In imaging applications, computation is often carried out in a derivative (gradient) domain. For example, we can attenuate small image differences by thresholding the gradient and then reintegrate. Unfortunately, the reintegration is an expensive task. Reintegration is often carried out in 2D (usually using 2D Fourier transform) or through multiple 1D paths as in Retinex. In this paper, we show that using a small number of non-random paths, each of which is a tour the size of the image, is an effective and fast method for reintegration.We apply our method to the problem of reintegrating a shadow free gradient derivative image. Results are competitive with those obtained using 2D methods. Yet, the reintegration presented here is an order of magnitude quicker.