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If you have 8 perfect tracked points from two images and avoided the degenerate cases why is the essential matrix still wrong some times (or not good enough). Is this a numerical problem?

For any hint I grateful.

EDIT

This is my virtual scene. The marked points are used to calculate E and to check E as well.

Both views of the camera are merged in the image on the right. rel rotation around Y= -15° and rel translationVec set to [64, 114, 0]

enter image description here

user3077796
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    what does "perfect tracked" mean? subpixel accuracy up to which decimal place? are you using a perfect pinhole camera or is there a lens distortion in your images? – Micka Jan 21 '16 at 19:32
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    I calculated the 2D images from a virtual 3D scene. Therefore I know already where every point sits perfectly (floating points). – user3077796 Jan 22 '16 at 09:05
  • so you don't have/need images at all, since you projected the points via mathematical projection? Can you provide your scene geometry and "camera" setting? Are there any constraints about the 8 points, like non-coplanarity etc? – Micka Jan 22 '16 at 09:09
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    Yes I don't need the picture in this case. I provided my scene and the data in the EDIT – user3077796 Jan 22 '16 at 10:38
  • Do you know whether the essential matrix computation is working if 4 or more points are coplanar (in your example the four points at the green side are coplanar)? Unfortunately I don't have any own experience with fundamental-/essential matrices, but maybe someone else can help you with this additional information. – Micka Jan 22 '16 at 10:45
  • I know this much. For many different setups it works perfectly. That means different rotation and translation. For example for the setup Ry = -15° and t = [64 140 0]. I know about the degenerated cases but i thought this could be the problem because it works with so many different setups – user3077796 Jan 22 '16 at 10:49
  • is it possible for you to easily move the 4th coplanar point to somewhere else? For example to an additional smaller quad - if possible not centric? (previous suggestion to move to the blue/yellow intersection is still coplanar) – Micka Jan 22 '16 at 11:33
  • I changed the points. Only 3 Points lie on a plane now. I'm not sure if that is what you wanted. But still the problem remains – user3077796 Jan 22 '16 at 12:03

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