1. A method for mapping an image from a first color space to a bounded display gamut in a second color space, said first and second color spaces each spanning a plurality of points each having one luminance (L) and two chrominance (C.sub.1, C.sub.2) values, wherein said two chrominance (C.sub.1, C.sub.2) values together represent a hue angle (H) value and a chroma magnitude (M) value, said method comprising the steps of: (a) converting said image into a plurality of signals including an image luminance signal (L.sub.I) and two image chrominance signals (C.sub.I1, C.sub.I2) that specify image hue angle (H.sub.I =arctan C.sub.I2 /C.sub.I1) and image chroma magnitude (M.sub.I =sqrt (C.sup.2.sub.I1 +C.sup.2.sub.I2)); (b) producing a chroma-maximized luminance signal (L.sub.CM) representing the luminance value of the point on said display gamut boundary having the maximum chroma magnitude (M.sub.BX) at said image hue angle (H.sub.I) value in said second color space; (c) subtracting said chroma maximized luminance signal (L.sub.CM) from said image luminance signal (L.sub.I) to create a color-biased luminance signal (L.sub.CB =L.sub.I -L.sub.CM); (d) producing a chroma-corrected weight signal (0.ltoreq.W&lt;1) corresponding to the difference between said image chroma magnitude (M.sub.I) and the chroma magnitude (M.sub.B) of a first point on said display gamut boundary in said second color space, wherein said chroma-corrected weight signal (W) is zero-valued when M.sub.B .gtoreq.M.sub.I ; and (e) weighting said color-biased luminance signal (L.sub.CB) and said image luminance signal (L.sub.I) according to said chroma-corrected weight signal (W) and combining both to produce a display luminance signal (L.sub.D =WL.sub.CB +(1-W)L.sub.I representing the luminance of said mapped image in said second color space.