Ambiguous figure-ground images, mostly represented as binary images, are fascinating as they present viewers a visual phenomena of perceiving multiple interpretations from a single image. In one possible interpretation, the white region is seen as a foreground figure while the black region is treated as shapeless background. Such perception can reverse instantly at any moment. In this paper, we investigate the theory behind this ambiguous perception and present an automatic algorithm to generate such images. We model the problem as a binary image composition using two object contours and approach it through a three-stage pipeline. The algorithm first performs a partial shape matching to find a good partial contour matching between objects. This matching is based on a content-aware shape matching metric, which captures features of ambiguous figure-ground images. Then we combine matched contours into a compound contour using an adaptive contour deformation, followed by computing an optimal cropping window and image binarization for the compound contour that maximize the completeness of object contours in the final composition. We have tested our system using a wide range of input objects and generated a large number of convincing examples with or without user guidance. The efficiency of our system and quality of results are verified through an extensive experimental study.