Spherical Acoustic Spatial Entropy: Predicting Acoustic Scene Complexity in Virtual Environments

The objective quantification of Acoustic Scene Complexity (ASC) remains a significant challenge. While existing entropy-based metrics capture spectro-temporal variability, a metric accounting for the spatial distribution of sources has been lacking. We introduce Spherical Acoustic Spatial Entropy (SASE), a novel information-theoretic metric designed for Virtual Acoustic Environments (VAEs). SASE leverages ground-truth spatial data, utilizing an equal-area spherical partition around the listener and weighting source contributions by their perceptual loudness (ITU-R BS.1770-4). We validated SASE through a psychoacoustic experiment (N=21) using a <tex-math notation="LaTeX">2× 2 × 2</tex-math> factorial design that manipulated masker count, spatial distribution, and motion. SASE was evaluated alongside energy and spectral entropy metrics against subjective ratings of complexity, effort, and spatial spread. Results show that SASE mean was the most robust predictor of perceived complexity in condition-level ratings (<tex-math notation="LaTeX">R²=0.714</tex-math>, <tex-math notation="LaTeX">$p=0.008$</tex-math>), outperforming spectral and energy entropy. A random-effects pooling of participant regression coefficients confirmed this relationship at the population level (<tex-math notation="LaTeX">R²_ pseudo=0.740</tex-math>, <tex-math notation="LaTeX">$p< .001$</tex-math>). Furthermore, a model combining SASE mean with spectral entropy standard deviation explained 84.4% of the variance in perceived complexity, indicating spatial and spectro-temporal metrics capture complementary scene dynamics. SASE provides an objective measure of spatial complexity, enhancing existing frameworks for predicting ASC in virtual environments.