Avoiding weird homography values when normalizing

Question

People familiar with Homographies will know that you have to normalize it dividing by any of the matrix components in order to keep homogeneous coordinates. An homography is a 3x3 matrix and it is usually normalized dividing by the element at (3,3).

The problem comes when that value is very small (for example 0.0000008) and divides a value that is supossed to be zero (0.0000007). The resulting value is almost 0.875 when it was supossed to be zero and the resulting projection has no sense.

I would like to know which is the common way to solve this. I use C++ and floating point arithmetic.

To expand on my facile comment, if you've already computed values that are of similar magnitude to the normalization value, then it's probably already too late. — Oliver Charlesworth, Jun 07 '12 at 16:08
The last column is a position vector (x,y,z). The problem comes when z is close to cero. I am avoiding that case as much as possible. But I doubt I am the first having this problem, so there should be a way to choose the normalization elment, I mean, a common way, the good way to proceed. — Jav_Rock, Jun 07 '12 at 16:49

score 3 · Accepted Answer · edited Jun 13 '12 at 08:13

3

So, if i understand the question:

0/0.000000001 = 0   = CORRECT

and:

0.000000001/0.000000001 ~ 1    INCORRECT

I will define a function to check the error, with a parameter sigma.

If value < sigma = 0.001, assume its zero, and return 0, else, return value.

So, it will work always with value over the sigma error, and 0 if not.

edited Jun 13 '12 at 08:13

Bojangles

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answered Jun 13 '12 at 08:06

vgonisanz

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Avoiding weird homography values when normalizing

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