Scene-Aware Audio for 360° Videos

Scene-Aware Audio for 360° Videos

Dingzeyu Li 0000-0002-4222-8105Columbia University dli@cs.columbia.edu Timothy R. Langlois 0000-0002-5043-8698Adobe Research tlangloi@adobe.com  and  Changxi Zheng 0000-0001-9228-1038Columbia University cxz@cs.columbia.edu
Abstract.

Although 360° cameras ease the capture of panoramic footage, it remains challenging to add realistic 360° audio that blends into the captured scene and is synchronized with the camera motion. We present a method for adding scene-aware spatial audio to 360° videos in typical indoor scenes, using only a conventional mono-channel microphone and a speaker. We observe that the late reverberation of a room’s impulse response is usually diffuse spatially and directionally. Exploiting this fact, we propose a method that synthesizes the directional impulse response between any source and listening locations by combining a synthesized early reverberation part and a measured late reverberation tail. The early reverberation is simulated using a geometric acoustic simulation and then enhanced using a frequency modulation method to capture room resonances. The late reverberation is extracted from a recorded impulse response, with a carefully chosen time duration that separates out the late reverberation from the early reverberation. In our validations, we show that our synthesized spatial audio matches closely with recordings using ambisonic microphones. Lastly, we demonstrate the strength of our method in several applications.

copyright: acmlicensedcopyright: acmlicensedjournal: TOGjournalyear: 2018journalvolume: 37journalnumber: 4article: 111publicationmonth: 8doi: 10.1145/3197517.3201391\acmSubmissionID

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1. Introduction

The ecosystem of 360° video is flourishing. Devices such as the Samsung Gear 360 and the Ricoh Theta have facilitated 360° video capture; software such as Adobe Premiere Pro has included features for editing 360° panoramic footage; and online platforms such as Youtube and Facebook have promoted easy sharing and viewing of 360° content. With these technological advances, video creators now have a whole new set of tools for creating immersive visual experiences. Yet, the creation of their auditory accompaniment, the immersive audio, is not as easy. Immersive 360° videos are noticeably lacking immersive scene-aware 360° audio.

Toward filling this gap, we propose a method that enables 360° video creators to easily add spatial audio from specified sound sources in a typical indoor scene, such as the conference room shown in Figure 1. Our method consists of two stages. We first record a single acoustic impulse response in a room using a readily available mono-channel microphone and a simple setup. Then, provided any 360° footage captured in the same environment and a piece of source audio, our method outputs the 360° video with an accompanying ambisonics spatial soundtrack. The resulting soundfield captures the spatial sound effects at the camera location, even if the camera is dynamic, as if the input audio is emitted from a user-specified sound source in the environment. Our method has no restriction on the input audio: it could be artificially synthesized, recorded in an anechoic chamber, or recorded in the same scene simply using a conventional mono-channel microphone (Figure 1). The generated ambisonic audio can be directly played back in realtime by a spatial audio player.

Figure 1. 360° audiovisual capture. Our method enables video creators to add ambisonic audio (bottom) in a 360° video of a indoor scene (top). When viewers watch the video and change the camera angle, they hear the binaural audio consistent with the current viewing angle. Our method has no restriction on the input audio. In the case shown here, the input audio is the person’s speech captured using a conventional mono-channel microphone collocated with the 360° camera, and our method converts the mono-channel input audio into a spatial audio in standard ambisonic format. The waveforms show a first-order ambisonic output (four channels), although our method supports an arbitrary order of ambisonics.

A conventional microphone and a sound source are the only requirements our method, in addition to a 360° camera. This contrasts starkly with the current approach of capturing spatial audio, which requires the use of a soundfield ambisonic microphone, which uses a microphone array consisting of multiple carefully positioned mono-channel microphones to record the spatial sound field. These devices are generally expensive, and currently very few 360° cameras have an integrated ambisonic microphone. When designing sound for traditional media, audio from each source is processed to add various effects: noise removal, frequency equalization, dynamic compression, panning, and so forth. Then, the audio clips are mixed into a cohesive soundtrack for a specific layout of speakers, with a fixed camera angle. While ambisonics could be created virtually from these sources, it is only feasible to do this manually in a space with no reflections. In real rooms reflections off of surfaces and sources need to account for direction. Our method provides an easy way to achieve these directed reflections.

Our method enables 360° video creators to incorporate spatial audio at a lower cost, without the need of ambisonic microphones. More importantly, it allows the creator to reuse the well-established audio production pipeline, where sound effects are designed, recorded, denoised, and composed — without worrying about downstream ambisonic effects. Afterwards, our method automatically incorporates room acoustic effects in the video-shooting scene, and converts the sound produced in the earlier stage into spatial audio, which is fully synchronized with the camera trajectory in the 360° video.

Technical insight and contributions

We propose to produce spatial audio by combining a lightweight measurement of room acoustics and a fast geometric acoustic simulation. A key step in our method is to construct directional impulse response (IR) functions. For traditional, non-spatial audio, an acoustic IR (see Figure 2) is the sound recorded omni-directionally at a listening location due to an impulsive signal at a source location. Then, given any input sound signals at the source, the received non-spatial sound signals can be computed by convolving the input signals with the IR. However, to produce spatial audio, we need instead directional IR functions that record the IR sound coming from each direction at the listening location. Even in the same scene, the IR varies with respect to the source and listening locations, and the directional IR further depends on incoming sound directions.

An interesting property of IR functions lays the foundation for our proposed method. The late part of the IR is the received sound energy after excessively interacting with the scene. Every time sound waves reach a scene object, a portion of their energy is reflected “diffusely”, effectively causing the sound energy distribution in the scene to become more uniform. Consequently, it is generally accepted that the late part of the IR is independent of the source and listening locations [Kuttruff, 2017]. Further, in directional IRs, the late part becomes isotropic (independent of incoming direction), as confirmed in our room acoustic measurements (see Figure 3 and §6.1).

Exploiting this property, we measure a single non-spatial IR in the scene and extract its late part through a novel method, which identifies when its energy distribution becomes truly uniform. This enables us to reuse the measured late IR when constructing the spatial IR at given source and listening locations, only relying on geometric acoustic simulation to generate the early part of the spatial IR. The simulated early IR part is further improved by a simple and effective frequency modulation method that accounts for room resonances.

To leverage acoustic simulation, we reconstruct rough scene geometry from the 360° video footage, using a state-of-the-art 360° structure-from-motion method, guided by a few user specifications. We develop an optimization approach that estimates the acoustic material properties associated with the geometry, based on the measured IR. The geometry and material parameters enable the acoustic simulation to capture the early, directional component of the spatial IR. Because the early part of the IR is oftentimes very short (typically 50-150 ms), the sound simulation is fast.

We demonstrate the quality of our resulting audio by comparing with spatial audio directly recorded by ambisonic microphones, and show that their differences are almost indistinguishable. Unlike ambisonic recordings, our method requires only a low-cost microphone, and offers the flexibility to add, replace, and edit spatial audio for 360° video. We explore the potential use of our method in several applications. While our method is designed for indoor 360° video, we further explore its use for those shot in outdoor spaces.

2. Related Work

Recent advances in 360° video research have focused mostly on improving visual quality. Rich360 and Jump designed practical camera systems and developed seamless stitching with minimal distortion, even for high-resolution 360° videos [Lee et al., 2016; Anderson et al., 2016]. To capture stereo omni-directional videos, Matzen et al. [2017] built a novel capturing setup from off-the-shelf components, providing a more immersive viewing experience in head-mounted displays with depth cues. Kopf [2016] introduced a 360° video stabilization algorithm for smooth playback in the presence of camera shaking and shutter distortion. Our work improves the audio experience in existing 360° videos, working in tandem with existing methods for capturing, post-processing, and playback for immersive visual media.

Spatial audio in virtual reality (VR) is also crucial to provide convincing immersion. Most recent work aims to enable efficient rendering of spatial audio at real-time rates. Schissler et al. [2016] proposed a novel analytical formulation for large area and volumetric sound sources in outdoor environments. Constructing spatial room impulse responses (SRIR) with geometric acoustics is expensive due to the number of rays and the disparity in energy distribution. Schissler et al. [2017b] partition the traditional IR into segments and project each segment onto a minimal order spherical harmonics bases to retain the perceptual quality. We build upon the concept of SRIR and observe that late reverberation is diffuse, which means that the late IR tail is uniform not only spatially but directionally. Our method combines early IR simulation with estimated material parameters and recorded late IR tails to generate scene-aware audio for 360° videos.

Figure 2. A typical impulse response. (top) An idealized illustration, showing the arrival time of rays and the amount of energy they carry. (bottom) A recorded impulse response in a lecture hall. The reflections become more dense and diffuse towards the later part. Traditionally, an IR is measured by recording sound omni-directionally. But for spatial audio generation, we need to estimate a directional IR, which is illustrated in Figure 10.

The simulation of sound propagation has been widely studied [Vorländer, 2008; Bilbao, 2009]. Wave-based methods usually provide high accuracy but require expensive computation [Raghuvanshi et al., 2009]. Alternatively, geometric acoustic (GA) methods can be used, which make the high-frequency Eikonal ray approximation [Savioja and Svensson, 2015]. These methods often bundle rays together and trace as beams for efficiency [Funkhouser et al., 1998]. While traditional GA does not include diffraction effects, they can be approximated via the uniform theory of diffraction for edges that are much larger than the wavelength [Tsingos et al., 2001; Schissler et al., 2014]. We use the GA method proposed by Cao et al. [2016], which exploits bidirectional path tracing and temporal coherence to provide significant speedups over previous work. For fast auralization in VR, many methods precompute IRs or wavefields [Pope et al., 1999; Tsingos, 2009; Raghuvanshi and Snyder, 2014]. Raghuvanshi et al. [2010] precompute and store one LRIR per room, similar to our method. We show how to use recorded IRs to optimize acoustics materials for simulation, and also how to directly use the recorded IR tails instead of simulating them, reducing the computation time and memory requirements. Moreover, our method accounts for a particular wave effect, the room resonances, using a frequency modulation algorithm, which further improves the generated audio quality.

To synthesize scene-aware audio, optimal material parameters are needed in the simulation. Given recorded IRs, we estimate the material parameters that best resemble the actual recording. For rigid-body modal sounds, Ren et al. [2013] optimized the material parameters based on recordings and demonstrated the effectiveness of optimized parameters to virtual objects. Most related to ours is Schissler et al. [2017a] where a pretrained neural network is used to classify the objects, followed by an iterative optimization process. Every iteration requires registering the simulated IR with a measured IR and solving a least-squares problem. We draw inspirations from inverse image rendering problems [Marschner and Greenberg, 1998], and derive an analytical gradient to the inverse material optimization problem, which we solve in a nonlinear least-squares sense. Our optimization runs in seconds, tens of times faster than previous work.

While our method aims to ease the audio editing process, this is a broad area with an abundance of prior work. Most methods strive to provide higher-level abstractions and editing powers, to help users avoid non-intuitive direct waveform editing. VoCo [Jin et al., 2017] allows realistic text-based insertion and replacement of audio narration using a learning-based text to speech conversion which matches the rest of the narration. Germain et al. [2016] present a method for equalization matching of speech recordings, to make recordings sound as if they were recorded in the same room, even if they weren’t. Rubin et al. [2013] present an interface for editing audio stories like interviews and speeches, which includes transcript-based speech editing, music browsing, and music retargeting. Like previous work, we aim to match the timbre of generated sounds with that of recordings. Moreover, we are able to produce spatial audio that blends in seamlessly with existing 360° videos, and provide a high-level “geometric” effect which can be applied to audio.

3. Rationale and Overview

An important concept used throughout our method is the acoustic impulse response (IR). We therefore start by discussing its properties in typical indoor scenes to motivate our algorithmic choices.

3.1. Properties of Room Acoustic Impulse Response

The room acoustic IR is a time-dependent function, describing the sound signals recorded at a listening location due to an impulsive (Dirac delta-like) signal at a source (Figure 2). In this paper, we use to denote an IR. If is known, then the sound signal received at the listening location can be computed by convolving with the sound signal emitted from the source: . Therefore, to add spatial audio to a 360° video, we need to estimate the IRs between the sound source and the camera location in the scene along all incoming directions.

The IR is usually split into three parts: i) the direct sound traveling from the source to the listener, ii) the first few early reflections (ER), and iii) the later reflections called late reverberation (LR). Part (i) and (ii) are the early reflection impulse response (ERIR). Perceptually, they give us a directional sense of the sound source, known as the precedence effect [Gardner, 1968].

The LR part of the impulse response (referred to as LRIR) has several properties significant to our goal. First, the LRIR is greatly “diffused” in the scene [Kuttruff, 2017], meaning that it has little dependence with respect to the source and listening locations. This is because whenever a directional sound wave encounters an obstacle, a portion of the energy is reflected diffusely, spreading the sound in many directions. Virtually all rooms include some diffuse reflection even when the walls appear smooth [Hodgson, 1991]. Thus, the longer the sound travels in a scene, the more it gets diffused. The LRIR has little perceptual contribution to our sense of directionality. Rather, it conveys a sense of “spaciousness” [Kendall, 1995] — the size of the room, but not where the listener and source are.

Another important implication of LRIR being diffused is that the sound energy carried by LRIR tends to be uniformly distributed, not only spatially [Kuttruff, 2017] but also directionally — it can be assumed isotropic. We justify this assumption with directional acoustic measurements, as described in Figure 3.

Figure 3. LRIR isotropy. We use a high-end directional (shotgun) microphone (RODE NTG8) to measure room acoustic IR received along particular directions. (left) The polar pickup plot of our shotgun microphone in comparison to the conventional omni-directional microphone. The shotgun microphone records sound mainly from its front direction. (right) For several recordings of an impulse with the shotgun microphone pointed in different directions (corresponding to different colors), we plot the amount of energy coming from each direction with respect to time. In the early part, more energy is in directions that face the source, but the energy is quickly distributed uniformly among all directions.

3.2. Method Overview

The room acoustic IR properties suggests a hybrid approach for estimating spatial IRs when we generate spatial audio for 360° videos: the LRIR can be measured at one pair of source and listening locations because of its spatial and directional independence, while the ERIR needs to be simulated with carefully chosen parameters to capture sound directionality. Also crucial is the time duration for separating ER from LR, in order to ensure the directional independence of LRIR satisfied. The major steps of our method are summarized as follows.

360° video analysis.  Provided a 360° video, we estimate rough scene geometry and the camera trajectory in the scene. The former is for running the simulation, and the latter is to locate the listener when we generate spatial audio. 3D scene reconstruction has been an active research area in computer vision. We adopt the recent

structure-from-motion approach [Huang et al., 2017] that generates a point cloud of the scene from a 360° video (see top of the adjacent figure), along with an aligned camera path through it. Our method does not depend on this particular approach: any future improvement could be easily incorporated. Then, we rely on the user to specify a few planar shapes that align with the point cloud to capture the main geometry of the scene, such as the roof, floor, and walls (see bottom of the adjacent figure). A benefit of our hybrid approach is that only approximate geometry is required: it does not need to be water-tight, or even manifold. The method of [Huang et al., 2017] takes 10-20 minutes, depending on the video resolution. Creating planar geometry to match the reconstructed point cloud only takes users several minutes per room.

Room IR analysis.  Next, we record an impulse response in the room using a conventional omni-directional microphone and speaker (§4.1). This measurement is straightforward and serves two purposes. First, it provides the LR component when we estimate the spatial IR between a sound source and a camera location. Second, it offers a means to sense the acoustic material properties in the room. Based on the measured IR, we estimate the acoustic material parameters for use in acoustic simulation, by formulating a nonlinear least-squares optimization problem (§4.2). After acquiring scene material parameters, we are then able to leverage the acoustic simulation to determine the transition point between the ERIR and LRIR based on a directionality analysis of the incoming sound energies (§4.4).

Spatial audio generation.  Lastly, we generate spatial 360° audio from input audio signals. As audio editors place sources in the scene, our simulator computes the ERIR from the source to positions on the reconstructed camera path (providing directional cues), and the LRIR is reused from the measured IR (providing a sense of spaciousness). Combining them together, we obtain spatial IRs for generating spatial audio (§5). We will show how to store the final spatial audio in ambisonics (in §5.2), which can be encapsulated in the standard 360° video format to adapt sound effects to the view direction when the video is played back.

3.3. Room Acoustic Simulation

Before diving into our technical details, we briefly describe the acoustic simulator that we use. We use a geometric acoustic (GA) model that describes sound propagation using paths along which sound energy propagates from the source to the receiver, akin to the propagation of light rays through an environment. Each path carries a certain amount of sound energy, and arrives at the receiver with a time delay proportional to the path length. Exploiting the sound energy carried by the paths and their arrival time, we are able to infer scene materials (§4.2), determine ER duration (§4.4), and synthesize ERIRs for ambisonic audio generation (§5.1).

Our method does not depend on any particular GA method. In this paper, we employ the bidirectional path tracing method recently developed in [Cao et al., 2016]. This technique simulates sound propagation by tracing paths from both the sound source and the receiver, and uses multiple importance sampling to connect the forward and backward paths. It offers a considerable speedup over prior GA algorithms and better balance between early and late acoustic responses.

While the GA model is an approximation of sound propagation and ignoring wave behaviors such as diffraction, it can reasonably estimate the impulse response of room acoustics, and has been widely used for decades [Savioja and Svensson, 2015]. Nevertheless, we consider an important wave effect, namely room resonance, and propose a frequency modulation method to incorporate the room resonance effect in our simulated ERIR (§4.3).

4. Room Acoustic Analysis for 360° Scenes

This section presents our method of analyzing an IR measurement to estimate acoustic material properties of the room and frequency modulation coefficients needed for compensating room resonances. We also determine the transition point between ERIR and LRIR.

4.1. IR Measurement

There exist many methods for acoustic IR measurement. In this work, we use the reliable sine sweep technique of [Farina, 2000, 2007]. We briefly summarize its theoretical foundation here: the signal recorded by a receiver is the convolution of the source signal and the room’s IR (i.e., ). It can be shown that can be reconstructed by measuring the cross-correlation between and , , as long as the autocorrelation of the source signals is a Dirac delta, or . For reliability, needs to have a flat power spectrum. A commonly used practical choice of is a sine sweep function that exponentially increases in frequency from to in a time period T [Farina, 2000]:

(1)

This signal spends more time sweeping the low-frequency regime, thus it is particularly robust to low-pass noise sources like those in most rooms. In practice, we choose Hz, kHz, and seconds. Also, we play the source and record simultaneously, so they are fully synchronized. This sine sweep is played only once (no average is needed), using a conventional speaker and a mono-channel microphone. Their simple setup is illustrated in Figure 4.

Figure 4. IR measurement. We measure the IR using a conventional speaker and a mono-channel microphone. The speaker plays a sine sweep noise, which is then recorded by a microphone. In practice, we put the speaker on soft foam to absorb any mechanical vibrations it produces, which can be propagated to the microphone through the table.

While the IR depends on the positions of source and receiver, our measurement is insensitive to where the source and receiver are positioned. This is because for ambisonic audio generation, we only need the LR component of the measured IR, which remains largely constant in the environment (recall §3.1). In practice, we position the source and receiver almost arbitrarily, as long as they are well separated. We only need to perform the IR measurement once in a room. If there are multiple rooms in the 360° scene, we measure one IR per room (an example is shown in §6.2). This step yields a measured IR, , and we also compute its energy response .

4.2. Material Analysis

Having the IR measured and the room’s rough geometry reconstructed from the 360° video, we now determine the acoustic material parameters needed for our room acoustic simulation. These parameters are associated with individual planar regions of the reconstructed room shape — for example, in a typical room, the walls are often painted with a particular acoustic material while the floor may have other acoustic properties. Our method also allows the user to manually select sections of the reconstructed geometry and group them as having the same acoustic material.

Acoustic properties of materials are frequency dependent. We therefore define these acoustic parameters in each octave frequency band. Without loss of generality, consider a particular octave band. When a sound wave in this octave band is reflected by a material , part of the sound energy is absorbed by the material, which is described by the material absorption coefficient in this octave band. Let stack the values of all types of materials in the room. We then formulate an optimization problem to solve for .

Path.  The ray-based room acoustic simulator generates numerous paths, along which sound signals propagate from a source to a speaker. Each path is described by a sequence of 3D positions, , where the first and last positions are the source and receiver, respectively. The other positions are surface points where the ray is reflected, each associated with an acoustic material (Figure 5). Depending on the material at position , , each is mapped to an absorption coefficient indexed in the aforementioned parameter vector . Let denote the index.

Energy.  With this notion, the energy fraction propagated along a path and arriving at the receiver is written as

(2)

where is the number of surface reflection points along the path , and accounts for the sound attenuation due to propagation in air; it depends on the path length but not on room materials [Dunn et al., 2015]. Our goal is to determine so that the energies delivered by all paths at the receiver match the energy distribution in the measured IR.

Objective function.  To this end, we propose the following nonlinear least-squares objective function,

(3)

where is the index of the paths resulted from the simulation, is the sound travel time along path , is the earliest sound arrival time in the measured IR (not in the simulation), and is a parametric model of the measured sound energy response at time , which we will elaborate on shortly.

Figure 5. Path and notation. A sound path connecting a source to a receiver may be reflected multiple times at the surface positions . Each is associated with a material indexed by , and its absorption coefficients over all frequency bands are stacked in the vector .

Moreover, is the energy delivered by the earliest path arriving at the receiver in the simulation. This is the path that directly connects the source and receiver, thus independent from material parameters. This is also the path whose arrival time is used to calibrate the reconstructed room size: before formulating the objective function (3), we scale the room size so that the arrival time of the first path matches , and in turn, the same scale is applied to the arrival time of all later paths. By taking the ratio of to , we avoid matching the absolute energy level between the simulation and the measurement.

We use a fitted parametric model in (3) instead of the measured energy response , because using is susceptible to measurement noise. Traer and McDermott [2016] measured the IRs of hundreds of different daily scenes, and discovered that decays exponentially, and the decay rates are consistently frequency dependent. Thus, we fit the measured in each frequency band with an exponentially decaying function, , and use it in (3), where we discard the subscript for simplicity, as Eq. (3) is solved for each frequency band independently.

We note that it is critical to formulate the objective function (3) using a logarithmic scale, because the ray energy drops exponentially with respect to the arrival time. Otherwise, the summation in the nonlinear least-squares sense would overemphasize the match of the early paths while sacrificing late paths, which also have significant perceptual contributions [Traer and McDermott, 2016].

Inverse Solve

We solve for by minimizing (3) with the constraint that all values in must lie in . This constrained nonlinear least-squares problem can be efficiently solved using the L-BFGS-B algorithm [Zhu et al., 1997]. This is a gradient-descent-based method, where the gradient of (3) is

(4)

In practice, the optimizations for individual frequency bands are performed in parallel, and often take less than seconds.

Figure 6. IR optimization. (top) The four plots correspond to four frequency bands (centered at 62.5Hz, 250Hz, 1000Hz, and 4000Hz). In each plot, the four curves correspond to the energy decay curves of four IRs obtained using different approaches. The orange curves are simulated using initial material parameters, and serve as a starting point. The blue target curves are directly recorded. The yellow curves are simulated using our optimized material parameters. They have the same energy decay rates as the measured (blue) curves but different scales. The purple curves are computed using the yellow curves modified using our frequency modulation algorithm (see §4.3 and Eq. 7), and they match the measured curves closely. The spectrograms of the four IRs are shown on the bottom, where the simulated IR with frequency modulation matches closely with the recorded IR.

As a validation, we substitute the optimized material absorption coefficient into (2), and evaluate the energy of every path we collected. Using these updated , we construct a simulated IR and compare it with the measured IR. As shown in the top row of Figure 6, the energy decay rate of the simulated IR with respect to time indeed matches with the measured IR at every frequency band. This verifies the plausibility of our optimized parameter values. Nevertheless, the energy intensities are still different. It is this discrepancy that motivates our frequency modulation analysis, as described next.

4.3. Frequency Modulation Analysis

In our simulated IR, the energy decay in every frequency band always starts from , the energy level delivered by the direct path from the source to the receiver. This is because the direct path has no surface reflection, and is thus independent of the material’s absorption. However, this reasoning contradicts what we observe in the measured IR, where the energy decay in different frequency bands start from different values (e.g., see the four dark blue curves in the top row plots of Figure 6). An important factor that cause the frequency-dependent variation is a wave behavior of sound. namely the room resonances. In essence, each room is an acoustic chamber. When a sound wave travels in the chamber, it boosts wave components at its resonant frequencies while suppressing others. Most rooms have their fundamental resonances in the 20-200Hz range. It is known that the room resonances affect the sound effects in the room and are one of the major obstacles for accurate sound reproduction [Cox et al., 2004]. Yet, room resonance, because of its wave nature, cannot be captured by a geometric acoustic (GA) simulation.

We propose a simple and effective method to incorporate room resonances in our simulated IR. We use to denote our simulated IR and to distinguish from the measured IR . Let be the arrival time of the direct path. We compute the discrete Fourier transforms of the simulated and measured IRs in a small time window at :

(5)

Both and in the discrete setting are vectors of complex numbers. We compute and store the ratio . Later, when we generate spatial IRs, we will use to modulate the frequency-domain energy of the IRs without affecting their phases (see §5.1).

In practice, we need to smooth in presence of measurement noise. According to the uncertainty principle of signal processing [Papoulis, 1977], we choose a small window that contains 256 samples of and . This gives us 128 samples of in frequency domain. We slide the small time window in a slightly larger window , repeat the computation of , and then average the resulting ratios. Figure 7 shows typical profiles of different rooms in our experiments.

Figure 7. Frequency modulation profiles. We plot the amplitude ratio measured in different rooms. It is interesting to observe the peaks of each curve, which reflect the room resonant frequencies. The larger the room is, the lower resonant frequency it has.

To our knowledge, methods that compensate room resonances remain elusive in existing GA-based audio generation approaches. As shown in Figure 6 and our supplemental video, our frequency modulation method improves the fidelity of the simulated IR and the realism of resulting spatial audio in a very noticeable way.

4.4. ER Duration Analysis

After obtaining the optimized material parameters, we now use simulation to obtain a reliable estimate of the ER duration .

ER-LR separation is traditionally defined based on subjective perception [Kuttruff, 2017]. There exist various heuristics for estimating the ER duration from IR measurement or simulation, from a simple kurtosis threshold [Traer and McDermott, 2016] to a threshold on the number of peaks per second in a simulated IR [Raghuvanshi et al., 2010], None of these heuristics rest on the observation that we exploit to combine a simulated ERIR with a measured LRIR for ambisonic audio generation — that is, the LR is isotropic, having uniformly distributed incoming sound energy along all directions. As a consequence, simple heuristics lead to unreliable estimates. We therefore propose a new algorithm to determine directly based on the observation of the LR’s isotropy.

Reusing the path energies collected in §4.2, we define the ER duration as the earliest time instant when the received acoustic energy is uniformly distributed among all directions. To identify , the collected rays with their energies are viewed as Monte-Carlo samples of the energy distribution over time and direction. From this vantage point, we consider a sliding time window , and check if the statistical distance between the energy distribution sampled by the rays in the time window and a uniform distribution is below a threshold.

Three statistical distance metrics are commonly used, including Kolmogorov-Smirnov (KS) Distance, the Earth Mover’s Distance, and the Cramér-von Mises Distance. They can be viewed as taking different kinds of norms of the cumulative distribution function (CDF) difference between two distributions. Here we choose to use KS distance, while the other two can be naturally used as well.

Our algorithm is as follows. Consider all the rays in a time window =10ms. The ray directions are described by two coordinates, the azimuthal and zenith angles. We process the distribution with respect to each coordinate separately. First, we put the sampled energies into histogram bins according to their zenith angles. After normalization, this histogram represents a discrete probability distribution of incoming sound energies with respect to zenith angle. We then convert this histogram into a discrete CDF, represented by a vector . If the energy is uniformly distributed, the expected CDF with respect to the zenith angle is

(6)

which is discretized into a vector with the same length as . The KS distance is computed as . Similarly, we compute the KS distance of the energy distribution with respect to the azimuthal angle . In this dimension, the expected CDF is simply a linear function, as needs to be uniformly distributed in . If both KS distances are smaller than a threshold (0.15 in all our examples), we consider the current sliding time window as having uniformly distributed directional energies. As we slide the time window, the first distance that passes the KS test determines .

To verify the robustness of this method, we run the acoustic simulation seven times, each set to produce a different number of total rays — the total number of rays increases from 15000 to 38000 evenly. After each simulation, we repeat the aforementioned analysis to compute . We verify that among all the values, the variance is small: less than 4.2% of the average .

Figure 8. Ray samples. We sample locations along the camera trajectory, and use geometric acoustic simulation to collect sound rays that arrive to each location within after an impulsive sound signal is emitted from the source. These rays will be used for synthesizing the ERIR for spatial audio.

5. Ambisonic Audio for 360° Videos

After analyzing the room geometry and acoustics, we are now able to generate ambisonic audio for any 360° video captured in the same scene. This section describes our method which produces ambisonic audio from a dry audio signal. This technique will be the cornerstone of various applications that we will explore in §6.2.

5.1. Constructing Direction-Aware Impulse Responses

Trajectory analysis

Provided a 360° video, we recover the camera motion path by performing structure-from-motion analysis [Huang et al., 2017]. This is the same technique that we use for reconstructing the room shape (recall §3.2). Our method does not critically depend on this technique; any source of geometry and a registered camera trajectory would suffice.

Simulating ER

To add ambisonic sound to a 360° video, the user first clicks a location in the reconstructed 3D scene to specify a sound source position. The source location, the camera trajectory, and the room geometry together with the optimized acoustic materials provide sufficient information to launch a room acoustic simulation. The goal of this simulation is to collect a set of incoming acoustic rays at each sampled location along the camera trajectory. These rays will be used to construct directional IRs for early reverberation. Therefore, in our path-tracing acoustic simulation, we cull a path whenever its travel time exceeds . This restriction of simulating only early paths significantly lowers the simulation cost. In our implementation, culling paths using yields 1020 speedups and memory savings in comparison to a simulation that lasts for the time length of measured IR.

In practice, we sample positions every 50 centimeters along the camera trajectory, and for each position, we collect incoming rays that arrived before . Each ray is described by its arrival time, its incoming direction (including azimuthal and zenith angles) and the carried sound energy of every octave band (see Figure 8).

Constructing IRs

Next, at every camera position, we construct spatial IRs for ambisonic audio synthesis. Each spatial IR is decomposed into two components. The early reverberation component (ERIR) is directional, constructed individually from the simulated early rays. Given a ray coming from the direction and carrying energies of all octave bands (index by ), we generate an ERIR component using the classic Linkwitz-Riley 4th-order crossover filter, as was used in [Schissler et al., 2014].

At this point, we apply the frequency modulation curve that we computed in §4.3 to , because the early rays resulting from GA-based simulation do not capture the room resonances. In particular, we compute the Fourier transform of to get , and scale it using before transforming it back in time domain. The resulting ERIR,

(7)

is what we will use for spatial audio generation (§5.2). As shown in the supplemental video’s soundtrack, this step improves the realism of resulting spatial audio in a noticeable way.

The LRIR component is omni-directional, directly taken by scaling the measured IR for :

The scale in front of is to match the energy level when combining simulated ERIR with the measured LRIR. It ensures that, in a small time window near , the ratio of ERIR energy to LRIR energy in the synthesized IR is the same as the ratio computed using the measured energy response . Here, denotes the set of rays whose arrival time is in the time window , and the index in the summation iterates through all octave bands.

5.2. Generating Ambisonic Audio

Lastly, provided a dry audio, we generate ambisonic audio received as the camera moves along its trajectory.

Background. Ambisonic audio uses multiple channels to reproduce the sound field arriving to a receiver from all directions. It can be understood as an approximation to the solution of the nonhomogeneous Helmholtz equation,

(8)

for each frequency band [Zotter et al., 2009], where is the received sound pressure, is the wave number of the frequency band, is the distance of sound sources from the receiver, and is the directional distribution of the sound sources at the frequency band . In our case, at each location along the camera trajectory, is specified by its incoming rays. If a receiver is located at a polar coordinate , then its sound pressure is described by the solution of (8),

(9)

where are the real-valued spherical harmonics, are the spherical Bessel functions, are the spherical Hankel functions, and are the coefficients of projected on the spherical harmonic basis,

(10)

Equation (9) is the sound pressure of frequency band . In the time domain, the received sound is a summation over all frequency bands, namely, , where is the frequency corresponding to the wave number . Correspondingly, in the frequency domain can be rewritten in the time domain using the Fourier transform,

(11)

where is the directional distribution of sound source signals in time domain.

In essence, ambisonic audio records the coefficients (normalized by a constant) up to a certain order . At runtime, an ambisonic decoder generates audio signals output to speaker channels (such as stereo and 5.1) according to (9) together with a head-related transfer function model. Currently, all the mainstream 360° video players, such as Youtube and Facebook video players, support only first order ambisonics, which takes four channels of signals corresponding to at and .

Generating ambisonic channels

Let denote the dry audio signals. Using the ambisonic model, we view each early ray as a directional sound source, whose signal is the dry audio convolved with its ERIR component (i.e., , where is introduced in (7)). Because this ray comes from direction , we model the corresponding in (11) as a Dirac delta distribution scaled by its incoming signal : . Then, the audio data due to early reverberation at each ambisonic channel is

(12)

In our examples, we compute only up to the first order because of the limitation in current 360° video players. This results in four channels of signals (named as the -, -, -, and -channel), and their corresponding are , , , and respectively, where and are the azimuthal and zenith angle of the direction . We iterate through all incoming rays collected in §5.1, compute their using (12) and accumulate them into corresponding channels.

Meanwhile, the LRIR component produces audio signals . We model as sound signals coming uniformly from all directions according to our observation of energy isotropy in LR (recall §4.4). Then, in (11) becomes a direction independent function, . In this case, the -channel is accumulated by , while the -, -, and -channels are not affected.

After this step, the four channels of audio data are encapsulated into the 360° video. Our method can readily produce ambisonic audio with higher-order channels for future 360° video players.

Figure 9. Position independence. We recorded 12 IRs in a room at different source and receiver locations, and perform our material estimation (§4.2) separately using each of the IRs. (left) We visualize the source (in green) and listening (in orange) positions used in each IR measurement indicated by the numbers inside the dots. (right) For each measurement, we optimize the material parameters, and plot the average value in each octave band (x-axis), along with error bars (indicating one standard deviation) shown on top of the bars. This plot shows that the material estimation is virtually independent from the choice of source and receiver locations.

6. Results

We now validate our method, and present several useful applications. To fully appreciate our results, we encourage readers to watch our accompanying video. Our results were computed on a 4-core Intel i7 CPU. Our system, including acoustic simulation, material optimization, determination of , frequency modulation, and ambisonic encoding, takes 10-20 seconds. In addition to our main supplemental video, we also provide our raw 360 videos and instructions in a supplemental zip file for full immersive experience. We use Ricoh Theta V with built-in first-order ambisonic audio microphones for the recordings.

6.1. Validation

Directionality of LRIR

While the common assumption that the LRIR is diffuse spatially has been exploited in previous methods like Raghuvanshi and Snyder [2014], its isotropy with respect to direction has received less attention. We provide evidence through room acoustic measurement using a highly directional “shotgun” microphone. The details are described in Figure 3. An additional plot that also appears in the supplemental video is explained in Figure 10.

Robustness of material parameter estimation

Part of the ease of our method rests on the fact that we only need one recorded impulse response per room using a conventional mono microphone, and that the positions of the source and receiver when recording do not matter. Figure 9 demonstrates the negligible impact these positions have on our IR measurement and material estimation steps. The same experiment also confirms that the LRIRs in all the measured IRs closely match each other. This bolsters the common assumption that the LRIR is spatially diffuse.

Figure 10. Directional energy response. We measure the directional energy response along five incoming directions (left) using a directional shotgun microphone. These measured (right) have different ER parts, but as time increases their LR tails converge.
Figure 11. Coherent temporal variation. Here we show the time-varying acoustic energy levels of simulated (top) and recorded (bottom) audio. The four curves correspond to the four ambisonic channels.

Agreement with recordings

We demonstrate that our algorithm can faithfully match recorded audio using ambisonic microphones. We compare recorded audio to the 360° audio synthesized by our method. In several rooms of varying size, our results match very well with the recordings (Figure 12). Again, please see our accompanying video to appreciate the high level of agreement our method has with recordings. To highlight the match with recordings, we stitch the recorded and synthesized audio side-by-side, to show the nearly seamless transitions.

Temporal Coherence

Figure 11 shows the temporal variation of the acoustic energy of the four ambisonic channels on our synthesized and recorded audios. In this validation, the camera first moves towards a sound source and then moves away. The simulated and recorded audio exhibit similar variations.

Figure 12. Matching recorded IRs. Our method (bottom) produces IRs that match closely recorded IRs (middle) for three different cases (top). Shown here are IRs of three distinct rooms. Their sizes, shapes, and materials vary largely (see Table 1). We refer to the supplemental materials that include audio clips of these IRs.

6.2. Applications

Our approach enables several novel applications which make spatial audio for 360° videos easier to work with.

Audio replacement in 360° video

While ambisonic microphones can be used to record spatial audio directly, they have limited use in the production pipeline. Many sounds are added to videos in post production, instead of during the video shooting. Our method allows adding sound to 360° video during post-production in a realistic spatialized fashion. We have done this in various classrooms, lecture halls, and auditoriums with varying sizes and reverberation characteristics, some of which are shown in Figure 12. An additional, concrete application is the removal of unwanted sound, shown in Figure 13. During one of our recordings, an unwanted car horn came from outside. Noise removal can be challenging, especially for non-stationary sources that overlap in frequency. Our method allows resimulating the desired dry audio, making it sound as if it was recorded in the same room, but with no noise.

Figure 13. Audio replacement. While recording sound in a classroom, there was an unwanted car horn outside. The car horn overlapped in frequency with our desired audio, which makes removing it challenging. Using our method to resimulate the dry audio provides noise free audio that sounds as if it was recorded in the scene.
size (m) (msec) # planes type
CEPSR401 15206 44 6 indoor
CEPSR620 463 21 11 indoor
CEPSR750 1184 37 6 indoor
Pupin301 12177 68 6 indoor
NWC501 11156 46 6 indoor
Lerner101 406012 121 6 indoor
Hallway 2155 40 17 multiroom
Outdoor 7050 164 21 outdoor
Table 1. Example Statistics. Here we list the estimated dimension, early cutoff time , number of planes used in our simulation, and type of scene.

Geometric effects

One of the main benefits our method provides to 360° video editors is the ability to automatically capture geometric effects. This can easily be seen when geometry occludes the source or receiver. In this example, we moved a speaker above and below a table, causing the sound to become muffled. Our method captures this effect automatically (Figure 14). Instead of painstakingly adjusting amplitude and frequency to approximate shadowing, sound editors can now just apply a geometric filter.

Extension to cross-room propagation

An even stronger geometric effect happens when a source or listener moves between rooms. This can cause very different sound due to the small opening between rooms, and different reverberation in each room. A simple extension of our method to two rooms is demonstrated (Figure 15). Consider a source located in room 1 and a listening location in room 2. Just like single rooms, the (directional) ERIR between and is computed from simulated rays with spatial effects. For the LRIR, we recorded an IR once in each room, and . We then compute the propagated IR between two rooms as

(12)

where are locations uniformly sampled in the planar region of the door , is the effective area of each sampled location , and are the LR components of the recorded IRs in each room, and and are simulated ERIRs from to in room 1 and from to in room 2. The derivation of (12) is presented in Appendix A. This formulation is similar to [Stavrakis et al., 2008]. Therefore, our algorithm could be easily extended to a general graph of connected rooms using their algorithm.

Figure 14. Geometric effects: occlusion. As a sound source moves below a table, it exhibits a low-pass muffling effect due to direct sound being blocked. Our method captures this effect.
{overpic}

[width=0.99]figures/multiroom.pdf (a)(b)(c)

Figure 15. Connected rooms. As a listener moves between rooms, the reverberation changes, and strong geometric shadowing effects are heard. Our method naturally works in these cases, requiring only one IR measurement in each room. (a) A photograph of the multi-room scene. (b) The layout of the rooms. (c) The spectrograms of the synthesized IRs at three distinct locations.

Re-spatialization of mono audio

The final application we present is a way to apply spatial effects to in-situ recorded mono audio, i.e., audio recorded in a room with reverberation. This problem is similar in spirit to the conversion of a 2D film into a 3D film without refilming it — a popular problem in the film industry. Theoretically, re-spatializing the audio could be done by deconvolving the impulse response from the recorded audio, to obtain the original (“dry”) source audio. The dry audio could then be spatialized with our method. However, deconvolution is a very ill-conditioned process and is difficult in practice. Instead, we present an ad-hoc effect that can give some spatial impression. Given a room model with estimated materials, we perform a full IR simulation and store the propagated rays. We can then take the input mono-channel audio and distribute its energy over the sphere to match the energy of the computed rays. While not fully principled, it provides a plausible effect and works well in many cases, shown in Figure 1 and Figure 16.

Figure 16. Re-spatialization. From recorded mono audio of a person talking while moving around a room, we can re-spatialize the sound. By using our method to compute the energy distribution due to the moving source, we distribute the mono sound energy appropriately. (top) Sound source moving from left to right in the camera frame. (bottom) The sound waveform (left) and the energy (right) after binauralizing our spatialization. Notice how the sound follows the source, moving from left to right.

7. Conclusion

We have presented a method for adding realistic, scene-aware spatial audio to 360° videos. By combining simulated early reflections with recorded late reverberation, our method is extremely fast and matches recorded audio well. It provides a practical way to incorporate geometric effects during audio post-production, requiring only a standard mono microphone and a 360° camera. We believe this will enable the next generation of sound design for emerging immersive content.

Limitations and future work

A major limitation to proper viewing of spatial audio currently is the lack of personalized head-related transfer functions. These functions describe how our head and ear geometry modifies sound before it reaches our ear drums, which is how humans detect directionality of sound. These functions are unique to individuals, but are laborious to measure. While the common/average models that current 360° video players use give a spatial impression, we expect the accuracy continue to increase in the future as personalized HRTFs become easier to obtain. We note again that our method supports an arbitrary order of ambisonics, while most current players support only first order.

Our method requires a good impulse response to work well. While much easier and faster than directly measuring acoustic properties of scene materials, it is still an extra step that requires access to the original room where the video was recorded. Future work could examine inferring an impulse response from the audio in the video. Large spaces such as outdoor scenes are challenging. The large amount of uncontrollable noise makes it difficult for our method to match recordings exactly, as shown in Figure 17. However, this could also be seen as a strength of our method: the ability to re-simulate only the audio sources of interest, noise free.

Figure 17. Challenging outdoor case. We applied our method to outdoor 360° videos. The major challenge is recording noise, due to e.g., environment and wind, which makes an exact match of our synthesized audio to the ambisonic recordings very challenging. However, the results sound plausible (see video). (left) An outdoor 360° recording scene at 6AM in the morning. (right) The recorded audio severely contaminated by noise. (middle) A typical indoor recording with much less noise.

To ease the IR measurement, only one measurement per room is needed in our method. However, this limits our ability to detect material differences among different indoor regions. While a single measurement appears to be sufficient in our method, more precise estimation of wall materials may be necessary in order to simulate an impulse response accurately. This could possibly be achieved using multiple recordings at different locations.

Currently we only model the major walls and obstacles in the scene, ignoring most other objects like chairs. While it is reasonable to drop small features when the sound wave length is large enough, we indeed oversimplify the reconstructed geometry. One issue occurs when the listening location becomes too close to an object that we do not model/optimize. In this case, the synthesized audio sounds may characteristically differ from the recordings. In our experiments, we found that keeping a safe distance between unmodelled objects prevents this discrepancy. In the future, we wish to investigate the impact of accurate geometric modeling on the optimization process as well as the resulting audio.

Currently, we separate ER and LR parts based on the point where the sound field becomes directionally diffuse. It remains an open question as to what the optimal way is to separate the IR, since the separation time depends on many factors, such as acoustic energy, directional distribution, number of sound sources, and others.

Realistic spatial audio authoring in 360° videos is an exciting and challenging research field. Thanks to recent hardware developments and surging interest in virtual reality, we expect to see an increased demand for immersive 360° audio. Our scene-aware audio is a first step towards the practical application of a more immersive audio-visual experience. In order to further advance the audio quality, still more accurate and efficient methods are required. Provided the current active research toward realtime GA simulation, an interesting future work is to extend our system with realtime simulation for virtual and augmented reality applications.

We believe that an intuitive spatial audio editing pipeline will go a long way to advance virtual reality audio editing. Unlike mono-channel or stereo audio, high-order ambisonics have quadratically increasing number of channels, i.e., 1st order has 4, 2nd order has 9, and so on. While low-level mixing and stitching works on one or two channels for traditional audio, we argue that a higher-level abstraction of the audio editing process can help users access the full potential of spatial audio. Our work abstracts the manipulation of different channels to intuitive concepts such as the virtual sound source location and listening location, allowing designers to think more about the scene and less about waveform editing. Lastly, we look forward to other avenues where spatial audio will enhance the user experience.

Acknowledgements.
We thank Chunxiao Cao for discussing and sharing his bidirectional sound simulation code, Carl Schissler for sharing the “infinite” audio file, James Traer for discussion on IR measurement, and Henrique Maia for proofreading and voiceover. This work was supported in part by the National Science Foundation (CAREER-1453101), SoftBank Group, and generous gift from Adobe. Dingzeyu Li was partially supported by an Adobe Research Fellowship.

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Appendix A Derivation for Cross-Room IR

Consider a source located in room 1 and a listening location in room 2. The IR between and is the result of propagating sound though the door, and thus can be written as

(13)

where is the door area that connects two rooms (the semi-transparent blue region in Figure 15-b), and is a point located in the door region. and are the IRs between and in room 1 and between and in room 2, respectively. They can be approximated as concatenations of the simulated ERIR and measured LRIR in each room, namely,

(14)

where and are the LR components of the IRs recorded in each room independently (following §4), and and are simulated ERIRs between and in room 1 and between and in room 2. We note that here we use but not because they are the same due to acoustic reciprocity. Then, the integrand in (13) becomes

(15)

where the ERIR is replaced by with our acoustic simulation. After we discretize the door region using sampled points, the LRIR becomes the expression (12).

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