of the weighting function for 2D-MSPC in Example 1. The image of $\mathcal{M}^*$ is obtained through methods , , and .[]{data-label="fig:lena-opt"}](pc_lena_Fronorm_Mpm_6or "fig:"){width="\linewidth"}

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[0.25]{} ![Detection of features from the Lena’s image. This is done by optimizing the parameters of the weighting function for 2D-MSPC in Example 1. The image of $\mathcal{M}^*$ is obtained through methods , , and .[]{data-label="fig:lena-opt"}](pc_lena_det_PC_6or "fig:"){width="\linewidth"}

[0.25]{} ![Detection of features from the Lena’s image. This is done by optimizing the parameters of the weighting function for 2D-MSPC in Example 1. The image of $\mathcal{M}^*$ is obtained through methods , , and .[]{data-label="fig:lena-opt"}](pc_lena_Fronorm_PC_6or "fig:"){width="\linewidth"}

[0.25]{} ![Comparison between determinant-based optimization methods and , also between norm-based optimization methods and .[]{data-label="fig:diff-2par"}](pc_lena_det_Mpm_m_PC_2par "fig:"){width="\linewidth"}

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[0.25]{} ![Comparison between determinant-based optimization methods and , also between norm-based optimization methods and .[]{data-label="fig:diff-2par"}](pc_lena_Fnorm_Mpm_m_PC_2par "fig:"){width="\linewidth"}

For 1-, 2-, $\infty-$ and $F-$ norms, the optimization method results in the optimal parameter vector $\upsilon_o^*=[0.1 ~ 50]$ with $\|\mathcal{M}\|^*_1=219.5310$, $\|\mathcal{M}\|^*_2=75.4579$, $\|\mathcal{M}\|^*_{\infty}=204.6513$, and $\|\mathcal{M}\|^*_F=114.1408$, respectively. The image of $\mathcal{M}^*$ with optimal settings for the weighting function is shown in Figure \[fig:lena-norm-opt\], obtained through based on 1-, 2-, $\infty-$ and $F-$ norms. Again, it is seen that all four norm types result in the same visual performance. This example shows 