All illusory surface jigures yield a perception of a surface occluding another one or the background. Occluded surfaces yield completion, a phenomena known as amodal completions. It is intriguing that for some images illusory surfaces are perceived, but not for other images (see jigure I). Also, illusory su faces may have portions occluded. We aim to understand these phenomena. Our approach detects intensity edges and junctions. From the junctions we seek to find an optimal image organization, i.e., multiple ordered suqaces with the ordering accounting for salience. The most salient being the figure, while the other sugaces are classified as background. A decision of which surface is the visible one (on top) is made locally, at each pixel, allowing the salient suqace (figure) to have portions occluded, i.e., with amodal completions. We accountfor a variety of imagery not explained before.