Accurate feature detection is fundamental for various computer vision tasks, including autonomous robotics, 3D reconstruction, medical imaging, and remote sensing. Despite advancements in enhancing the robustness of visual features, no existing method measures the utility of visual information before processing by specific feature-type algorithms. To address this gap, we introduce PIXER and the concept of "Featureness," which reflects the inherent interest and reliability of visual information for robust recognition, independent of any specific feature type. Leveraging a generalization on Bayesian learning, our approach quantifies both the probability and uncertainty of a pixel's contribution to robust visual utility in a single-shot process, avoiding costly operations such as Monte Carlo sampling and permitting customizable featureness definitions adaptable to a wide range of applications. We evaluate PIXER on visual odometry with featureness selectivity, achieving an average of 31% improvement in RMSE trajectory with 49% fewer features.