Network Flow - based optimization in renowned paper appears to have a wrong step

This is probably going to be an easy question for most people and embarass me. I've been reading the Zhang et al. 08 paper on detection-based tracking through network flows: http://iris.usc.edu/outlines/papers/2008/zhang-li-nevatia-cvpr08.pdf. In this paper, equation (11), the authors seem to go from: $-\log(1-\beta_i)\cdot f_i - \log\beta_i \cdot (1-f_i)$ to $C_i \cdot f_i$ where $C_i = \log\frac{\beta_i}{1-\beta_i}$. I've been going over this for about an hour now, shifting logarithms and exponents around but the derivation doesn't seem possible.

What am I missing here?

• You haven't written any equations here. Could you rewrite this in the form of an equation? – Bill Barth Jul 25 '13 at 2:33
• The original paper doesn't assert that these expressions are equal, but rather that the arg min of a sum of these expressions is equal. It appears to me that they differ by a constant, which won't affect the arg min. – Brian Borchers Jul 25 '13 at 12:55