FAST 3D ACOUSTIC SCATTERING VIA DISCRETE LAPLACIAN BASED IMPLICIT FUNCTION ENCODERS

Abstract

Acoustic properties of objects corresponding to scattering characteristics are frequently used for 3D audio content creation, environmental acoustic effects, localization and acoustic scene analysis, etc. The numeric solvers used to compute these acoustic properties are too slow for interactive applications. We present a novel geometric deep learning algorithm based on discrete-laplacian and implicit encoders to compute these characteristics for general 3D objects at interactive rates. We use a point cloud approximation of each object, and each point is encoded in a high-dimensional latent space. Our multi-layer network can accurately estimate these acoustic properties for arbitrary topologies and takes less than 1ms per object on a NVIDIA GeForce RTX 2080 Ti GPU. We also prove that our learning method is permutation and rotation invariant and demonstrate high accuracy on objects that are quite different from the training data. We highlight its application to generating environmental acoustic effects in dynamic environments.

1. INTRODUCTION

Acoustic scattering corresponds to the disturbance of a given incident sound field due to an object's shape and surface properties. It can be regarded as one of the fundamental characteristics of an object. The effect of scattering can be expressed in terms of a scattered sound field, which satisfies Sommerfield's radiation condition. There is considerable work on modeling and measuring the acoustic scattering properties in physics and acoustics and these characteristics are widely used for sound rendering in games and virtual reality (Mehra et al., 2015; Rungta et al., 2018) , noise analysis in indoor scenes (Morales & Manocha, 2018) , acoustic modeling of concert halls (Shtrepi et al., 2015) , non-line-of-sight (NLOS) imaging (Lindell et al., 2019) , understanding room shapes (Dokmanić et al., 2013 ), receiver placement (Morales et al., 2019) , robot sound source localization (An et al., 2019 ), 3D mapping (Kim et al., 2020 ), audio-visual analysis (Sterling et al., 2018) , etc. Acoustic scattering of objects can be modeled accurately using the theory of wave acoustics (Kuttruff, 2016) . The scattering characteristics of objects are widely used for sound propagation, which reduces to solving the wave equation in large environments. Given a sound source location and its vibration patterns, acoustic simulation methods are used to predict the perceived sound at another specified location considering the medium it passes through and objects/boundaries it interacts with. While the wave behavior of sound is well understood in physics, it is much more difficult to compute acoustic scattering and sound propagation effects, especially for higher frequencies. Even with state-of-the-art acoustic wave solvers, it can take from hours to days to solve a moderately modeled room environment on a powerful workstation. One of the contributing factors to this difficulty is that wave behaviors are frequency dependent, so many frequency bands need to be analyzed separately. Current methods for computing the acoustic scattering characteristics can use numeric solvers like boundary-element methods (BEM). However, their complexity increases as a cubic function of the frequencies and most current implementations are limited to static scenes or environments. No good or practical solutions are known to compute the acoustic scattering properties for dynamic environments or when objects move or undergo deformation. Main Results: We present novel techniques based on geometric deep learning on differential coordinates to approximate the acoustic scattering properties of arbitrary objects. Our approach is general and makes no assumption about object's shape, genus, or rigidity. We approximate the

