  Mukherjee (Pattern Recognition Letters, vol. 32, pp. 824-831, 2011) recently
introduced a class of distance functions called weighted t-cost distances that
generalize m-neighbor, octagonal, and t-cost distances. He proved that weighted
t-cost distances form a family of metrics and derived an approximation for the
Euclidean norm in $\mathbb{Z}^n$. In this note we compare this approximation to
two previously proposed Euclidean norm approximations and demonstrate that the
empirical average errors given by Mukherjee are significantly optimistic in
$\mathbb{R}^n$. We also propose a simple normalization scheme that improves the
accuracy of his approximation substantially with respect to both average and
maximum relative errors.
