1. A gray-scale improvement circuit, comprising: a gray-scale conversion means for receiving an input video signal, converting its gray scale as necessary, and outputting the video signal with the converted gray scale; a first video signal conversion means for converting the input video signal to red, green, and blue color signals when the input video signal includes a luminance signal and color difference signals; a statistical processing means for detecting a statistical quantity in each field or each frame of the red, green, and blue color signals output by the first video signal conversion means when the input video signal includes said luminance signal and color difference signals, and for detecting a statistical quantity in each field or each frame of the input red, green, and blue color signals when the input video signal includes said red, green, and blue color signals; a scene change detection means for detecting scene changes in the input video signal; a target conversion characteristic setting means for using the output of the statistical processing means to set a target conversion characteristic as a target for the gray-scale conversion means; and an applied conversion characteristic determination means for determining a conversion characteristic for use for the video signal in the current field or frame from the target conversion characteristic set by the target conversion characteristic setting means, an output of the scene change detection means, and the conversion characteristic used for the video signal in the preceding field or frame; wherein the gray-scale conversion means converts the gray scale by using the conversion characteristic determined by the applied conversion characteristic determination means; the conversion characteristic used by the gray-scale conversion means is a selected one of a plurality of conversion characteristics; each of the plurality of conversion characteristics is identified by a characteristic number, the value of the characteristic number being associated with a feature of the conversion characteristic identified by the characteristic number, the feature gradually intensifying as the characteristic number increases; the target conversion characteristic setting means and applied conversion characteristic determination means specify the conversion characteristics by specifying their characteristic numbers; the applied conversion characteristic determination means limits the difference between the characteristic number identifying the conversion characteristic used for the preceding field or frame and the characteristic number identifying the target conversion characteristic set by the target conversion characteristic setting means for use in the current field or frame to within a prescribed limiting value; and the applied conversion characteristic determination means alters the prescribed limiting value according to the output of the scene change detection means.