*longtabletable

# Political regime and COVID 19 death rate: efficient, biasing or simply
different autocracies?

Guilhem Cassan and Milan Van Steenvoort University of Namur, CEPR, DEFIPP,
CRED and CEPREMAP. Email<EMAIL_ADDRESS>University.
Email<EMAIL_ADDRESS>
We are grateful to Jeremie Decalf, Romain Lutaud, Glenn Magerman, Marc
Sangnier and Vincenzo Verardi for helpful discussions and suggestions. We
thank seminar participants at UNamur. Guilhem Cassan thanks CEPREMAP and the
FNRS for financial support. Research on this project was financially supported
by the Excellence of Science (EOS) Research project of FNRS O020918F. All
errors remain our own.

###### Abstract

The difference in COVID 19 death rates across political regimes has caught a
lot of attention. The “ _efficient autocracy_ ” view suggests that autocracies
may be more efficient at putting in place policies that contain COVID 19
spread. On the other hand, the “ _biasing autocracy_ ” view underlines that
autocracies may be under reporting their COVID 19 data. We use fixed effect
panel regression methods to discriminate between the two sides of the debate.
Our results show that a third view may in fact be prevailing: once pre-
determined characteristics of countries are accounted for, COVID 19 death
rates equalize across political regimes. The difference in death rate across
political regime seems therefore to be primarily due to omitted variable bias.

##  1 Introduction

While democratic countries have previously been shown to overperfom compared
to autocracies with respect to health outcomes (Franco et al.,, 2004; Besley
and Kudamatsu,, 2006; Kudamatsu,, 2012; Bollyky et al.,, 2019; Pieters et
al.,, 2016), data shows that, in the specific case of the COVID 19 pandemic,
democratic countries may be fairing much worse (Sorci et al.,, 2020), as
illustrated in Figure 1. Indeed, 50 days after the beginning of the
pandemic111Defined as when the number of cases reaches 0.4 per 100,000 in a
country., democratic countries’ COVID 19 death rate is on average larger than
that of non democratic countries by approximately 3.9 per 100,000. That is, 50
days after the beginning of the pandemic in a democratic country, the fatality
rate in a democracy is on average 7.3 times larger than in an autocracy.

Figure 1: Evolution of COVID 19 data reporting by political regime, time since
first 0.4 cases per 100,000 Total deaths per 100,000. Country level average
per type of regime. Democratic countries are defined as a country with a
polity score $>$ 0.

A debate (Ang,, 2020) has emerged trying to unpack the reasons behind such
wide differences across political regimes: a priori, _all other things equal_
, the political regime should not be related to the spread of a disease. We
distinguish three main hypothesis to explain this difference.

A first interpretation relates to the relative efficiency of social distancing
measures in democracies and autocracies. Some have argued that democracies may
be less well equipped to implement and enforce social distancing policies
(Cepaluni et al.,, 2020; Sorci et al.,, 2020), or that they may be
implementing them with a sub optimal timing (Sebhatu et al.,, 2020). That is,
in this view, autocracies are more able to implement social distancing
measures. We will refer to this interpretation as the _efficient autocracy_
hypothesis.

A second interpretation is that there may be _voluntarily_ misreporting of
COVID 19 data, in particular by non democratic countries. For example, Tuite
et al., 2020a  report that Egypt may have underreported its number of cases,
Tuite et al., 2020b  report that Iran may also have underreported its number
of cases, while Kavanagh, (2020) discusses that China’s political regime may
have hindered its initial response to the pandemic. In this view, there are
systematic differences between the _real_ and the _reported_ death rate. These
differences are _voluntary_ and systematically linked to the type of political
regime. We will refer to this interpretation as the _biasing autocracy_
hypothesis.

A third interpretation has caught less attention (Ashraf,, 2020): democracies
and autocracies tend to have systematically different characteristics apart
from their political regimes. These differences, once accounted for, may in
fact be sufficient to explain the difference in both the _real_ and _reported_
death rate. This would leave the contributions due to _voluntary_ under-
reporting or differences in policies to matter only marginally. An example of
such differences would be that autocracies tend to have much younger
populations (and therefore, a much smaller _real_ death rate, all other things
equal) but also a lower ability to test (and therefore, a much smaller
_reported_ death rate, all other things equal). We refer to this
interpretation as the _simply different autocracy_ hypothesis.

The three aforementionned hypotheses are not mutually exclusive, and simple
reduced form econometric approaches can help measuring how much each of them
contributes to explain the differences observed across political regimes. Take
the case where the econometrician only observes a _reported_ death rate rather
than the _real_ death rate but can observe the variables determining COVID 19
_real_ and _reported_ death rate. Also assume that there are two such types of
variables: fixed characteristics222We call fixed characteristics the variable
that are pre determined and can not be changed in the time horizon of interest
in the paper. In the long run, all characteristics determining the death rate
such as, say, the GDP per capita, can of course be considered at least partly
as an outcome of the political regime (Acemoglu et al.,, 2019). (say, the
share of the population aged 65+ who would determine real death rate or the
number of hospital beds per capita who would determine both real and reported
death rates) and policy response. Under the _efficient autocracy_ hypothesis,
regressing the _reported_ death rate on a measure of democracy and controlling
for all fixed parameters would lead to a positive and significant coefficient
on democracy. However, further controlling for policy response in the
regression should bring the coefficient on democracy close to zero and render
it non significant. That is, all the differences observed between democracies
and autocracies in their _reported_ death rate, once fixed characteristics are
accounted for, would be due to the difference in policy response across these
two types of regime. In this case, there may be a difference between the
_real_ and the _reported_ death rate, but this difference is not
systematically linked to the political regime. In fact, these results would
indicate that the policy response of autocracies is better than that of
democracies, from the perspective of COVID 19 death rate.

Under the _biasing autocracy_ hypothesis, in a regression of _reported_ death
rates on a measure of democracy and all relevant controls (including policy
response), the coefficient on democracy should be positive and significant.
That is, despite controlling for all relevant characteristics and policy
response, there still is a systematic difference between democratic and non
democratic countries which is not accounted for. In that case, the only reason
why a difference may remain would be due to systematic underreporting of
casualties by non democratic regimes. This would be due to the fact that the
difference between the _real_ and the _reported_ death rate is always larger
for autocracies.333Note that our methodology is neutral with respect to which
political regime may be biasing and allows for democratic regimes to be
underreporting more than non democratic regimes. While the _real_ death rate
would be identical once all confounding factors are accounted for, the
_reported_ death rates remain different _even when controlling for the
characteristics influencing non voluntary under reporting_.

We use daily level data of COVID 19 death rates of 137 countries for the first
50 days of the epidemic and resort to simple reduced form econometric methods
using the panel structure of the data. First we start by looking into the
evolution of daily total death rates across political regimes, using a
regression with no controls except country fixed effects (Regression 1). We
then include controls for fixed characteristics of countries that are likely
to determine the real COVID 19 death rate and allow them to matter differently
across time (Regression 2). Finally, we also include controls for the
stringency of social distancing measures and allow these to matter differently
across time (Regression 3). Comparing Regression 2 to Regression 3 addresses
the _efficient autocracy_ hypothesis: any difference between the coefficient
on democratic regime between Regressions 2 and 3 would be due to the
differential in policy response across political regimes. An increase would
indicate that autocracies implement more stringent social distancing measures
that are successful in decreasing the death rate. Comparing Regression 1 to
Regression 3 addresses the _biasing autocracy_ and the _simply different
autocracy_ hypothesis: once all controls for both fixed characteristics and
policy response are accounted for, does the difference between autocratic and
democratic regimes remains (_biasing autocracy_ hypothesis) or vanishes
(_simply different autocracy_ hypothesis)?

Our results indicate that the inclusion of controls for country
characteristics and policy response is in fact enough to remove almost all
cross regime difference in COVID 19 mortality rates. In particular, the
population susceptibility to die upon contamination and geographical
characteristics seem to be the main contributors explaining the differences
observed across political regimes.

Section 2 of this paper presents the data. Section 3 elaborates on the
methodology used to test our hypotheses. Section 4 and 5 present our main
results. Finally, Section 6 provides a discussion of our main findings and
Section 7 concludes.

##  2 Data

In order to investigate our hypothesis, we assemble a dataset that comprises
information on daily cases and deaths in the first 50 days of the pandemic for
137 countries. Our dependent variable, the daily country-level total number of
reported cases and reported deaths due to the COVID-19 virus is from Dong et
al., (2020) 444Last accessed: 16.10.2020. Our main variable of interest, the
classification of political regimes along the autocratic-democratic scale,
comes from the Polity IV project (Center for Systemic Peace,, 2015).

Under the _simply different autocracy_ hypothesis, accounting for the
differences in characteristics of countries would suffice to explain the
difference in reported mortality rates across political regimes. We therefore
collected an extensive array of country level variables. To proxy for income
and health infrastructure differences, we gathered data on gross domestic
product per capita in 2018 from the World economic outlook survey (IMF), and
completed it with the World Factbook (CIA). Furthermore, information on the
number of available hospital beds (per thousand inhabitants) is retrieved from
the World Bank, to account for differences in health infrastructure that may
drive the mortality difference (actual and reported death rates).

To capture differences in demographic characteristics which may explain the
speed of the spread of the disease, we use data on countries’ total population
and density in 2019 from the World Bank, and data on countries’ urbanization
rate in 2019 from the World in Data website. To control for the effect of
geographical characteristics, we collect data on the latitude and longitude of
each country’s capital from the World Cities Database, and classify each
country according to its World Bank region.555These are: East Asia and
Pacific, Europe and Central Asia, Latin America and Caribbean, Middle East and
North Africa, North America, South Asia and Sub-Saharan Africa. Finally, to
control for population risk of mortality, we include the share of population
aged 65+ (from the World Bank) and, since air pollution has been shown to be
associated with COVID 19 death rates (Zhu et al.,, 2020), we use summary
exposure values to ambient ozone pollution and ambient particle matter
pollution from the Global Burden Disease dataset (2017).

To test the _efficient autocracy_ hypothesis, we use information on countries’
different COVID 19 containment policies from the “Variation in Government
Responses to COVID-19” dataset (Hale et al.,, 2020). This dataset includes a
daily policy stringency index based on the aggregation of 17 policy
indicators666Policy indicators include policies with respect to closures or
movement restrictions as well as economic and health system policies. Last
accessed: 16.10.2020..

Given that the data on our dependent variable is at the daily level, this
allows us to construct a panel dataset that comprises a total of 137
countries777See Appendix A.2 for the list of the countries present in our
dataset and their classification as democratic or non democratic., classified
as either democratic or non democratic, for which we have information on all
the previously mentioned national characteristics. Therefore, our dataset
displays information (by day and by country) on the total number of reported
deaths due to the COVID-19 virus, on the stringency of policy measures taken
by a given country, and on all other relevant characteristics of that country.
We focus on the first 50 days since the beginning of the pandemic in each
country, which we define as having more than 0.4 cases per 100,000 888Because
our outcome of interest is death per capita, it makes sense to use cases per
capita rather than the absolute number of cases to determine the beginning of
the pandemic. In Appendix A.4, we show that results are robust to using
alternatives thresholds. In Appendix A.3, we show that the timing of the
beginning of the pandemic does not seem to differ significantly across
political regimes.

##  3 Methodology

Given the country-day panel structure of our data, we resort to fixed effect
panel reduced form econometric methods to look into the differences in COVID
19 casualty rates across political regimes and time. This method allows us to
remove the influence of all time invariant differences across countries by
including countries fixed effects. This further allows us to control for an
extensive set of countries’ pre-determined characteristics and for differences
in containment policies across countries.

We specify the following regression equation, which we run using Ordinary
Least Squares:

$\begin{array}[]{lll}DeathRate_{ct}&=&\sum_{t=1}^{T}\beta_{t}*\mathrm{democratic}_{c}*time.from.start_{t}\\\
&+&\sum_{t=1}^{T}\alpha_{t}*time.from.start_{t}\\\
&+&\sum_{t=1}^{T}\delta_{t}*\mathrm{X}_{c}*time.from.start_{t}\\\
&+&\sum_{t=1}^{T}\gamma_{t}*\mathrm{Y}_{ct}*time.from.start_{t}+\mathrm{\delta}_{c}+\omega_{ct}\\\
&+&\epsilon_{ct}\end{array}$ (1)

$\mathrm{DeathRate}_{ct}$ is the log of daily declared total deaths per
100,000 inhabitants in country c plus one, t days after the beginning of the
pandemic in country c. $\mathrm{democratic}_{c}$ is a dummy indicating that
the Polity IV score of country c is positive. $time.from.start_{t}$ is a set
of fixed effect for each day since the beginning of the pandemic. The
interaction of $\mathrm{democratic}_{c}$ with $time.from.start_{t}$ allows us
to track day by day the evolution of the difference in death rates across
political regimes, a standard approach in economics (see Duflo, (2001) or
Cassan, (2019) among others).

$X_{c}$ is a large set of controls for countries’ pre determined
characteristics: GDP per capita, number of hospital beds per 1000, population,
density, urbanization rate, share of population aged 65+, summary exposure
value to particle matters pollution, summary exposure value to ambient ozone
pollution, as well as for the square of these variables, World Bank regions
fixed effects, latitude and longitude. We interact all these variables with
the $time.from.start_{t}$ fixed effects to allow their effect to vary over
time.

$Y_{ct}$ is a measure of country policy response to the pandemic. It is a
stringency index of governmental response (as measured at t-15 to allow for
lags in its effect) We also include the square level of this variable to allow
for non-linear effects. Furthermore, we interact these variables with the set
of $time.from.start_{t}$ fixed effects, to control for their time varying
effect. $\mathrm{\delta}_{c}$ is a set of country fixed effects. Finally,
$\omega_{ct}$ is a set of day of the week fixed effect interacted with
$time.from.start_{t}$ fixed effects, to control for variations in reporting
across days of the week.

We perform this regression iteratively. First, we do not implement any of the
$X_{c}$ and $Y_{ct}$ controls (Regression 1). This allows us to see the
evolution of the difference in casualty rates across political regimes when no
confounding factors are accounted for. Then, we implement $X_{c}$ but not
$Y_{ct}$ (Regression 2). This will allow us to see how much of the difference
across political regimes survives once the different pre-determined
characteristics of countries are accounted for. Finally, we add the $Y_{ct}$
policy response controls (Regression 3).

This iterative procedure allows us to address the different sides of the
debate on the role of political regime in fighting COVID 19. Comparing
Regression 2 to Regression 3 addresses the _efficient autocracy_ hypothesis:
any difference between the $\beta_{t}$ coefficients on democratic regime
between Regressions 2 and 3 would be due to the differential in policy
response across political regimes. An increase would indicate that autocracies
implement more stringent social distancing measures that are successful in
decreasing the COVID 19 death rate.

Comparing Regression 1 to Regression 3 addresses the _biasing autocracy_ and
_simply different autocracy_ hypothesis: once all controls for both fixed
characteristics and policy response are accounted for, do the $\beta_{t}$
coefficients remain positive (_biasing autocracy_) or do they equalize to zero
(_simply different autocracy_)? Note that these hypotheses are not mutually
exclusive: autocracies may well be efficient, biasing and different at the
same time. Our methodology allows to capture this possibility: if the
$\beta_{t}$ coefficients decrease but remain large and significant when
passing from Regression 1 to Regression 3 and change but remain large and
significant between Regression 2 and Regression 3, then this would support the
simultaneous presence of the three hypotheses.

##  4 Results

Figure 2 presents the $\beta_{t}$ coefficients from Equation 1 for all three
versions of the specification.999In Appendix A.4, we show that results are
robust to using alternatives definition of the start of the pandemic in a
country. The first panel presents the results of Regression 1, when no
controls excepting country and day of the week fixed effects are included. The
death rates start diverging across political regimes roughly 10 days after the
beginning of the pandemic. After 50 days, the $\beta_{t}$ coefficient reaches
0.5, which represents 135% of the mean.

The second panel includes controls for pre-determined characteristics
interacted with day fixed effects. The $\beta_{t}$ coefficients become
precisely estimated zeros. That is, once countries’ differences in
characteristics are taken into account, the difference in death rates across
political regimes does not survive. Hence, we do not find support for the
_biasing autocracy_ hypothesis with our methodology.

The third panel adds controls for countries’ policy response to the pandemic.
As a result, our coefficients of interest $\beta_{t}$ remain virtually
unaffected. That is, our results do not support the _efficient autocracy_
hypothesis.101010To test if these results are driven by an outlier country, we
run Regression 1, 2 and 3 137 times, removing one country at a time. We plot
the 50 coefficients of interests of each of these 411 regressions in Figure 6
of Appendix A.5. It can be seen that the results are robust to the omission of
any single country. Therefore, once systematic differences across countries’
characteristics and policy responses are taken into consideration, the
differences in death rates apparent in Figure 1 and in the first panel of
Figure 2 vanish. The reason why reported COVID 19 death rates differ across
political regimes is fully accounted for by factors which systematically
differ between democracies and autocracies. That is, our results indicate that
the _simply different autocracy_ hypothesis is prevailing. That is, our
results do not support neither the fact that autocracies are more efficient at
controlling the pandemic nor that they are voluntarily under reporting
casualty more often.

Figure 2: Evolution of COVID 19 log death per 100,000 since 0.4 cases per
100,000. 95% CI.

No Controls

Controlling for pre-determined characteristics

Controlling for pre-determined characteristics and policy response

Standard errors are two way clustered at the country and day level.

##  5 Which characteristics matter?

Having seen that the inclusion of controls is sufficient to remove the
“political regime” effect on COVID 19 death rate, we now move to a related
question: which characteristics are contributing to closing the COVID 19 death
rate gap between autocratic and democratic gap? In order to do so, we group
our control variables in five categories:
\- Geographical controls (latitude, longitude, World Bank region fixed
effects)
\- Wealth controls (GDP per capita, hospital beds per capita). These will
proxy for the quality of the health system in the country, and will likely
influence both the _real_ and the _reported_ death rate.
\- Demographic controls (population, density, urbanization rate): these are
likely to influence the speed of the spread of the pandemic.
\- Population fragility controls (share of population aged 65+ and exposure to
pollution): these are likely to influence the lethality of COVID 19 for a
given spread of the disease.
\- Policy response.
We run Regression 1, removing each of these groups of controls one at a time.
Figure 3 presents the $\beta_{t}$ coefficients for each of these regressions.
It also includes the coefficients of the original results of Regression 1 for
comparison (we do not report the confidence intervals on these coefficients
for readability).

Two set of controls seem to matter most. The first set of controls are the
controls related to population fragility (which contain notably the share of
population aged 65+). The second set of controls that seems to affect the
coefficient is the geographic controls set. That is, the main reason why
mortality rates from COVID seem to differ across political regimes may be that
autocratic regime tend to have a population that is less susceptible to die
from COVID 19 and to be located in regions in which COVID 19 appears to be
less lethal. Interpreting the geographic controls is not straightforward, but
it is reasonable to say that they seem to indicate that country
characteristics correlated with geography and not captured by our extensive
set of controls may play an important part in explaining COVID 19 mortality.

Figure 3: Coefficient on “Democracy” and introduction of controls

No Population fragility controls

No Geographic controls

No Economic controls

No Demographic controls

No Policy Response controls

Standard errors are two way clustered at the country and day level.

##  6 Discussion

A few remarks are in order to help interpret our results. First, one should
keep in mind that the variables that we consider pre-determined
characteristics, such as the GDP per capita are only pre-determined in the
time horizon that we are considering. Over the long run, they are an outcome
of the political regime. See for example Acemoglu et al., (2019), who show
that democracy causes growth. In that sense, our results do not take into
consideration the long term effect of political regimes on the variables that
may determine COVID 19 death rates.

For instance, a better health care system will lead to both a lower _real_
death rate (infected individuals are better treated) and a higher _reported_
death rate (infected individuals’ death is better attributed to COVID 19). If,
as has been argued in the literature (Franco et al.,, 2004; Besley and
Kudamatsu,, 2006; Kudamatsu,, 2012; Bollyky et al.,, 2019; Pieters et al.,,
2016), democracies tend to have better health care policies; in the long run,
the health care system (which we consider as pre-determined) will be better in
democracies because of the political regime, which will causally affect both
_real_ and _reported_ death rates across political regimes.

Second, our focus is only on COVID 19 death rates. Arguably, however, one may
have wanted to study death rates from all causes rather than just from COVID
19. Even in times of pandemic, governments should aim at preserving the health
of their citizens from all sources of harm, not from one specific cause. Given
the attention given to COVID 19 death rates, a pro-democracy argument would be
that while there does not seem to be differences across political regimes for
COVID 19 death rates, this may hide the fact that autocracies have focused on
decreasing COVID 19 death rate at the expense of death from other sources.

One could develop this idea even further and argue that democracies have
higher COVID 19 mortality rates because they are better at preventing non
COVID 19 deaths, leading to a population which is on average older and
therefore more likely to die if infected by COVID 19. This question can
unfortunately not be tackled with the available data, and we leave it to
future research (when mortality data from all causes will be available for a
sufficient number of countries), but note that the differences in countries’
population’s susceptibility to die from COVID 19 upon contamination seem to be
one of the main drivers of the difference in COVID 19 mortality rates across
political regimes, all other things equal.

Third, our findings do not contradict previous studies on under reporting of
COVID 19 data, in particular country specific studies. Indeed, because of the
statistical analysis used, our results do not imply that no single country
underreported or manipulated its COVID 19 mortality data. However, our results
do address the widespread idea that autocracies are systematically and
willingly under reporting COVID 19 casualties. What our results do indicate is
that under reporting (by any political regime) is primarily due to the
different characteristics of countries that are correlated with the political
regime rather than a direct causal effect of the political regime.

That is, a plausible interpretation is that autocratic governments may well
under report data while not manipulating it. One could argue that even if
autocracies are under reporting COVID 19 death rates, this may be primarily
driven by their overall incapacity to link death to its cause rather than to a
direct attempt at data manipulation. The low reported COVID 19 death rate in
autocracies may in part be due to the lower level of development of both the
public health infrastructure and the statistical apparatus of autocracies.
However, and this goes back to our first point, over the long run, public
health infrastructure and statistical apparatus may well be determined by the
political regime.

##  7 Conclusion

In this paper, we investigated the COVID 19 death rate gap between democratic
and autocratic countries. We formulated three main hypotheses based on the
previous literature: the gap can be due to the fact that autocracies are more
efficient at implementing restricting policy measures; that autocracies are
underreporting their COVID 19 data and that autocracies simply have different
characteristics that can explain the death rate gap. Our analysis, relying on
simple econometric tools, allows to make progress in the debate around the
sources of the observed differences in COVID 19 death rates across political
regimes.

We show that once pre-determined characteristics and policy responses are
taken into account, COVID 19 death rates do not exhibit any difference across
political regimes: the coefficients on democracy become precisely estimated
zeros. Our results therefore do not show support neither for the _efficient
autocracy_ nor for the _biasing autocracy_ hypotheses, as we do not find
evidence that autocracies are neither systematically better at preventing
COVID 19 death nor that they are more often under reporting casualties.

Our findings indicate that democracies and autocracies are _simply different_
, and that these differences are sufficient to account for all the observed
differences in COVID 19 death rates. Finally, we analyzed which controls
matter most in explaining the difference in COVID 19 death rates. We found
that characteristics related to the vulnerability of the population to the
disease and geographical controls appeared to be of significant importance.

## References

  * Acemoglu et al., (2019) Acemoglu, D., Naidu, S., Restrepo, P., and Robinson, J. A. (2019).  Democracy does cause growth.  Journal of Political Economy, 127(1):47–100.
  * Ang, (2020) Ang, Y. Y. (2020).  When covid-19 meets centralized, personalized power.  Nature Human Behavior, 4:445–447.
  * Ashraf, (2020) Ashraf, B. N. (2020).  Devastation caused by covid-19: Is democracy to blame?  Working Paper.
  * Besley and Kudamatsu, (2006) Besley, T. and Kudamatsu, M. (2006).  Health and democracy.  American Economic Review, 96(2):313–318.
  * Bollyky et al., (2019) Bollyky, T. J., Templin, T., Cohen, M., Schoder, D., Dieleman, J. L., and Wigley, S. (2019).  The relationships between democratic experience, adult health, and cause-specific mortality in 170 countries between 1980 and 2016: an observational analysis.  The Lancet, 393(10181):1628 – 1640.
  * Cassan, (2019) Cassan, G. (2019).  Affirmative action, education and gender: Evidence from India.  Journal of Development Economics, 136(C):51–70.
  * Center for Systemic Peace, (2015) Center for Systemic Peace (2015).  Polity IV Project.
  * Cepaluni et al., (2020) Cepaluni, G., Dorsch, M. T., and Branyiczki, R. (2020).  Political regimes and deaths in the early stages of the covid-19 pandemic.  Working Paper.
  * Dong et al., (2020) Dong, E., Du, H., and Gardner, L. (2020).  An interactive web-based dashboard to track covid-19 in real time.  The Lancet Infectious Diseases, 20(5):533 – 534.
  * Duflo, (2001) Duflo, E. (2001).  Schooling and labor market consequences of school construction in indonesia: Evidence from an unusual policy experiment.  American Economic Review, 4(91):795–813.
  * Franco et al., (2004) Franco, Á., Álvarez-Dardet, C., and Ruiz, M. T. (2004).  Effect of democracy on health: ecological study.  BMJ, 329(7480):1421–1423.
  * Hale et al., (2020) Hale, T., Webster, S., Petherick, A., Phillips, T., and Kira, B. (2020).  Oxford covid-19 government response tracker.
  * Kavanagh, (2020) Kavanagh, M. M. (2020).  Authoritarianism, outbreaks, and information politics.  The Lancet Public Health, 5(3):e135 – e136.
  * Kudamatsu, (2012) Kudamatsu, M. (2012).  Has Democratization Reduced Infant Mortality in Sub-Saharan Africa? Evidence from Micro Data.  Journal of the European Economic Association, 10(6):1294–1317.
  * Pieters et al., (2016) Pieters, H., Curzi, D., Olper, A., and Swinnen, J. (2016).  Effect of democratic reforms on child mortality: a synthetic control analysis.  The Lancet Global Health, 4(9):e627 – e632.
  * Sebhatu et al., (2020) Sebhatu, A., Wennberg, K., Arora-Jonsson, S., and Lindberg, S. I. (2020).  Explaining the homogeneous diffusion of covid-19 nonpharmaceutical interventions across heterogeneous countries.  Proceedings of the National Academy of Sciences, 117(35):21201–21208.
  * Sorci et al., (2020) Sorci, G., Faivre, B., and Morand, S. (2020).  Why does covid-19 case fatality rate vary among countries?  SSRN.
  * (18) Tuite, A. R., Ng, V., Rees, E., Fisman, D., Wilder-Smith, A., Khan, K., and Bogoch, I. I. (2020a).  Estimation of the covid-19 burden in egypt through exported case detection.  The Lancet Infectious Diseases, 20(8):894.
  * (19) Tuite, A. R., Sherbo, R., Watts, A., Fisman, D., and Khan, K. (2020b).  Estimation of coronavirus disease 2019 (covid-19) burden and potential for international dissemination of infection from iran.  Annals of Internal Medicine, 10(172):699–701.
  * Zhu et al., (2020) Zhu, Y., Xie, J., Huang, F., and Cao, L. (2020).  Association between short-term exposure to air pollution and covid-19 infection: Evidence from china.  Science of The Total Environment, 727:138704.

##  Appendix A Appendix

###  A.1 Data sources and descriptive statistics

Table 1 presents the data sources used to compute the variables exploited in
our analysis.

Table 1: Datasources. Data | Source
---|---
COVID19 Death Rate | Dong et al. (2020)
COVID19 Cases | Dong et al. (2020)
Democratic | Polity IV project (Center for Systemic Peace, 2015)
Stringency Index of Policy Response | Variation in Government Responses to COVID-19 (Hale et al., 2020).
Gross Domestic Product per capita | World Economic Outlook, IMF (2018) + World Factbook, CIA (2018)
Share of 65+ | World Bank (2019)
Population Density | World Bank (2019)
Population | World Bank (2019)
Urbanization Rate | World in Data
Hospital Beds per 1000 | World Bank
Summary Exposure Value to Air Pollution | Global Burden of Disease (2017)
Summary Exposure Value to Ambiant Ozone Pollution | Global Burden of Disease (2017)
Latitude and Longitude | World Cities Database
World Regions | World Bank

Table 2: Descriptive statistics  | Mean | sd | Min | Max
---|---|---|---|---
Democratic | 0.76 | 0.43 | 0.00 | 1.00
Log total deaths per 100,000 | 0.37 | 0.65 | 0.00 | 4.08
Share of 65+ | 9.56 | 6.64 | 1.16 | 28.00
GDP Per Capita | 23,636 | 23,544 | 727 | 132,886
Population in million | 52.97 | 170.10 | 0.55 | 1,397.71
Hospital beds per 1000 | 3.0 | 2.5 | 0.1 | 13.4
Population Density | 206.9 | 779.5 | 2.1 | 8,829.1
Urbanization rate | 62 | 22 | 13 | 100
Summary exposure value to ambient ozone pollution - Age standardized | 36 | 13 | 2 | 53
Summary exposure value to ambient particulate matter pollution - Age standardize | 32 | 17 | 7 | 90
Stringency t-15 | 63 | 29 | 0 | 100
Observations | 6,987 |  |  |

Table 2 presents the descriptive statistics for our variable. Our final
dataset comprises a total of 137 countries for which we have all the variables
and for which we observe 50 days of data since the beginning of the pandemic.

###  A.2 Polity score, by country

Table LABEL:tab:polity_score presents the polity IV score of all countries
that are included in our sample. Countries whose score is higher than 0 are
classified as democratic.

Table 3: Polity Score, by country Country | Polity Score | Country | Polity Score
---|---|---|---
Afghanistan | -1 | Kuwait | -7
Albania | 9 | Kyrgyz Republic | 8
Algeria | 2 | Latvia | 8
Argentina | 9 | Lebanon | 6
Australia | 10 | Liberia | 7
Austria | 10 | Libya | -7
Azerbaijan | -7 | Lithuania | 10
Bahrain | -10 | Luxembourg | 10
Bangladesh | -6 | Madagascar | 6
Belarus | -7 | Malawi | 6
Belgium | 8 | Malaysia | 7
Benin | 7 | Mali | 5
Bhutan | 7 | Mauritius | 10
Bolivia | 7 | Mexico | 8
Botswana | 8 | Moldova | 9
Brazil | 8 | Mongolia | 10
Bulgaria | 9 | Morocco | -4
Burkina Faso | 6 | Mozambique | 5
Burundi | -1 | Myanmar | 8
Cabo Verde | 10 | Nepal | 7
Cambodia | -4 | Netherlands | 10
Cameroon | -4 | New Zealand | 10
Canada | 10 | Nicaragua | 6
Central African Republic | 6 | Niger | 5
Chile | 10 | Nigeria | 7
China | -7 | Norway | 10
Colombia | 7 | Oman | -8
Costa Rica | 10 | Pakistan | 7
Croatia | 9 | Panama | 9
Cuba | -5 | Paraguay | 9
Cyprus | 10 | Peru | 9
Czech Republic | 9 | Philippines | 8
Denmark | 10 | Poland | 10
Djibouti | 3 | Portugal | 10
Dominican Republic | 7 | Qatar | -10
Ecuador | 5 | Romania | 9
Egypt, Arab Rep. | -4 | Russian Federation | 4
El Salvador | 8 | Saudi Arabia | -10
Estonia | 9 | Singapore | -2
Eswatini | -9 | Slovakia | 10
Ethiopia | 1 | Slovenia | 10
Fiji | 2 | Spain | 10
Finland | 10 | Sri Lanka | 6
France | 9 | Sudan | -4
Gabon | 3 | Suriname | 5
Gambia, The | 4 | Sweden | 10
Georgia | 7 | Switzerland | 10
Germany | 10 | Syrian Arab Republic | -9
Ghana | 8 | Tajikistan | -3
Greece | 10 | Tanzania | 3
Guatemala | 8 | Thailand | -3
Guinea | 4 | Timor-Leste | 8
Guyana | 7 | Togo | -2
Haiti | 5 | Trinidad and Tobago | 10
Honduras | 7 | Tunisia | 7
Hungary | 10 | Turkey | -4
India | 9 | Uganda | -1
Indonesia | 9 | Ukraine | 4
Iran | -7 | United Arab Emirates | -8
Iraq | 6 | United Kingdom | 8
Ireland | 10 | United States | 8
Israel | 6 | Uruguay | 10
Italy | 10 | Uzbekistan | -9
Jamaica | 9 | Venezuela | -3
Japan | 10 | Vietnam | -7
Jordan | -3 | Yemen, Rep. | 3
Kazakhstan | -6 | Zambia | 6
Kenya | 9 | Zimbabwe | 4
Korea, Rep. | 8 |  |

###  A.3 Political regime and start of the pandemic

Our analysis focuses on the evolution of the death rates across time since the
beginning of the pandemic in each country. We verify whether the political
regime determines when these first contaminations are reached, which may imply
that the timing that we rely on is biased. In order to do so, we run the
following OLS regressions:

$\displaystyle\mathrm{time.to.start}_{c}=\alpha+\beta_{1}*\mathrm{democratic}_{c}+\
\mathrm{X}_{c}+\epsilon_{c}$ (2)

$\mathrm{time.to.start}_{c}$ is the number of days between the start of the
pandemic in country c and the $20^{th}$ of January. We specify three
variations of Equation 2: if the country has declared 4 or 6 per 100,000 cases
or has reached 100 cases. Table 4 presents the results. We find no
statistically significant difference across political regimes for the start of
the pandemic. Note that the number of countries reaching both 100 total cases
and for which we observe 50 days since the first 100 case is 135: two
countries do not reach 50 days after the first 100 cases in our data compared
to our main sample.

Table 4: Time to first cases and political regime

| 0.4 c. per 100,000 | 0.6 c. per 100,000 | 100 c.
---|---|---|---
Democracy | -1.19 | -0.68 | 4.11
| (5.91) | (6.46) | (5.04)
R-sq | 0.58 | 0.57 | 0.57
Observations | 137 | 137 | 135

Heteroskedasticity-robust standard errors in parentheses * p$<$.10 ** p$<$.05
*** p$<$.01. Controls included are: GDP per capita, population, density,
urbanization rate, share of 65 and above, number of hospital beds per capita
and the square of all preceding variables, latitude, longitude, World Bank
region fixed effect.

###  A.4 Alternative definitions of the start of the pandemic

Figures 4 and 5 reproduce Figure 2, using 0.6 cases per 100,000 and 100 cases
reported cases as the definition of the start of the pandemic in a country,
respectively. Results remain unaffected by this change in definition of the
beginning of the pandemic. Note that the number of countries reaching both 100
total cases and for which we observe 50 days since the first 100 case is 135:
two countries do not reach 50 days after the first 100 cases in our data
compared to our main sample.

Figure 4: Evolution of COVID 19 log death per 100,000 since 0.6 cases per
100,000. 95% CI.

No Controls

Controlling for pre-determined characteristics

Controlling for pre-determined characteristics and policy response

Standard errors are two way clustered at the country and day level. Figure 5:
Evolution of COVID 19 log death per 100,000 since 100 cases. 95% CI.

No Controls

Controlling for pre-determined characteristics

Controlling for pre-determined characteristics and policy response

Standard errors are two way clustered at the country and day level.

###  A.5 Robustness check: removing one country at a time

In order to test if an outlier country is driving our findings, we run each
regression 133 times, removing one country at a time. We plot the 50
coefficients of interests of each of these 399 regressions in Figure 6, which
replicates Figure 2. It can be seen that the results are robust to the
omission of any single country.

Figure 6: Removing countries one by one: Evolution of COVID 19 log death per
100,000 since 0.4 cases per 100,000.

No Controls

Controlling for pre-determined characteristics

Controlling for pre-determined characteristics and policy response

CI not reported for readability


capbtabboxtable[][]

# PanoHead: Geometry-Aware 3D Full-Head Synthesis in 360∘

Sizhe An1,2 Hongyi Xu1 Yichun Shi1 Guoxian Song1 Umit Y. Ogras2 Linjie Luo1
1ByteDance Inc. 2University of Wisconsin-Madison

###### Abstract

Synthesis and reconstruction of 3D human head has gained increasing interests
in computer vision and computer graphics recently. Existing state-of-the-art
3D generative adversarial networks (GANs) for 3D human head synthesis are
either limited to near-frontal views or hard to preserve 3D consistency in
large view angles. We propose PanoHead, the first 3D-aware generative model
that enables high-quality view-consistent image synthesis of full heads in
$360^{\circ}$ with diverse appearance and detailed geometry using only in-the-
wild unstructured images for training. At its core, we lift up the
representation power of recent 3D GANs and bridge the data alignment gap when
training from in-the-wild images with widely distributed views. Specifically,
we propose a novel two-stage self-adaptive image alignment for robust 3D GAN
training. We further introduce a tri-grid neural volume representation that
effectively addresses front-face and back-head feature entanglement rooted in
the widely-adopted tri-plane formulation. Our method instills prior knowledge
of 2D image segmentation in adversarial learning of 3D neural scene
structures, enabling compositable head synthesis in diverse backgrounds.
Benefiting from these designs, our method significantly outperforms previous
3D GANs, generating high-quality 3D heads with accurate geometry and diverse
appearances, even with long wavy and afro hairstyles, renderable from
arbitrary poses. Furthermore, we show that our system can reconstruct full 3D
heads from single input images for personalized realistic 3D avatars.

Figure 1: Our PanoHead enables $360^{\circ}$ view-consistent photo-realistic
full-head image synthesis with high-fidelity geometry, enabling authentic 3D
portraits creation from a single-view image.

††Project page: https://sizhean.github.io/panohead

##  1 Introduction

Photo-realistic portrait image synthesis has been a continuous focus in
computer vision and graphics, with a wide range of downstream applications in
digital avatars, telepresence, immersive gaming, and many others. Recent
advances in Generative Adversarial Networks (GANs) [12] has demonstrated
strikingly high image synthesis quality, indistinguishable from real
photographs [21, 22, 19]. However, contemporary generative approaches operate
on 2D convolutional networks without modeling the underlying 3D scenes.
Therefore 3D consistency cannot be strictly enforced when synthesizing head
images under various poses.

To generate 3D heads with diverse shapes and appearances, traditional
approaches require a parametric textured mesh model [2, 25] learned from large
3D scan collections. However, the rendered images lack fine details and have
limited perceptual quality and expressiveness. With the advent of
differentiable rendering and neural implicit representation [28, 47],
conditional generative models have been developed to generate more realistic
3D-aware face images [44, 45, 17, 53]. However, those approaches typically
require multi-view image or 3D scan supervision, which are hard to acquire and
have limited appearance distribution as those are usually captured in
controlled environments.

3D-aware generative models have recently seen rapid progress, fueled by the
integration of implicit neural representation in 3D scene modeling and
Generative Adversarial Networks (GANs) for image synthesis [37, 6, 29, 5, 40,
31, 48]. Among them, the seminal 3D GAN, EG3D [5], demonstrates striking
quality in view-consistent image synthesis, trained only from in-the-wild
single-view image collections. However, these 3D GAN approaches are still
limited to synthesis in near-frontal views.

In this paper, we propose _PanoHead_ , a novel 3D-aware GAN for high-quality
full 3D head synthesis in $360^{\circ}$ trained from only in-the-wild
unstructured images. Our model can synthesize _consistent 3D heads viewable
from all angles_ , which is desirable by many immersive interaction scenarios
such as digital avatars and telepresence. To the best of our knowledge, our
method is _the first_ 3D GAN approach to achieve full 3D head synthesis in
$360^{\circ}$.

Extending 3D GAN frameworks such as EG3D [5] to full 3D head synthesis poses
several significant technical challenges: Firstly, many 3D GANs [5, 31] cannot
separate foreground and background, inducing 2.5D head geometry. The
background, formulated typically as a wall structure, is entangled with the
generated head in 3D and therefore prohibits rendering from large poses. We
introduce a _foreground-aware tri-discriminator_ that jointly learns the
decomposition of the foreground head in 3D space by distilling the prior
knowledge in 2D image segmentation.

Secondly, while being compact and efficient, current hybrid 3D scene
representations, like tri-plane [5], introduce strong projection ambiguity for
360∘ camera poses, resulting in ‘mirrored face’ on the back head. To address
the issue, we present a novel 3D _tri-grid volume representation_ that
disentangles the frontal features with the back head while maintaining the
efficiency of tri-plane representations.

Lastly, obtaining well-estimated camera extrinsics of in-the-wild back head
images for 3D GANs training is extremely difficult. Moreover, an image
alignment gap exists between these and frontal images with detectable facial
landmarks. The alignment gap causes a noisy appearance and unappealing head
geometry. Thus, we propose a novel _two-stage alignment scheme_ that robustly
aligns images from any view consistently. This step decreases the learning
difficulty of 3D GANs significantly. In particular, we propose a camera self-
adaptation module that dynamically adjusts the positions of rendering cameras
to accommodate the alignment drifts in the back head images.

Our framework substantially enhances the 3D GANs’ capabilities to adapt to in-
the-wild full head images from arbitrary views, as shown in Figure 1. The
resulting 3D GAN not only generates high-fidelity 360∘ RGB images and
geometry, but also achieves better quantitative metrics than state-of-the-art
methods. With our model, we showcase compelling 3D full head reconstruction
from a single monocular-view image, enabling easily accessible 3D portrait
creation.

In summary, our main contributions are as follows:

  * •

The first 3D GAN framework that enables view-consistent and high-fidelity
full-head image synthesis with detailed geometry, renderable in $360^{\circ}$.
We demonstrate our approach in high-quality monocular 3D head reconstruction
from in-the-wild images.

  * •

A novel tri-grid formulation that balances efficiency and expressiveness in
representing 3D $360^{\circ}$ head scenes.

  * •

A foreground-aware tri-discriminator that disentangles 3D foreground head
modeling from 2D background synthesis.

  * •

A novel two-stage image alignment scheme that adaptively accommodates
imperfect camera poses and misaligned image cropping, enabling training of 3D
GANs from in-the-wild images with wide camera pose distribution.

##  2 Related Work

Figure 2:  Our framework consists of three main components: a foreground-aware
generator G, discriminator D, and a neural renderer R. A mapping network first
maps latent code $z$ and conditioned camera pose $c_{con}$ into the
intermediate latent code $w$. The generator G then takes $w$ to obtain the 3D
tri-grid representation features $f$. With $f$ and rendering camera pose
$c_{cam}$, the neural renderer R synthesizes super-resolved image $I^{+}$,
bilinear-upsampled image $I$, and super-resolved mask $I^{m+}$. Finally, the
foreground-aware tri-discriminator D critiques ($I^{+}$, $I$, $I^{m+}$) along
with real images. The data processing pipeline is shown in the right side. The
real images are cropped with modified YOLO bounding boxes yet they often
differ at scale and location due to lacking accurate facial landmarks. With
the camera self-adaptation scheme, the rendering camera pose $c_{cam}$ is able
to correct itself to generate images with consistent scale and location.

#### 3D Head Representation and Rendering.

To represent 3D heads with diverse shapes and appearances, a line of work has
targeted parametric textured mesh representation, such as 3D Morphable Model
(3DMM) [2, 33, 3, 4] for faces and FLAME head model [25], learned from 3D
scans. However, these parametric representations do not model photo-realistic
appearance and geometry beyond the front face or skull. The neural implicit
functions [47] have recently emerged as powerful continuous and differential
representations of 3D scenes. Among them, Neural Radiance Field (NeRF) [28, 1]
has been widely adopted in digital head modeling [17, 32, 10, 15, 34, 43] due
to its superiority in modeling complex scene details and synthesizing
multiview images with inherited 3D consistency. In contrast to optimizing a
person-specific neural radiance field from multiview images or temporal
videos, our approach builds a generative NeRF from unstructured 2D monocular
images. Recently implicit-explicit hybrid 3D representation has been explored
for better efficiency [5, 9, 27]. Among them, the tri-plane formulation
proposed in EG3D [5] demonstrates a highly efficient 3D scene representation
with high-quality view-consistent image synthesis. The tri-plane
representation can scale efficiently with resolution, enabling greater detail
for equal capacity. Our tri-grid representation transforms the tri-plane
representation into a more expressive space for better feature embedding in
unconditional 3D head synthesis.

#### Single- or Few-view Supervised 3D GANs.

Given the impressive progress of GANs on 2D image generation [12, 21, 22, 19],
many studies have attempted to extend them to 3D-aware generation. These GANs
aim to learn a generalizable 3D representation from 2D image a collections.
For face synthesis, Szabo  _et al_. [42] first proposed using vertex position
maps as the 3D representation to generate textured mesh outputs. Shi  _et al_.
[39] proposed a self-supervised framework to convert 2D StyleGANs [21] into 3D
generative models, although its generalizability is bounded by its base 2D
StyleGAN. GRAF [37] and pi-GAN [6] are the first to integrate NeRF into 3D
GANs. However, their performance is limited by the intense computation cost of
forwarding and backwarding a complete NeRF. Many recent studies [8, 29, 48,
13, 31, 49, 5, 40, 11, 30, 38] have attempted to improve the efficiency and
quality of such NeRF-based GANs. Specifically, EG3D [5], which we build our
work upon, introduces tri-plane representation that can leverage a 2D GAN
backbone for generating efficient 3D representation and is shown outperforming
other 3D representations [38]. Parallel to these works, another thread of
studies [50, 41, 46, 30] have been working on controllable 3D GANs that can
manipulate the generated 3D faces or bodies.

##  3 Methodology

###  3.1 PanoHead Overview

To synthesize realistic and view-consistent full head images, we build
PanoHead upon a state-of-the-art 3D-aware GAN, _i.e_. EG3D [5], due to its
efficiency and synthesis quality. Specifically, EG3D leverages StyleGAN2 [22]
backbone to output a tri-plane representation that represents a 3D scene with
three 2D feature planes. Given a desired camera pose $c_{cam}$, the tri-plane
is decoded with a MLP network and volume rendered into a feature image,
followed by a super-resolution module to synthesize a higher resolution RGB
image $I^{+}$. Both the low and high resolution images are then jointly
optimized by a dual discriminator $\bm{\mathbf{D}}$.

In spite of EG3D’s success in generating frontal faces, we found it to be a
much more challenging task to adapt to 360∘ in-the-wild full head images for
the following reasons: 1) foreground-background entanglement prohibit large
pose rendering, 2) strong inductive bias from tri-plane representation causes
mirroring face artifacts on the back head, and 3) noisy camera labels and
inconsistent cropping of back head images. To address these problems, we
introduce a background generator and a tri-discriminator for decoupling
foreground and background (Section 3.2), an efficient yet more expressive tri-
grid representation while still being compatible with StyleGAN backbone
(Section 3.3), and a two-stage image alignment scheme with an self-adaptation
module that dynamically adjusts rendering cameras during training (Section
3.4). The overall pipeline for our model is illustrated in Figure 2.

###  3.2 Foreground-Aware Tri-Discrimination

A typical challenge of state-of-the-art 3D-aware GANs, like EG3D [5], is the
entangled foreground with the background of synthesized images. Regardless of
the highly detailed geometry reconstruction, directly training the 3D GAN from
in-the-wild RGB image collections, such as FFHQ [21], results in a 2.5D face,
as illustrated in Figure 3 (a). Augmenting with image supervisions from the
side and back of the head helps build up the full-head geometry with
reasonable back head shapes. However, it does not solve the problem because
the tri-plane representation itself is not designed to represent separated
foreground and background.

To disentangle the foreground from the background, we first introduce an
additional StyleGAN2 network [22] to generate 2D backgrounds at the same
resolution of raw feature image $I^{r}$. During volume rendering, the
foreground mask $I^{m}$ can be obtained by:

$\displaystyle
I^{r}(r)=\int_{0}^{\infty}w(t)f(r(t))dt,\,\,I^{m}(r)=\int_{0}^{\infty}w(t)dt,$
(1) $\displaystyle
w(t)=exp\bigl{(}-\int_{0}^{t}\sigma(r(s))ds\bigr{)}\sigma(r(t)),$ (2)

where $r(t)$ represents a ray emitted from the rendering camera center. The
foreground mask is then used to compose a new low-resolution image $I^{gen}$:

$I^{gen}=(1-I^{m})I^{bg}+I^{r},$ (3)

which is fed into the super-resolution module. Note that the computation cost
of background generator is insignificant since its output has a much lower
resolution than the tri-plane generator and super-resolution module.

Figure 3: Geometry and RGB images from dual-discrimination (a) and foreground-
aware tri-discrimination (b, c). EG3D (a) fails to decouple the background.
PanoHead’s tri-discrimination offers both background-free geometry (b) and
background-switchable full head image synthesis (c).

Simply adding a background generator does not fully decouple it from the
foreground since the generator tends to synthesize foreground content in the
background. Thus, we propose a novel foreground-aware tri-discriminator to
supervise the rendered foreground mask along with the RGB images.
Specifically, the input of the tri-discriminator has 7 channels, composed with
a bilinearly-upsampled RGB image $I$ , a super-resolved RGB image $I^{+}$ and
single-channel upsampled foreground mask $I^{m+}$. The additional mask channel
allows the 2D segmentation prior knowledge to be back-propagated into the
density distribution of the neural radiance field. Our approach reduces the
learning difficulty in shaping the 3D full head geometry from unstructured 2D
images, enabling authentic geometry ((Figure 3 (b))) and appearance synthesis
of a full head composable with various backgrounds (Figure 3 (c)). We note
that in constrast from ENARF-GAN [30] that employs a single discriminator for
RGB images composed of synthesized foreground and background images using a
dual-generated mask, our tri-discriminator better ensures view-consistent
high-resolution outputs.

Figure 4: Comparison between tri-plane (a) and tri-grid (b) architecture in
$Z$ axis. With tri-plane, two different points’ projections share the feature
from the plane $P^{XY}$, which introduces representation ambiguity. With tri-
grid, the features for the above two points are trilinearly interpolated from
two different planes, thus generating distinct features. Figure 5: Images
synthesis with tri-plane and tri-grid ($D=3$). Due to the projection
ambiguity, tri-plane representation (a) can generate good-quality front face
image yet with a ‘mirrored face’ on back head, while our tri-grid
representation synthesizes high-quality back head appearance and geometry (b).

###  3.3 Feature Disentanglement in Tri-Grid

The tri-plane representation, proposed in EG3D [5], offers an efficient
representation for 3D generation. The neural radiance density and appearance
of a volume point are obtained by projecting its 3D coordinate over three
axis-aligned orthogonal planes and decoding the sum of three bilinearly
interpolated features with a tiny MLP. However, when synthesizing a full head
in $360^{\circ}$, we observe tri-plane is limited in expressiveness and
suffers from mirroring-face artifacts. The problem is even pronounced when the
camera distribution of the training images is unbalanced. The root cause is
the inductive bias originating from tri-plane projection, where one point on a
2D plane has to represent features of different 3D points. For example, a
point on the front face and a point on the back hair will be projected to the
same point on the $XY$ plane $P^{XY}$ (orthogonal to $Z$ axis), as illustrated
in Figure 4 (a). Although the other two planes should theoretically provide
complementary information to alleviate this projection ambiguity, we found it
not the case when there is less visual supervision from the back or when the
structure of the back head is challenging to learn. The tri-planes are prone
to borrow features from the front face to synthesize the back head, referred
to as mirroring-face artifacts here (Figure 5(a)).

To reduce the inductive bias of the tri-plane, we lift its formulation into a
higher dimension by augmenting tri-plane with an additional depth dimension.
We call this enriched version as a tri-grid. Instead of having three planes
with a shape of $H\times W\times C$ with $H$ and $W$ being the spatial
resolution and $C$ being the number of channel, each of our tri-grid has a
shape of $D\times H\times W\times C$, where $D$ represents the depth. For
instance, to represent spatial features on the $XY$ plane, tri-grid will have
$D$ axis-aligned feature planes $P^{XY}_{i},i=1,\ldots,D$ uniformly
distributed along the $Z$ axis. We query any 3D spatial point by projecting
its coordinate onto each of the tri-grid, retrieving the corresponding feature
vector by _tri-linear interpolation_. As such, for two points sharing the same
projected coordinates but with different depths, the corresponding feature
would be likely to be interpolated from non-shared planes (Figure 4 (b)). Our
formulation disentangles the feature presentation of the front face and back
head and therefore largely alleviates the mirroring-face artifacts (Figure 5).

Similar to tri-plane in EG3D [5], we can synthesize the tri-grid as $3\times
D$ feature planes using the StyleGAN2 generator [21]. That is, we increase the
number of output channels of the original EG3D backbone by $D$ times. Thus,
tri-plane can be regarded as a naïve case of our tri-grid representation with
$D=1$. The depth $D$ of our tri-grid is tunable and larger $D$ offers more
representation power at the cost of additional computation overhead.
Empirically we find a small value of $D$ (_e.g_. $D=3$) is sufficient in
feature disentanglement while still maintaining its efficiency as a 3D scene
representation.

Figure 6: Image synthesized without (a) and with the camera self-adaptation
scheme(b). Without it, the model generates misaligned back head images,
leading to a defective dent in back head.  Figure 7: Qualitative comparison
between GRAF [37], GIRAFFEHD [48], StyleSDF [31], EG3D [5], multi-view
supervised NeRF [43] (different methods from top to bottom on left side), and
our PanoHead (right). Except [43], all models are trained on FFHQ-F. We render
the results at a yaw angle of 0, 45, 90, 135, and 180∘. GRAF, GIRAFFEHD, and
StyleSDF fail to model the correct camera distribution in latent space due to
the unsupervised camera pose mechanism, thus not turning to the back. EG3D is
able to rotate to the back with ‘mirroring face’ artifacts and entangled
background. Multi-view supervised NeRF is comparable to ours, however, it
requires multi-view data of a single person and is not a generative model.

###  3.4 Self-Adaptive Camera Alignment

For adversarial training of our full head in $360^{\circ},$ we need in-the-
wild image exemplars from a much wider range of camera distribution than the
mostly frontal distribution, as in FFHQ [21]. Although our 3D-aware GAN is
only trained from widely-accessible 2D images, the key to the best quality
training is accurate alignment of visual observations across images labeled
with well-estimated camera parameters. While a good practice has been
established for frontal face images cropping and alignment based on facial
landmarks, it has never been studied in pre-processing large-pose images for
GAN training. Both camera estimation and image cropping are no longer
straightforward due to the lack of robust facial landmarks detection for
images taken from the side and back.

To resolve the aforementioned challenge, we propose a novel two-stage
processing. In the first stage, for images with detectable facial landmarks,
we still adopt the standard processing where the faces are scaled to a similar
size and aligned at the center of the head using state-of-the-art face pose
estimator 3DDFA [14]. For the rest of the images with large camera poses, we
employ a head pose estimator WHENet [52] that provides a roughly-estimated
camera pose, and a human detector YOLO [18] with a bounding box centered at
the detected head. To crop the images at a consistent head scale and center,
we apply both YOLO and 3DDFA on a batch of front-face images, from which we
adjust the scale and translation of the head center of YOLO with constant
offsets. This approach enables us to pre-process all head images with labeled
camera parameters and in a consistent alignment to a large extent.

Due to the presence of various hairstyles, there is still inconsistency in the
alignment of back head images, inducing significant learning difficulties for
our network to interpret the complete head geometry and appearance (see Figure
6 (a)). We, therefore, propose a self-adaptive camera alignment scheme to
fine-tune the transformation of volume rendering frustum for each training
image. Specifically, our 3D-aware GAN associates each image with a latent code
$z$ that embeds the 3D scene information of geometry and appearance, which can
be synthesized at a view of $c_{cam}.$ $c_{cam}$ might not align well with the
image content for our training images; so, it is hard for the 3D GAN to figure
out a reasonable full head geometry. Therefore we co-learn a residual camera
transformation $\Delta c_{cam}$ mapped from $(z,c_{cam})$ together with our
adversarial training. The magnitude of $\Delta c_{cam}$ is regularized with a
L2 norm. Essentially, the network dynamically self-adapts the image alignment
with refined correspondence across different visual observations. We note that
this is only possible credited to the nature of 3D-aware GAN that can
synthesize view-consistent images at various cameras. Our two-stage alignment
enables 360-degree view-consistent head synthesis with authentic shape and
appearance, learnable from diverse head images with widely distributed camera
poses, styles, and structures.

##  4 Experiments

###  4.1 Datasets and Baselines

We train and evaluate our framework on a balanced combination of FFHQ [21],
K-hairstyle dataset [24], and an in-house large-pose head image collection.
FFHQ contains $70K$ diverse high-resolution face images, yet mainly fall in
the absolute yaw range from 0∘ to 60∘, assuming up-front camera pose
corresponds to 0∘. We augment the FFHQ dataset with $4K$ back-head images from
K-hairstyle dataset and $15K$ in-house large-pose images with diverse styles,
ranging from 60∘ to 180∘. For brevity, we name this dataset combination as
FFHQ-F. We refer to the supplementary paper for more dataset analysis and
network training details.

We compare against state-of-the-art 3D-aware GANs including GRAF [37], EG3D
[5], StyleSDF [31], and GIRAFFEHD [48]. All baselines are retrained from the
same FFHQ-F dataset. We measure the quality of generated multiview images and
geometry both quantitatively and qualitatively.

Table 1: Metrics comparison across all baselines. For segmentation MSE, only
GIRAFFEHD and PanoHead decouple the background and foreground. For ID score,
GRAF’s low-quality images lead to facial detection failure.

GRAF GIRAFFEHD StyleSDF EG3D Ours FID-all $\downarrow$ 68.2 37.3 78.5 6.2 5.4
MSE ($10^{-2}$) $\downarrow$ N/A 42.6 N/A N/A 9.1 ID $\uparrow$ N/A 0.39 0.41
0.74 0.74

Table 2: Ablation studies on different components. +seg. means with
foreground-aware tri-discrimination. +self-adpat. means with camera self-
adaptation scheme. All are trained with FFHQ-F

EG3D +seg. +seg.&self-adapt. tri-plane tri-grid tri-grid FID-back $\downarrow$
50.4 44.1 44.0 40.9 FID-front $\downarrow$ 6.6 5.0 5.5 5.4 FID-all
$\downarrow$ 6.2 5.2 5.2 5.4 IS-back $\uparrow$ 4.3 3.9 4.2 4.4 IS-front
$\uparrow$ 3.9 4.1 4.1 4.1 IS-all $\uparrow$ 3.8 4.0 4.0 4.1 Runtime
$\downarrow$ 1 1.14$\times$ 1.26$\times$ 1.28$\times$

###  4.2 Qualitative Comparisons

360∘ Image Synthesis. Figure 7 visually compares the image quality against the
baselines, all trained with FFHQ-F, by synthesizing images from five different
views, ranging the yaw angle from 0 to 180${}^{\circ}.$ GRAF [37] fails to
synthesize compelling head images and its background is entangled with
foreground head. StyleSDF [31] and GIRAFFEHD [48] are able to synthesize
realistic frontal face images but in low perceptual quality when rendered from
a larger camera pose. Without explicit reliance on camera labels, we suspect
the above methods have difficulty in interpreting the 3D scene structures by
themselves directly from images with 360∘ camera distribution. We observe that
EG3D [5] is able to synthesize high-quality view-consistent frontal head
images before rotating the view to the side or even the back. Mirroring face
artifacts are clearly observable from the back, due to the tri-plane’s
projection ambiguity and the entangled fore-background. The method proposed in
[43] builds personalized full-head NeRF at the extra cost of multi-view
supervision. Regardless of its good quality images at all views, the model
itself is not a generative model. In strong contrast, our model generates
superior photo-realistic head images for all camera poses while retaining
multi-view consistency. It delivers photo-realism with fine details at diverse
appearances, ranging from shaved head with glasses to long curly hairstyles.
To better appreciate our multi-view full-head synthesis, please refer to our
supplementary video for more comprehensive visual results.

Geometry Generation. Figure 8 compares the visual quality of the underlying 3D
geometry extracted by running Marching Cubes algorithms [26]. While StyleSDF
[31] generates decent appearances of the front face, the complete geometry of
the head is noisy and broken. EG3D presents detailed geometry of front face
and hair, but either with background concrete entangled (Figure 3(a)) or with
a hollowed back head (Figure 8). In contrast, our model can consistently
generate high-fidelity background-free 3D head geometry even with various
hairstyles.

###  4.3 Quantitative Results

To quantify the visual quality, fidelity, and diversity of the generated
images, we employ Frechet Inception Distance (FID) [16] of 50K real and fake
image samples. We measure the multi-view consistency using the identity
similarity score (ID) by calculating the average Adaface [23] cosine
similarity score from paired synthesized face images rendered from different
camera poses. Note that this metric can only be applied to those images with
detected facial landmarks. We assess mean square error (MSE) to calculate the
accuracy of the generated segmentation against the mask obtained with
DeepLabV3 ResNet101 network [7]. Table 1 compares these metrics across all
baselines and our method. We observe that our model outperforms other
baselines consistently from all perspectives. Refer to supplemental material
for metrics definition and implementation details.

To evaluate the image quality at different views, we employ FID and Inception
Score (IS) [36] for synthesized images with only back poses ($|yaw|\geq
90^{\circ}$), front poses ($|yaw|<90^{\circ}$), and all camera poses. FID
measures on the similarity and diversity of real and fake image distributions
while IS focuses more on the image quality itself. Our GAN model follows EG3D
for the main backbone, where the tri-plane generator is conditioned on a
camera pose. We observe that such a design leads to biased image synthesis
quality toward the conditioning camera pose. Specifically, when conditioning
on the front view, our generator achieves inferior quality for synthesizing
the head images from the back, and vice versa. However, when calculating FID-
all, the conditioning camera is always the same as the rendering view.
Therefore the generator could still achieve an excellent FID-all score even
though the quality of generated heads might degenerate in unseen views. Hence,
the original FID metrics (FID-all and FID-front) can hardly thoroughly reflect
the overall generation quality of full heads in $360^{\circ}$. To alleviate
this issue, we propose FID-back, where we condition on the front view but
synthesize the images from the back. It leads to higher FID scores but
reflects the quality in $360^{\circ}$ image synthesis better.

We perform an ablation study on our method to quantitatively evaluate the
efficacy of each individual component (Table 2). As shown in the second
column, we notice a significant quality boost after adding the foreground-
aware discrimination for all cases, compared with the original EG3D. That
indicates the prior segmentation knowledge largely ease the network learning
difficulty of 3D heads from in-the-wild image collections. Frontal face
synthesis quality is comparable among all methods given the strong supervision
from the large amount of well-aligned frontal images. However, for the back
head, decoupling foreground and background largely improves the synthesis
quality. In addition, changing tri-plane to tri-grid representation further
enhances the image quality. With tri-discrimination, tri-grid, and camera
self-adaption scheme altogether, PanoHead achieves the lowest FID-back and the
highest IS for back head generation. As reflected in the row of run-time
analysis, our novel component only introduces minor computation overhead, but
with significant image synthesis quality improvements. Note that the frontal
image quality is superior to the back head, largely due to the significant
learning difficulty in various hairstyles and unstructured back-head
appearances.

Figure 8: PanoHead achieves high-quality complete head geometry whereas
StyleSDF [31] and EG3D [5] produce 3D noises or hallowed heads.

###  4.4 Single-view GAN Inversion

Figure 9 demonstrates full-head reconstruction from a single-view portrait
using PanoHead’s generative latent space. To achieve that, we first perform an
optimization to find the corresponding latent noise $z$ for the target image
using pixel-wise L2 loss and image-level LPIPS loss [51]. To further improve
reconstruction quality, we perform pivotal tuning inversion (PTI) [35] to
alter the generator parameters with a fixed optimized latent code $z.$ From a
single-view target image, PanoHead not only reconstructs photo-realistic image
and high-fidelity geometry but also enables novel-view synthesis in
$360^{\circ}$, including large pose and back head.

##  5 Discussion

Limitations and Future Work. While PanoHead exhibits excellent images and
shapes quality from $360^{\circ}$, it still contains minor artifacts, e.g. in
the teeth area. Similar to the original EG3D, flickering texture issue is also
noticeable in our model. Switching to StyleGAN3 [20] as the backbone would
help preserve high-frequency details. In practice, we also observe more
noticeable flickering artifacts with a higher swapping probability of the
conditional camera pose. We set this value to 70% as opposed to 50% in EG3D
since we empirically find it enhances $360^{\circ}$ rendering quality but at
the minor cost of flickering texture artifacts. Another observation is that it
lacks finer high-frequency geometric details, e.g. hair tips. We leave it as
future work to quantitatively evaluate our geometric quality such as using
depth maps. Finally, although PanoHead is able to generate diverse images in
terms of gender, races, and appearances, reliance on training with only
several datasets combination still makes it suffer from data bias, to some
extent. In spite of our data collection effort, large-scale full-head
annotated training image dataset is one of the most critical directions to
facilitate full-head synthesis research. We anticipate such datasets can
resolve some of the limitations aforementioned.

Figure 9: Single-view reconstruction from different camera poses. The first
column shows the target images, second column projected RGB images and
reconstructed 3D shapes using GAN inversion, last two columns rendered images
from any given camera poses.

Ethical considerations. PanoHead is not specifically designed for any
malicious uses, yet we do realize that the single-view portrait reconstruction
could be manipulated, which might pose a social threat. We do not encourage
the method being used for violating others’ rights in any forms.

##  6 Conclusion

We propose PanoHead, the first 3D GAN framework that synthesizes view-
consistent full head images with only single-view images. With our novel
design in foreground-ware tri-discrimination, 3D tri-grid scene
representation, and self-adaptive image alignment, PanoHead enables authentic
multiview-consistent full-head image synthesis in $360^{\circ}$ and
demonstrates compelling qualitative and quantitative results compared with
state-of-the-art 3D GANs. Furthermore, we present 360-degree photo-realistic
reconstruction with highly detailed geometry from single-view real portraits.
We believe the proposed method presents an interesting direction for 3D
portraits creation, which sheds light on many potential downstream tasks.

## References

  * [1] Jonathan T Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P Srinivasan.  Mip-nerf: A multiscale representation for anti-aliasing neural radiance fields.  In iccv, pages 5855–5864, 2021.
  * [2] Volker Blanz and Thomas Vetter.  A morphable model for the synthesis of 3d faces.  In Proceedings of the 26th annual conference on Computer graphics and interactive techniques, pages 187–194, 1999.
  * [3] James Booth, Anastasios Roussos, Allan Ponniah, David Dunaway, and Stefanos Zafeiriou.  Large scale 3d morphable models.  International Journal of Computer Vision, 126(2):233–254, 2018\.
  * [4] James Booth, Anastasios Roussos, Stefanos Zafeiriou, Allan Ponniah, and David Dunaway.  A 3d morphable model learnt from 10,000 faces.  In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 5543–5552, 2016.
  * [5] Eric R Chan, Connor Z Lin, Matthew A Chan, Koki Nagano, Boxiao Pan, Shalini De Mello, Orazio Gallo, Leonidas Guibas, Jonathan Tremblay, Sameh Khamis, et al.  Efficient geometry-aware 3d generative adversarial networks.  CVPR, 2022.
  * [6] Eric R Chan, Marco Monteiro, Petr Kellnhofer, Jiajun Wu, and Gordon Wetzstein.  pi-gan: Periodic implicit generative adversarial networks for 3d-aware image synthesis.  In CVPR, 2021.
  * [7] Liang-Chieh Chen, George Papandreou, Florian Schroff, and Hartwig Adam.  Rethinking atrous convolution for semantic image segmentation.  arXiv preprint arXiv:1706.05587, 2017.
  * [8] Yu Deng, Jiaolong Yang, Jianfeng Xiang, and Xin Tong.  Gram: Generative radiance manifolds for 3d-aware image generation.  CVPR, 2022.
  * [9] Terrance DeVries, Miguel Angel Bautista, Nitish Srivastava, Graham W Taylor, and Joshua M Susskind.  Unconstrained scene generation with locally conditioned radiance fields.  In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 14304–14313, 2021.
  * [10] Guy Gafni, Justus Thies, Michael Zollhofer, and Matthias Nießner.  Dynamic neural radiance fields for monocular 4d facial avatar reconstruction.  In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 8649–8658, 2021.
  * [11] Jun Gao, Tianchang Shen, Zian Wang, Wenzheng Chen, Kangxue Yin, Daiqing Li, Or Litany, Zan Gojcic, and Sanja Fidler.  Get3d: A generative model of high quality 3d textured shapes learned from images.  nips, 2022.
  * [12] Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio.  Generative adversarial nets.  In NeurIPS, 2014.
  * [13] Jiatao Gu, Lingjie Liu, Peng Wang, and Christian Theobalt.  Stylenerf: A style-based 3d-aware generator for high-resolution image synthesis.  CVPR, 2022.
  * [14] Jianzhu Guo, Xiangyu Zhu, Yang Yang, Fan Yang, Zhen Lei, and Stan Z Li.  Towards fast, accurate and stable 3d dense face alignment.  In ECCV, 2020.
  * [15] Yudong Guo, Keyu Chen, Sen Liang, Yongjin Liu, Hujun Bao, and Juyong Zhang.  Ad-nerf: Audio driven neural radiance fields for talking head synthesis.  In iccv, 2021.
  * [16] Martin Heusel, Hubert Ramsauer, Thomas Unterthiner, Bernhard Nessler, and Sepp Hochreiter.  Gans trained by a two time-scale update rule converge to a local nash equilibrium.  NeurIPS, 2017.
  * [17] Yang Hong, Bo Peng, Haiyao Xiao, Ligang Liu, and Juyong Zhang.  Headnerf: A real-time nerf-based parametric head model.  In cvpr, pages 20374–20384, 2022.
  * [18] Marina Ivašić-Kos, Mate Krišto, and Miran Pobar.  Human detection in thermal imaging using yolo.  In Proceedings of the 2019 5th International Conference on Computer and Technology Applications, pages 20–24, 2019.
  * [19] Tero Karras, Miika Aittala, Samuli Laine, Erik Härkönen, Janne Hellsten, Jaakko Lehtinen, and Timo Aila.  Alias-free generative adversarial networks.  NeurIPS, 2021.
  * [20] Tero Karras, Miika Aittala, Samuli Laine, Erik Härkönen, Janne Hellsten, Jaakko Lehtinen, and Timo Aila.  Alias-free generative adversarial networks.  In NeurIPS, 2021.
  * [21] Tero Karras, Samuli Laine, and Timo Aila.  A style-based generator architecture for generative adversarial networks.  In CVPR, 2019.
  * [22] Tero Karras, Samuli Laine, Miika Aittala, Janne Hellsten, Jaakko Lehtinen, and Timo Aila.  Analyzing and improving the image quality of StyleGAN.  In CVPR, 2020.
  * [23] Minchul Kim, Anil K Jain, and Xiaoming Liu.  Adaface: Quality adaptive margin for face recognition.  In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 18750–18759, 2022.
  * [24] Taewoo Kim, Chaeyeon Chung, Sunghyun Park, Gyojung Gu, Keonmin Nam, Wonzo Choe, Jaesung Lee, and Jaegul Choo.  K-hairstyle: A large-scale korean hairstyle dataset for virtual hair editing and hairstyle classification.  In 2021 IEEE International Conference on Image Processing (ICIP), pages 1299–1303. IEEE, 2021.
  * [25] Tianye Li, Timo Bolkart, Michael. J. Black, Hao Li, and Javier Romero.  Learning a model of facial shape and expression from 4D scans.  36(6):194:1–194:17, 2017.
  * [26] William E Lorensen and Harvey E Cline.  Marching cubes: A high resolution 3d surface construction algorithm.  ACM siggraph computer graphics, 21(4):163–169, 1987.
  * [27] Julien NP Martel, David B Lindell, Connor Z Lin, Eric R Chan, Marco Monteiro, and Gordon Wetzstein.  Acorn: Adaptive coordinate networks for neural scene representation.  arXiv preprint arXiv:2105.02788, 2021.
  * [28] Ben Mildenhall, Pratul P Srinivasan, Matthew Tancik, Jonathan T Barron, Ravi Ramamoorthi, and Ren Ng.  Nerf: Representing scenes as neural radiance fields for view synthesis.  In ECCV, 2020.
  * [29] Michael Niemeyer and Andreas Geiger.  Giraffe: Representing scenes as compositional generative neural feature fields.  In CVPR, 2021.
  * [30] Atsuhiro Noguchi, Xiao Sun, Stephen Lin, and Tatsuya Harada.  Unsupervised learning of efficient geometry-aware neural articulated representations.  In Computer Vision–ECCV 2022: 17th European Conference, Tel Aviv, Israel, October 23–27, 2022, Proceedings, Part XVII, pages 597–614. Springer, 2022.
  * [31] Roy Or-El, Xuan Luo, Mengyi Shan, Eli Shechtman, Jeong Joon Park, and Ira Kemelmacher-Shlizerman.  Stylesdf: High-resolution 3d-consistent image and geometry generation.  CVPR, 2022.
  * [32] Keunhong Park, Utkarsh Sinha, Jonathan T Barron, Sofien Bouaziz, Dan B Goldman, Steven M Seitz, and Ricardo Martin-Brualla.  Nerfies: Deformable neural radiance fields.  In ICCV, 2021.
  * [33] Pascal Paysan, Reinhard Knothe, Brian Amberg, Sami Romdhani, and Thomas Vetter.  A 3d face model for pose and illumination invariant face recognition.  In 2009 sixth IEEE international conference on advanced video and signal based surveillance, pages 296–301. Ieee, 2009.
  * [34] Amit Raj, Michael Zollhoefer, Tomas Simon, Jason Saragih, Shunsuke Saito, James Hays, and Stephen Lombardi.  Pva: Pixel-aligned volumetric avatars.  CVPR, 2021.
  * [35] Daniel Roich, Ron Mokady, Amit H Bermano, and Daniel Cohen-Or.  Pivotal tuning for latent-based editing of real images.  ACM TOG, 2021.
  * [36] Tim Salimans, Ian Goodfellow, Wojciech Zaremba, Vicki Cheung, Alec Radford, and Xi Chen.  Improved techniques for training gans.  NeurIPS, 2016.
  * [37] Katja Schwarz, Yiyi Liao, Michael Niemeyer, and Andreas Geiger.  Graf: Generative radiance fields for 3d-aware image synthesis.  NeurIPS, 2020.
  * [38] Katja Schwarz, Axel Sauer, Michael Niemeyer, Yiyi Liao, and Andreas Geiger.  Voxgraf: Fast 3d-aware image synthesis with sparse voxel grids.  arXiv preprint arXiv:2206.07695, 2022.
  * [39] Yichun Shi, Divyansh Aggarwal, and Anil K Jain.  Lifting 2d stylegan for 3d-aware face generation.  In cvpr, pages 6258–6266, 2021.
  * [40] Ivan Skorokhodov, Sergey Tulyakov, Yiqun Wang, and Peter Wonka.  Epigraf: Rethinking training of 3d gans.  arXiv preprint arXiv:2206.10535, 2022.
  * [41] Keqiang Sun, Shangzhe Wu, Zhaoyang Huang, Ning Zhang, Quan Wang, and HongSheng Li.  Controllable 3d face synthesis with conditional generative occupancy fields.  arXiv preprint arXiv:2206.08361, 2022.
  * [42] Attila Szabo, Givi Meishvili, and Paolo Favaro.  Unsupervised generative 3D shape learning from natural images.  arXiv, 2019.
  * [43] Stanislaw Szymanowicz, Virginia Estellers, Tadas Baltrusaitis, and Matthew Johnson.  Photo-realistic 360 head avatars in the wild.  arXiv preprint arXiv:2210.11594, 2022.
  * [44] Ayush Tewari, Michael Zollhöfer, Pablo Garrido, Florian Bernard, Hyeongwoo Kim, Patrick Pérez, and Christian Theobalt.  Self-supervised multi-level face model learning for monocular reconstruction at over 250 hz.  In CVPR, 2018.
  * [45] Luan Tran, Feng Liu, and Xiaoming Liu.  Towards high-fidelity nonlinear 3d face morphable model.  In CVPR, 2019.
  * [46] Yue Wu, Yu Deng, Jiaolong Yang, Fangyun Wei, Qifeng Chen, and Xin Tong.  Anifacegan: Animatable 3d-aware face image generation for video avatars.  arXiv preprint arXiv:2210.06465, 2022.
  * [47] Yiheng Xie, Towaki Takikawa, Shunsuke Saito, Or Litany, Shiqin Yan, Numair Khan, Federico Tombari, James Tompkin, Vincent Sitzmann, and Srinath Sridhar.  Neural fields in visual computing and beyond.  In Computer Graphics Forum, volume 41, pages 641–676. Wiley Online Library, 2022.
  * [48] Yang Xue, Yuheng Li, Krishna Kumar Singh, and Yong Jae Lee.  Giraffe hd: A high-resolution 3d-aware generative model.  In CVPR, 2022.
  * [49] Lior Yariv, Jiatao Gu, Yoni Kasten, and Yaron Lipman.  Volume rendering of neural implicit surfaces.  In NeurIPS, 2021.
  * [50] Jianfeng Zhang, Zihang Jiang, Dingdong Yang, Hongyi Xu, Yichun Shi, Guoxian Song, Zhongcong Xu, Xinchao Wang, and Jiashi Feng.  Avatargen: a 3d generative model for animatable human avatars.  arXiv preprint arXiv:2208.00561, 2022.
  * [51] Richard Zhang, Phillip Isola, Alexei A Efros, Eli Shechtman, and Oliver Wang.  The unreasonable effectiveness of deep features as a perceptual metric.  In cvpr, pages 586–595, 2018.
  * [52] Yijun Zhou and James Gregson.  Whenet: Real-time fine-grained estimation for wide range head pose.  In BMVC, 2020.
  * [53] Yiyu Zhuang, Hao Zhu, Xusen Sun, and Xun Cao.  Mofanerf: Morphable facial neural radiance field.  arXiv preprint arXiv:2112.02308, 2021.