Incorrect Equations in “Review and Analysis of Solutions of the Three Point Perspective Pose Estimation Problem”

In the 1994 paper “Review and Analysis of Solutions of the Three Point Perspective Pose Estimation Problem” by R. M. Haralick, C-N Lee, K. Ottenberg, and M. Nolle, I found a couple of important typos in the equations for the Finsterwalder solution.  This paper describes several solutions to the Perspective Three Point (P3P) problem, two of those solutions I ended up implementing.  The Grunert solution is correct and easy to implement, while the Finsterwalder solution is a little bit more involved.  However since the equations are incorrect for Finsterwalder you could be in for a bit of frustration.

I could not find an e-mail address on the first author’s website.  The paper is also a bit old (but still relevant) and the problem was most likely already reported.  If I’m the first person to notice or try to report the problem after 18 years then it’s a non issue.  However, to help others out there (the one or two which have found this website) here are the corrections:

After it has been corrected, the first line in equation (16) should be:

(b^2 - m^2c^2)u^2 + 2(c^2(cos\beta -n)m - b^2cos\gamma)u

Note that a power of 2 has been added to ‘m’. The equations on the top of the right column of page 337 also needs to be correct and should be:

A = b^2 - m^2c^2
B = c^2(cos\beta -n)m -b^2cos\gamma
C = -c^2 n^2 + 2c^2 n cos\beta + b^2 - c^2

Here a power of two was added to ‘m’ in the first line and ‘c’ in the third line.  Hopefully this post will save someone a few hours of aggravation and deriving equations.

 

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