<p>As indoor robots are expected to operate in increasingly complex environments, the need for rich and scalable semantic representations has become critical. While semantic mapping is a standard tool, existing representations often fall at two extremes: dense voxel-based maps that are computationally expensive to query, or schematic graphs that lack geometric detail. This trade-off limits the scalability of semantic maps in real-world tasks. We propose an object-aware semantic mapping framework that models key static objects using probability density functions (PDFs). Objects like beds, fridges or desks are detected via 3D point cloud processing and encoded as 2D probabilistic occupancy distributions. This formulation provides a compact, robust representation that preserves semantic identity and geometric shape, while handling noise and partial views. The map is structured around rooms and their contents, enabling global relocalization and semantically informed path planning. Using Differential Evolution and Kullback-Leibler divergence, our method achieves robust relocalization without prior pose. Its object-centric, probabilistic nature also supports functional scene understanding for context-aware navigation. We validate our approach on a benchmark dataset and in a real apartment, showing improved performance over traditional methods in ambiguous or cluttered scenes, and demonstrating the advantages of a unified representation for multiple robotic behaviors.</p>