unfortunately, there's no way to recover all symmetries from the continuum on a discrete grid. You always get some kind of artifacts and you can only work to reduce them for the case you are considering.
Breaking the continuum into pieces breaks your symmetries. For example on a finite rectangular grid, a sphere is not rotationally invariant. Even if your maths is valid in the continuum, for the implementation, you still need to prove that it is valid (i.e. fulfills all desired properties) on a discrete grid.
I have zero experience with video compression, however, the author states that the issues get less severe when the video is rotated by 90˚. I guess the compression algorithm is designed to work irrespective of orientation. Therefore, my humble guess is that they failed to implement the desired symmetry of the continuum in the compression algorithm that acts upon discrete spatial coordinates. Unfortunately, there's no way to recover all symmetries from the continuum on a discrete grid. You always get some kind of artifacts and you can only work to reduce them for the case you are considering.