  In this paper, we propose a novel, effective and fast method to obtain a
color illumination invariant and shadow-free image from a single outdoor image.
Different from state-of-the-art methods for shadow-free image that either need
shadow detection or statistical learning, we set up a linear equation set for
each pixel value vector based on physically-based shadow invariants, deduce a
pixel-wise orthogonal decomposition for its solutions, and then get an
illumination invariant vector for each pixel value vector on an image. The
illumination invariant vector is the unique particular solution of the linear
equation set, which is orthogonal to its free solutions. With this illumination
invariant vector and Lab color space, we propose an algorithm to generate a
shadow-free image which well preserves the texture and color information of the
original image. A series of experiments on a diverse set of outdoor images and
the comparisons with the state-of-the-art methods validate our method.
