1. An image processing apparatus which performs soft proof processing of reproducing, on a monitor, a print product under observation illumination, comprising: a characteristics holding unit configured to hold specular reflection of the observation illumination at a sample print product having a plurality of colors printed thereon as color-specific glossy components, diffuse reflection of the observation illumination at the sample print product as color-specific diffuse components, and color-specific gonio-spectral reflection characteristics at the sample print product; an evaluation value holding unit configured to hold an evaluation value for each of the held color-specific gonio-spectral reflection characteristics; an intensity distribution holding unit configured to hold an intensity distribution of the observation illumination; a lowpass filter generation unit configured to obtain the gonio-spectral reflection characteristics for each of representative colors from said characteristics holding unit, and to generate a lowpass filter corresponding to the gonio-spectral reflection characteristics for each of the representative colors, where the representative colors corresponding to the evaluation values held in said evaluation value holding unit; a map generation unit configured to perform filter processing on the intensity distribution of the observation illumination held in said intensity distribution holding unit, for each of the representative colors, by means of the lowpass filter corresponding to the representative color, in order to generate a map indicating a capture intensity distribution of observation illumination for the representative color; an intensity calculation unit configured to obtain an evaluation value corresponding to a color of a pixel in a proofing-target image from said evaluation value holding unit, and to interpolate a capture intensity at a position corresponding to the pixel in the map for each of the representative colors, based on the evaluation value, in order to calculate a capture intensity of the observation illumination for the pixel, for each pixel in the proofing-target image; a proofing color calculation unit configured to obtain the glossy component and the diffuse component corresponding to a color of a pixel in the proofing-target image from said characteristics holding unit, to multiply the difference between the glossy component and the diffuse component by the capture intensity to calculate a proofing glossy component, and to add the diffuse component to the proofing glossy component in order to calculate a proofing color of the pixel, for each pixel in the proofing-target image; and a display image generation unit configured to convert the proofing color into a signal value for the monitor to generate a display image, for each pixel in the proofing-target image.