Algorithms for intrinsic images reduce color differences in RGB images caused by the temperature of black-body radiators. Based on the reference light and detecting single invariant direction, these algorithms are weak in real images which can have multiple invariant directions when the scene illuminant is a colored illuminant. To solve these problems, this paper proposes a method of acquiring an intrinsic image by omnidirectional projection of an ROI and a translation of white patch in the ${chi}$-chromaticity space. Because it is not easy to analyze an image in the three-dimensional RGB space, the ${chi}$-chromaticity is also employed without the brightness factor in this paper. After the effect of the colored illuminant is decreased by a translation of white patch, an invariant direction is detected by omnidirectional projection of an ROI in this chromaticity space. In case the RGB image has multiple invariant directions, only one ROI is selected with the bin, which has the highest frequency in 3D histogram. And then the two operations, projection and inverse transformation, make intrinsic image acquired. In the experiments, test images were four datasets presented by Ebner and evaluation methods was the follows: standard deviation of the invariant direction, the constancy measure, the color space measure and the color constancy measure. The experimental results showed that the proposed method had lower standard deviation than the entropy, that its performance was two times higher than the compared algorithm.