$\varepsilon$         [Small scalar, typically 0.0001 ]{}
     $N_o$                 [Try values 3 to 6 ]{}
     $O$                   [A filter spacing of $30^{\circ}$ has found good. ]{}

\[table:par\]

As discussed in [@Kovesi1996], the calculation of PC makes sense only in locations where the spread of frequencies is significant. In 2D-MSPC formulation, $W_o(x)$ is a weighting function, which penalizes the information at locations where the spread of frequencies is narrow at the $o-$th orientation. It is defined by a sigmoid function $$\begin{aligned}
W_o(x)=\frac{1}{1+\exp \left(g_o(c_o-s_o(x))\right)}\end{aligned}$$ where, $c_o$ denotes the cutoff (mid-point) point of the sigmoid function; $g_o$ is a gain that controls the rate of weighting; $s_o$ is a measure of frequency spread, which ranges between 0 and 1, and is given by $$\begin{aligned}
s_o(x)=\frac{1}{N_o}\frac{\textstyle \sum_{n}A_{no}(x)}{A_{\max}(x)+\varepsilon}.\end{aligned}$$ where, $\textstyle \sum_{n}A_{no}(x)$ is computed through and $A_{\max}(x)$ is the amplitude of the filter pair having maximum response at $x$.

The parameter $T_o$ is an estimation of noise power that is subtracted from the energy of the signal. It is computed based on the assumptions that the image noise is additive, that the noise power spectrum is constant, and that the image features occur at isolated locations: $$\begin{aligned}
T_o=\mu_{Ro}+k_o \sigma_{Ro}\end{aligned}$$ where, $\mu_{Ro}$ and $\sigma_{Ro}^2$ are the mean and variance of 