Visual simultaneous location and mapping (SLAM) using RGB-D cameras has been a necessary capability for intelligent mobile robots. However, when using point-cloud map representations as most RGB-D SLAM systems do, limitations in onboard compute resources, and especially communication bandwidth can significantly limit the quantity of data processed and shared. This article proposes techniques that help address these challenges by mapping point clouds to parametric models in order to reduce computation and bandwidth load on agents. This contribution is coupled with a convolutional neural network (CNN) that extracts semantic information. Semantics provide guidance in object modeling which can reduce the geometric complexity of the environment. Pairing a parametric model with a semantic label allows agents to share the knowledge of the world with much less complexity, opening a door for multi-agent systems to perform complex tasking, and human–robot cooperation. This article takes the first step towards a generalized parametric model by limiting the geometric primitives to a planar surface and providing semantic labels when appropriate. Two novel compression algorithms for depth data and a method to independently fit planes to RGB-D data are provided, so that plane data can be used for real-time odometry estimation and mapping. Additionally, we extend maps with semantic information predicted from sparse geometries (planes) by a CNN. In experiments, the advantages of our approach in terms of computational and bandwidth resources savings are demonstrated and compared with other state-of-the-art SLAM systems.