method of the up sampling a method of copying a single pixel to four color difference pixels a method of effecting interpolation etc can be adopted when two color difference pixels are assigned to four luminance pixels the transmitting color judging unit 39 judges a portion having the luminance 0 or r u2212 1 as the transmitting color in general white or black specified as the transmitting color is colorless and for this reason the color difference value is r 2 128 when r 256 that is an intermediate value of the grayscale however the color difference value may take a value other than r 2 due to influences of noises caused by the sub sampling and the irreversible coding which may give a color to the transmitting color in order to avoid such an inconvenience the transmitting color judging unit 39 changes the color difference value forcedly to r 2 when the luminance has the value specified as that of the transmitting color the color converting unit 40 converts a color space represented by the luminance and the color differences to a color space specific to the display device which allows an image to be displayed for example an rgb color space is used when the display device is a display and a cmyk color space is used when the display device is a printer fig6 a through 6d are views used to explain the principle based on which the image processing apparatus 30 reduces noises in a transmitting color portion surrounding the object when 0 is given to the transmitting color in the drawings the ordinate is used for the grayscale value and the abscissa is used for the pixel position on one line of an image fig6 a shows.