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The equation $z=a x + b y$ defines a plane passing through the origin of coordinates $(x,y,z)$. If the plane is horizontal, i.e., perpendicular to the $z$ axis, the range of $z$ values is just $[0,0]$. That corresponds to $a=b=0$. For all other $a,b$ the plane is tilted with respect to the horizontal plane, and the range of $z$ values for points on the plane ...

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I cannot help but suspect that the working function you've provided is less efficient than it can be, but I must also admit that I have only dabbled in computer vision myself. Here's a suggestion for how it might be improved. As you've mentioned, the fundamental matrix $F$ is defined as the matrix that satisfies $x_{1}^{T} F x_{2} = 0$ for all points $x_{1}$ ...

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This is not what you asked for, but I'll point out the low hanging fruit in your implementation anyway. You have many for loops, which will be extremely slow in Python and can be easily sped up with minimal effort using Cython. In my experience the many vstacks will also be slow, since iirc numpy allocates a new contiguous array when concatenating. It would ...

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