Sensing the presence of people in indoor spaces allows smart systems to be aware of and responsive to the occupants, and paves the way for a wide range of applications. In this paper, we show how the reflection patterns of ultrasonic signals can be leveraged to detect the presence of still persons. We propose the use of supervised learning over segmented reflection patterns, and prove that this method is capable of detecting minute variations in the environment's response. The experimental evaluation of the proposed method in an office and a residential environment shows that it achieves a high presence sensing accuracy in the case of low signal-to-noise ratio (SNR), and a perfect accuracy in the case of high SNR, even in the case of non line-of-sight. Among the different tested classifiers, we found that the linear Support Vector Machine (SVM) achieves the best performance, yielding a presence detection accuracy of 84.3%-98.4% for low SNR, and 100% for high SNR, in the tested environments.