1. A video signal processing apparatus comprising: an enhancement gain generating section obtaining an enhancement gain for each pixel based on an luminance signal forming part of an input video signal and a predetermined enhancement gain; and an enhancing section performing a process of enhancing the luminance signal forming part of the input video signal based on the enhancement gain for each pixel obtained by the enhancement gain generating section, wherein the enhancement gain generating section includes a mean deviation calculating portion obtaining a mean deviation of luminance values of a plurality of pixels included in a predetermined region centered at a pixel of interest that is the pixel for which the enhancement gain is to be obtained, a weighting coefficient generating portion generating a weighting coefficient for the pixel of interest according to the value of the mean deviation calculated by the mean deviation calculating portion, and a multiplication portion multiplying the predetermined enhancement gain by the weighting coefficient generated by the weighting coefficient generating portion to obtain the enhancement gain for the pixel of interest.