This paper proposes a new framework for estimating the Manhattan Frame (MF) of an indoor scene from a single RGB-D image. Our technique formulates this problem as the estimation of a rotation matrix that best aligns the normals of the captured scene to a canonical world axes. By introducing sparsity constraints, our method can simultaneously estimate the scene MF, the surfaces in the scene that are best aligned to one of three coordinate axes, and the outlier surfaces that do not align with any of the axes. To test our approach, we contribute a new set of annotations to determine ground truth MFs in each image of the popular NYUv2 dataset. We use this new benchmark to experimentally demonstrate that our method is more accurate, faster, more reliable and more robust than the methods used in the literature. We further motivate our technique by showing how it can be used to address the RGB-D SLAM problem in indoor scenes by incorporating it into and improving the performance of a popular RGB-D SLAM method.