A spatial compression technique for head-related transfer function interpolation and complexity estimation

A head-related transfer function (HRTF) model employing Legendre polynomials (LPs) is evaluated as an HRTF spatial complexity indicator and interpolation technique in the azimuth plane. LPs are a set of orthogonal functions derived on the sphere which can be used to compress an HRTF dataset by transforming it into a lower dimensional space. The LP compression technique was applied to various HRTF datasets, both real and synthetic, to determine how much different HRTFs can be compressed with respect to their structural complexity and their spatial resolution. The spatial complexity of different datasets was evaluated quantitatively by defining an HRTF spatial complexity index, which considers the rate of change in HRTF power spectrum with respect to spatial position. The results indicate that the compression realized by the LP technique is largely independent of the number of spatial samples in the HRTF dataset, while compressibility tracks the HRTF spatial complexity index so that more LP coefficients are needed to represent an HRTF dataset with a larger complexity index. The slope of the complexity index with respect to sub-sampling density can be used as a predictor for high interpolation error.