Individualized Head-Related Transfer Functions: Efficient Modeling and Estimation from Small Sets of Spatial Samples

This dissertation develops and evaluates a novel way of modeling and estimating individualized head-related transfer functions (HRTFs) from a priori information and a limited number of acoustic measurements. Head-related transfer functions represent and describe the acoustic transformations caused by interactions of sound with a listener’s head, shoulders, and outer ears which give a sound its directional characteristics. Once this transformation is measured, it can be combined with any non-directional sound to give a listener the perceptual illusion that the sound originated from a designated location in space. The ability to manipulate these spatial auditory cues has many applications for both immersive and informational spatial auditory displays (SADs). Unfortunately, high fidelity SADs require the use of individualized head-related transfer functions that are measured for the specific end user of the spatial auditory display. These measurements are typically impractical for widespread commercialization, in large part because traditional HRTF measurement techniques require several hundred spatial locations to be measured around a listener, a procedure which requires expensive and complicated equipment, and which can take upwards of two hours. This dissertation introduces a novel way to represent a spatially continuous HRTF with a relatively small number of parameters via a spherical harmonic decomposition. This representation is shown to be perceptually equivalent to a full HRTF in terms of the resulting localization accuracy, while providing a convenient form for making HRTF comparisons across individuals and spatial locations. With this new framework it is shown that HRTFs from a large group of individuals can be modeled effectively with a multivariate normal distribution, and that this underlying distribution can be used to provide a priori information for individualized HRTF estimation allowing accurate estimates from as few as 12 spatially distributed locations. The new representation is also shown to be particularly well suited for the separation of individual and non-individual components of the HRTF. Analysis of the underlying distributions characterizing the HRTF, as well as perceptual evidence, indicates that only the spatial variation in an HRTF which corresponds to the vertical and front-back dimensions of a sound source location need to be individualized. This finding forms the basis of what is referred to as the sectoral HRTF model. The sectoral HRTF model is shown to be valid in terms of localization accuracy and provides a way to capture the individual components in an HRTF with only nine parameters at a single frequency. The relationship between these parameters and the spatial variance along the vertical and front-back dimensions is also exploited to allow relatively accurate HRTF estimation from acoustic measurements that are limited to a single plane. Together, these developments provide significant advancements in the ease with which individualized HRTFs are collected, as well as a wealth of new information relvent to efficient HRTF modeling.