intuition behind this idea is that, if one identifies a local maximum point from a $k\times k$ region, its surrounding $2k\times2k$ region can further support whether this point is a part of a boundary or only an isolated noise point. This idea can be easily implemented by enlarging the convolutional kernel size and with appropriate padding.

In Table \[tab:complexity\_comparison\], we summarize the model complexity of different index networks used at a single downsampling and upsampling stage. We assume the convolution kernel has a size of $K\times K$ applied on a $C$-channel feature map. The number of parameters in BN layers is excluded. When considering weak context, we assume the kernel size is $2K\times 2K$. Since $C\gg K$, generally we have the model complexity *M2O DINs*$>$*HINs*$>$*Unshared Stagewise O2O DINs*$>$*Shared Stagewise O2O DINs*$>$*Modelwise O2O DINs*.

  IndexNet    Type                       \# Param.
  ---------- ------ ----------------------------------------------------
               L                 $K\times K\times C\times4$
               NL          $K\times K\times C\times2C+2C\times4$
              NL+C        $2K\times 2K\times C\times2C+2C\times4$
               L                    $(K\times K)\times4$
               NL              $(K\times K\times2+2)\times4$
              NL+C            $(2K\times 2K\times2+2)\times4$
               L                    $(K\times K)\times4$
               NL              $(K\times K\times2+2)\times4$
              NL+C            $(2K\times 2K\times2+2)\times4$
               L                $(K\times K\times C)\times4$
               NL         $(K\times K\times 2C+2C\times C)\times4$
              NL+C       $(2K\times 2K\times 2C+2C\times C)\times4$
               L            $(K\times K\times C\times C)\times4$
               NL     $(K\times K\times C\times 2C+2C\times C)\times4$
              NL+C   $(2K\times 2K\times C\times 2C+2C\times 