Biomedical Imaging

Fig. 2.18: Two different definitions of contrast: Weber contrast $K_W=\frac{g_f-g_b}{g_b}$utilizes the typical brightness gf of small, isolated features in front of a rather uniform background gb, while Michelson contrast $K_{\text{M}}=\frac{g_{\max }-g_{\min }}{g_{\max }+g_{\min }}$considers the ratio of the maximum variation, divided by its mean.

is used instead if high and low signal strength make up similar fractions of the image. As was already noted above, for a cosine signal with constant background (Figure 2.15), this definition yields the amplitude of the signal variation divided by the mean value (Figure 2.18, right)

$g\left(x\right)=A+B\cos \left(2\pi x\right)\Rightarrow K_{\text{M}}=\frac{\left(A+B\right)-\left(A-B\right)}{\left(A+B\right)+\left(A-B\right)}=\frac{B}{A}.$