Signal Processing - May 2017 - 48

for a long time, made it difficult to predict whether an individual reflection would be audible in the presence of the direct
sound and other reflections. This is mainly due to the fact that
the audibility of a reflection depends on many parameters.
One of the first models that aimed to parameterize the audibility of reflections, named reflection masked threshold (RMT),
was proposed by Buchholz et al. [70]. The RMT is the lowest
level at which a reflection will be audible, and it is a function of
the directions of the reflection and of the corresponding direct
sound, the time delay of the reflection with respect to the direct
sound, the level of the direct sound, the difference of the frequency spectra between the direct sound and the reflection,
the effect of other reflections and reverberation, and the signal
content. The RMT can be used for simplifying room acoustic
models via culling inaudible reflections. A simpler decision rule
for culling inaudible early reflections was proposed by Begault
et al. [71]-[73], based on the relative level of the reflection. In the
absence of reverberation, the audibility threshold of a reflection
is 21 dB below the level of direct sound for a delay of 3 ms. The
presence of diffuse reverberation has the effect of increasing this
threshold by 11 dB. This threshold is also known to decrease
with the angle between the direct sound and the early reflection.
Some properties of binaural hearing, such as the precedence
effect, may also make some reflections inaudible. The exclusion of those reflections from the audio rendering pipeline can
further reduce the associated computational cost. To that end, a
model of the precedence effect was proposed in [74], according
to which perceived directions of acoustic events are modeled as
normally distributed variables. If the direct path and a reflection
are present, then the distribution of the perceived direction is a
mixture of two Gaussians. The audibility of the reflection was
then shown to be related to the number of modes in the mixture:
if the mixture is unimodal, the reflection is masked, and if it is
bimodal, it is audible. The derivation of the model parameters
was made via subjective localization experiments. This model
was applied for the culling of reflections in binaural room auralization [75]. More specifically, the ISM was used to obtain a
number of secondary sources, and these were clustered according to their distance from the listener position and their azimuth
angle. A single reflection masker was obtained for each cluster
using the precedence effect model, and the rest of the secondary sources in the same cluster are excluded from the rendering
pipeline, thereby reducing the computational cost. Subjective
evaluations were carried out using different audio material,
different room geometries, and different listening positions to
compare the room auralizations using full-room response, level-based reflection selection, and perceptually motivated selection based on the precedence effect model. These experiments
showed that reflection culling based on the precedence effect
is capable of reducing the number of early reflections by over
60%, without any significant degradation in subjective localization, spaciousness, presence, and envelopment experience.
Another approach to perceptually motivated simplification
of auralization based on the absolute threshold of hearing was
recently proposed [76]. According to this model, the duration of
ray tracing for calculating the room impulse responses for a given
48

source depends on a temporal cutoff point determined by the last
audible ray. It was shown that this approach resulted in noticeable improvements in the computation time of impulse responses
without significantly degrading the auditory experience.

Perceptually motivated artificial reverberation
Room impulse responses can be divided in two parts: early
reflections, where reflections are separated in time and have
strong directional characteristics, and the reverberation tail,
where higher-order reflections begin to overlap in time and the
sound field becomes diffuse (i.e., omnidirectional). The
human auditory system is sensitive to the direction of the
direct wave front and the early reflections, while it cannot discern the directions of individual reflections within the reverberation tail [77]. The level and directions of lateral early
reflections are related directly to the perception of the width of
a sound source and the spatial impression of an enclosure [78].
As the density of reflections increases, statistical properties
like reflection density and decay slope become more important than the fine temporal structure. In real enclosures, sound
energy decays exponentially, and the point at which the total
energy of the room impulse response drops 60 dB below its
initial value is called the reverberation time [79]. The reverberation time has a strong influence on how spacious an enclosure is perceived to be [77]. Other quantities that have a strong
influence on the perceived quality of reverberation include
the density of the individual reflections in the late reverberation tail, called the reflection density [79]; the time-dependent
profile of the reflection density, called the echo density profile [80]; and the number of damped resonant frequencies per
Hertz, called the mode density [81]. The typical objective of
perceptually motivated artificial reverberators is to accurately
render the reverberation properties described previously.
Since the early part and the reverberation tail are perceived
differently, a common approach is to model and render them
separately in a typical room auralization algorithm. For the
reverberation tail, a statistically compatible model is usually
acceptable, due to the fact that the human auditory system is not
sensitive to its fine structure. Figure 10 shows the diagram of
a typical binaural auralization system. Here, one module simulates and renders binaurally the direct path and a number of
early reflections, while an artificial reverberator unit renders the
reverberation tail. In this context, we refer to an artificial reverberator as a room acoustic model (typically a delay network)
that aims only at reconstructing important perceptual features
of room reverberation with little regard to its physical accuracy.
By targeting only the perceptual aspects of room reverberation,
vast reductions in computational complexity are possible.
Various room auralization systems have been developed in
the past 20 years [10], [82], [83]. The Digital Interactive Virtual Acoustics system [10], one of the first parametric interactive room auralization systems, simulates all the first- and
second-order reflections and synthesizes them binaurally or for
rendition over loudspeakers. It is capable of simulating the absorption characteristics of different wall materials, air absorption, and
source directivity. Late reverberation is provided via an artificial

IEEE Signal Processing Magazine

May 2017

Table of Contents for the Digital Edition of Signal Processing - May 2017