This paper proposes a novel approach to synthesize an image invariant to illumination geometry when the illumination spectrum cannot be measured. Under the assumption that the kinds of illumination generally used are limited, the illumination invariant image is synthesized using an image and several illumination spectrum data. A light reflected from an object surface is projected onto the hyper-plane orthogonal to every conceivable illumination spectra. Using this method, images of an object captured under different illumination geometries are converted to the same image. In the experiments, texture hidden by the specular reflection was visualized well even when an object was illuminated by multiple light sources whose illumination spectra are different. This method requires multi-spectral image capturing, but RGB color images can be used only when one or two kinds of illumination are used and the illumination sources are specified.