In recent years, research into object classification based on ultrasonic sensing has shown that sonar is a rich source of data suitable for robust classification for specific classes of objects. However, these systems lack generality, precision, and are often slow as they need to collect and integrate multiple scans. The objective was the development of more efficient techniques for ultrasonic based object recognition through an inversion of the extended form of Freedman’s “image pulse” model. Earlier work extended this model, originally developed for a fluid medium with coincident transmitter/receiver configurations, to noncoincident configurations in air. This extended model was inverted, producing one that would calculate the geometry of a scattering body from an analysis of echoes received after insonification of the body with ultrasonic pulses. Quantitative verification of this model with various scattering bodies proved elusive, with low correlation between experiment and theory due to matrix instability and difficulties in obtaining data of sufficient accuracy. However, qualitative trends in the data indicate the model is essentially correct, though very sensitive to measurement precision and media characteristics, and there is reason to believe that further work under more controlled laboratory conditions and/or a different medium would verify the model’s validity quantitatively.