Reducing integrability artefacts for data fusion through colour space manipulation

In data fusion, we have a multichannel image comprising information from different sources, such as colour, infrared or other sensor, and we want to obtain a single channel image capturing all the contrast information available. Here we consider Socolinsky and Wolff's technique that composites the contrast information of n channels into a single gradient field, whose reintegration produces a greyscale image. Unfortunately, the resulting gradient field is non-integrable, it has non-zero curl and so can only be reintegrated approximately (e.g., in a least-squares sense). The approximate reintegration often suffers from unpleasant bending and smearing artefacts. In this paper we show how, by diminishing the saturation of the original image (in the hsv sense), the gradient field inconsistencies should decrease, thus yielding better results after its integration. This technique is remarkably simple, and yet can produce surprising improvements in the integrability error. Moreover, and this is the main point of this paper, a small decrease in saturation is shown to lead to a large improvement in integrability. Thus, by modifying, slightly, the multichannel image (whose contrast we wish to capture) we arrive at a gradient field that is much more integrable. Finally, we will show that when working in the logarithm of the image in order to use a retinex-based integration, the integration error diminishes even more quickly.