o} \times \eta_o^{(n-1)}}$$ where, $\lambda_{\min o}$ is the minimum wavelength (maximum centre frequency) of wavelets in banks of $\{M_{1o}^e, \ldots, M_{No}^e\}$ and $\{M_{1o}^o, \ldots, M_{No}^o\}$, and $\eta_o$ represents the distance between successive filters in the bank. It is noted that $M_{no}^e$ and $M_{no}^o$ are identical with a $90^{\circ}$ shift. Figure \[fig:gf\] shows the spectra of 4-scale logarithmic Gabor wavelets at the $o-$th orientation with $\lambda_{\min o}=3$, $\eta_o=3$ and $\sigma_{no}=0.55$, $n=1,\ldots,4$. Note that in the logarithmic frequency scale, the spectra of all Gabor functions are identical.

![Spectra of 4-scale Gabor wavelets.[]{data-label="fig:gf"}](gff.png)

Subsequently, the normalization factor in the 2D-MSPC is computed in the wavelet’s framework as follows $$\begin{aligned}
\label{eq:nf}
\sum_{n}A_{no}=\sum_{n} \sqrt{  (I(x) * M_{no}^{e})^2+(I(x) * M_{no}^{o})^2}.\end{aligned}$$

     Parameter             Tuning hints
  -- --------------------- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------
     $c_o$                 [Between 0 and 1, typical 0.4 or 0.55]{}
     $g_o$                 [Typical value, 10]{}
     $ \lambda_{\min o}$   [The smallest value is the Nyquist wavelength of 2 pixels. Because of aliasing 3 pixels or above is suggested.]{}
     $\sigma_{no}$         [The smaller $\sigma_{no}$, the larger the bandwidth of the filter. The following sets are suggested: $[\sigma_{no}=0.85,\eta_o=1.3]$, or ]{}
     $\eta_o$              [$[\sigma_{no}=0.75,\eta_o=1.6]$ (Bandwidth $\approx$ 1 octave), or $[\sigma_{no}=0.65,\eta_o=2.1]$, or $[\sigma_{no}=0.55,\eta_o=3]$ (Bandwidth $\approx$ 2 octaves)]{}
     $k_o$                 [Typical value 2, up to 10 or 20 for noisy images]{}
     