Abstract: This article presents a new, unified technique to perform general edge-sensitive editing operations on n-dimensional images and videos efficiently. The first contribution of the article is the introduction of a Generalized Geodesic Distance Transform (GGDT), based on soft masks. This provides a unified framework to address several edge-aware editing operations. Diverse tasks such as denoising and nonphotorealistic rendering are all dealt with fundamentally the same, fast algorithm. Second, a new Geodesic Symmetric Filter (GSF) is presented which imposes contrast-sensitive spatial smoothness into segmentation and segmentation-based editing tasks (cutout, object highlighting, colorization, panorama stitching). The effect of the filter is controlled by two intuitive, geometric parameters. In contrast to existing techniques, the GSF filter is applied to real-valued pixel likelihoods (soft masks), thanks to GGDTs and it can be used for both interactive and automatic editing. Complex object topologies are dealt with effortlessly. Finally, the parallelism of GGDTs enables us to exploit modern multicore CPU architectures as well as powerful new GPUs, thus providing great flexibility of implementation and deployment. Our technique operates on both images and videos, and generalizes naturally to n-dimensional data. The proposed algorithm is validated via quantitative and qualitative comparisons with existing, state-of-the-art approaches. Numerous results on a variety of image and video editing tasks further demonstrate the effectiveness of our method.