Separation of Reflection Components by Fourier Decoupling

Reflections exist in many natural images. For example, shiny surfaces attempt to reflect the surrounding scene, thus, resulting in a composite image that contains the mixture of reflected light and transmitted light. When viewed from a moving camera, different components appear to move differently relative to each other. Although multiple motion recovery problem has been previously studied by many researchers, few algorithms have been proposed to recover the component images themselves. In this paper, we present a novel approach to accurately separate the individual image components from a sequence of composite images. The separation of the images is realized in the Fourier domain, where each image component is represented by its frequency elements. A minimization framework exploring the magnitude and phase constraints between each frequency element is devised to find the correct motion vectors and decouple the composite frequency elements into individual components. Experimental results using both synthetic and real images demonstrate the efficiency and robustness of our algorithm.