The olfactory system employs responses of an ensemble of odorant receptors (ORs) to sense molecules and to generate olfactory percepts. Here we hypothesized that ORs can be viewed as 3D spatial filters that extract molecular features relevant to the olfactory system, similarly to the spatio-temporal filters found in other sensory modalities. To build these filters, we trained a convolutional neural network (CNN) to predict human olfactory percepts obtained from several semantic datasets. Our neural network, the DeepNose, produced responses that are approximately invariant to the molecules' orientation, due to its equivariant architecture. Our network offers high-fidelity perceptual predictions for different olfactory datasets. In addition, our approach allows us to identify molecular features that contribute to specific perceptual descriptors. Because the DeepNose network is designed to be aligned with the biological system, our approach predicts distinct perceptual qualities for different stereoisomers. The architecture of the DeepNose relying on the processing of several molecules at the same time permits inferring the perceptual quality of odor mixtures. We propose that the DeepNose network can use 3D molecular shapes to generate high-quality predictions for human olfactory percepts and help identify molecular features responsible for odor quality.