This paper presents a method for estimating color face images from near-infrared monochrome face images. This estimation is done by the regression from a monochrome image to a color image. One difficult problem is that the regression depends on face organs. That is, the same intensity pixels in an infrared monochrome image do not correspond to the same color pixels. Therefore, entirely uniform regression cannot colorize the pixels correctly. This paper presents a colorization method for monochrome face images by position-dependent regressions, where the regression coefficients are obtained in different image regions corresponding to facial organs. Also, we can extend the independent variables by adding texture information around the pixels so as to obtain accurate color images. However, unrestricted extension may cause multi-collinearity problem, which may produce inaccurate results. This paper also proposes CCA based dimensionality reduction for avoiding this problem. Comparative experiments on the restoration accuracy demonstrate the superiority of our method.