We propose a novel highly efficient method for filling disparity holes, regions where disparity estimation fails to produce correct result, with the most plausible values. While the filling values may not exactly match the missing disparities, the filled disparity map has cohesive and smooth areas. Such disparity map enables many applications, such as refocusing and layer effects and other new 3D photography apps, to overcome artifacts due to holes and be visually pleasant for the user. To solve for the filling disparities, we incorporate the visual saliency in our model and decouple the solution complexity from the resolution of the original disparity map. Hence, our technique strikes a good balance between perceptual quality and computational efficiency. Overall, our method produces high quality results fulfilling or exceeding the requirements of practical applications that use depth. Moreover, it is fast and hence adequate to run on the ubiquitous mobile platforms.