A new method for the classification of respiratory diseases is presented. The method is based on a novel class of features, extracted from pulmonary sounds, by parameterizing their spectrograms that are represented as surfaces, and by utilizing geometrical distortions defined with reference to these surfaces. This method yields a set of highly descriptive features for the analysis of pulmonary sound recordings. Furthermore, by combining these features with Mel-frequency cepstral coefficients, we introduce a powerful model for the automatic diagnosis of common respiratory pathologies. Compared with baseline methods, our model achieves superior results for binary and multi-class classifications of common respiratory diseases. Our new approach to the classification of one-dimensional signals is applicable to other signals in the context of their representations in combined spaces or manifolds.