I will present our latest results on image and video processing. First, I will introduce the bilateral grid, a new image representation that enables fast edge-aware image processing. Image data is stored in a coarse 3D grid where an intensity axis is added to the traditional x and y axes. By working in the bilateral grid, algorithms such as bilateral filtering, edge-aware painting, and local histogram equalization become simple and can be efficiently parallelized on modern graphics hardware to achieve real-time performance on HD video. I will demonstrate our method on a variety of applications such as image editing, transfer of photographic style, and contrast enhancement of medical images. In a second part, I will present a new interpretation of the mean-shift algorithm for image and video segmentation. I will show that a mean-shift segmentation is equivalent to a topological decomposition of the underlying feature space. Using Morse theory and the notion of topological persistence, this decomposition is used to build a hierarchical segmentation of the data at a negligible computational cost. Our experiments demonstrate that our algorithm achieves the same accuracy level as existing techniques while being significantly faster for high-resolution images and videos for large kernels.