Figure 8

Bias as a function of structuring element size for normal and lognormal distributions. Mean pixel value versus n = cardinal(B) for γ _B δ_{3 × 3}-filtered (similar to morph.close.open) simulated images with independent and identically distributed pixels from various normal distributions N(0,σ); σ = (30, 50, 70) (top), and from various log-normal distributions (LN(m, 0.4) - $e^{(m+{0.4}^2/2)}$); m = 3,4,5 (bottom). As indicated by the dashed vertical line, the background estimates are unbiased only for one specific size of structuring element B. The estimates will be biased with different amounts depending on the distribution of background noise for all other choices of B.