Colour image gradient regression reintegration

Suppose we process an image and alter the image gradients in each colour channel R,G,B. Typically the two new x and y component fields p,q will be only an approximation of a gradient and hence will be nonintegrable. Thus one is faced with the problem of reintegrating the resulting pair back to image, rather than derivative of image, values. This can be done in a variety of ways, usually involving some form of Poisson solver. Here, in the case of image sequences or video, we introduce a new method of reintegration, based on regression from gradients of log-images. The strength of this idea is that not only are Poisson reintegration artifacts eliminated, but also we can carry out the regression applied to only thumbnail images. The novel approach here is to regress derivatives (using only thumbnails) and then replace reintegration itself by the much simpler use of the resulting regression coefficients on non-derivative, full-size images. We investigate the utility of the method by applying it to the intrinsic-image problem as a first test, and then also to the night-to-day problem as a second test. We find that the new algorithm performs well, and is fast. Moreover eliminating Poisson artifacts results in clearer, more sharp output images that can show far less ghosting.