Help me please resolve some questions in the article

1) "A Robust Method for Computing Vehicle Ego-motion", Gideon P. Stein et al.

According to this paper we can find three components of motion (one translation and two rotational components) using model from the article:

2) "The interpretation of a moving retinal image" Longuet-Higgins (1980).

As for me, the equation (1) from the first paper doesn't correspond to the equation from the second. There are velocities in the second paper that seems to be more correct than in the first where measurement units are not matched with left and right sides.

The second question is how can we find the motion parameters (translation and two rotations)? In the 1) paper they suggest to minimize cost function using gradient descent. But how can we do this? The function doesn't depend directly on motion variables $t_z, w_x, w_y $.

And the last question: if we got two subsequent frames $ I_1 $ at time $t_1$ and $I_2$ at time $t_2$, in what point of time $t$ we must consider estimated motion parameters? I guess at $(t_1 + t_2) / 2 $, but I'm not sure.

Help me please with these questions.


1 Answer 1


The equation in your first reference comes from taking the time derivative of the pixel location of a feature. I suspect that the equations are different because the second paper is looking at features projected on to a sphere, not an image plain.

It looks like all the terms you are looking for are present in the equation being solved.


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