We describe a simple and fast algorithm for optimizing Markov random fields over images. The algorithm performs block coordinate descent by optimally updating a horizontal or vertical line in each step. While the algorithm is not as accurate as state-of-the-art MRF solvers on traditional benchmark problems, it is trivially parallelizable and produces competitive results in a fraction of a second. As an application, we develop an approach to increasing the accuracy of consumer depth cameras. The presented algorithm enables high-resolution MRF optimization at multiple frames per second and substantially increases the accuracy of the produced range images.