This paper reports on a robust RGB-D SLAM system that performs well in scarcely textured and structured environments. We present a novel keyframe-based continuous visual odometry that builds on the recently developed continuous sensor registration framework. A joint geometric and appearance representation is the result of transforming the RGB-D images into functions that live in a Reproducing Kernel Hilbert Space (RKHS). We solve both registration and keyframe selection problems via the inner product structure available in the RKHS. We also extend the proposed keyframe-based odometry method to a SLAM system using indirect ORB loop-closure constraints. The experimental evaluations using publicly available RGB-D benchmarks show that the developed keyframe selection technique using continuous visual odometry outperforms its robust dense (and direct) visual odometry equivalent. In addition, the developed SLAM system has better generalization across different training and validation sequences; it is robust to the lack of texture and structure in the scene; and shows comparable performance with the state-of-the-art SLAM systems.