# Business disruptions from social distancing

Miklós Koren and Rita Pető Koren: Central European University, KRTK KTI and
CEPR. 1051 Budapest, Nádor u. 9., Hungary. E-mail<EMAIL_ADDRESS>Pető: KRTK
KTI. E-mail<EMAIL_ADDRESS>
(March 2020)

###### Abstract

Social distancing interventions can be effective against epidemics but are
potentially detrimental for the economy. Businesses that rely heavily on face-
to-face communication or close physical proximity when producing a product or
providing a service are particularly vulnerable. There is, however, no
systematic evidence about the role of human interactions across different
lines of business and about which will be the most limited by social
distancing. Here we provide theory-based measures of the reliance of U.S.
businesses on human interaction, detailed by industry and geographic location.
We find that 49 million workers work in occupations that rely heavily on face-
to-face communication or require close physical proximity to other workers.
Our model suggests that when businesses are forced to reduce worker contacts
by half, they need a 12 percent wage subsidy to compensate for the disruption
in communication. Retail, hotels and restaurants, arts and entertainment and
schools are the most affected sectors. Our results can help target fiscal
assistance to businesses that are most disrupted by social distancing.

## Introduction

Social distancing measures are effective non-pharmaceutical interventions
against the rapid spread of epidemics [1, 2, 3, 4]. Many countries have
implemented or are considering measures such as school closures, prohibition
of large gatherings and restrictions on non-essential stores and
transportation to slow down the spread of the 2019–20 coronavirus pandemic [5,
6, 7, 8]. What are the economic effects of such social distancing
interventions? Which businesses are most affected by the restrictions?

Past research has analyzed the efficacy of social distancing interventions on
reducing the spread of epidemics using the 1918 Spanish Flu in the U.S. [3, 2,
1] and seasonal viral infections in France [9]. Our knowledge of economic
impacts, however, is limited [10]. For this question, past data may be less
relevant, as the importance of face-to-face communication has increased
steadily in the last 100 years through urbanization [11, 12] and
specialization increased in business services as well [13, 14].

The starting point of this paper is the observation that many sectors rely
heavily on face-to-face communication in the production process [15, 16]. We
build a model of communication to understand how limiting face-to-face
interaction increases production costs. Without social distancing, workers
specialize in a narrow range of tasks and interact with other workers
completing other tasks. This division of labor reduces production costs but
requires frequent contact between workers. In the model, the number of
contacts per worker is the most frequent in high-population-density areas in
businesses where the division of labor is important. When face-to-face
interaction is limited, these are exactly the businesses that suffer the most.

To measure business disruptions from social distancing, we turn to recent data
on the task descriptions of each occupation [17] and the precise geographic
location of non-farm businesses in the U.S. [18]. We construct three groups of
occupations and study their distribution in space. First, some occupations
require face-to-face communication several times a week with other workers.
Examples of these _teamwork-intensive_ occupations include maintenance,
personal care related occupations and health care professionals. Other
occupations require frequent contact with customers. Counselors, social
workers and salespersons are examples of such _customer-facing_ occupations.
The third group of workers may need to be in physical proximity of one another
even if they do not communicate, for example, to operate machinery or access
key resources. Examples of such occupations requiring _physical presence_ are
drivers and machine operators, especially in mining and water transport, where
crammed working environments are common.

The spatial distribution of employment matters because face-to-face
interactions are more frequent in dense cities [15, 16]. So any social
distancing intervention imposes disproportionately more limitation on urban
sectors. We use our theory-motivated measures to estimate which sectors and
which locations will be particularly hurt by social distancing.

## A model of communication

When workers communicate with others, they can divide labor more effectively.
Production involves sequentially completing tasks indexed by $z\in[0,1]$. A
single worker can do a range of tasks, but there is a benefit to
specialization and division of labor [19, 20]. The labor cost of a worker
completing $Z<1$ measure of tasks is $Z^{1+\gamma}/\gamma$, where $\gamma>0$
captures the benefits to the division of labor. As we show below, the higher
the $\gamma$, the more specialized each worker will be in a narrower set of
tasks. Without loss of generality, we normalize the wage rate of workers to
one so that all costs are expressed relative to worker wages.

Once the range of tasks $Z$ is completed, the worker passes the unfinished
product on to another worker. This has a cost of $\tau$, which can capture the
cost of communicating and interacting across workers. The determinants of
communication cost will be parametrized later. After all the tasks are
completed, another step of communication with cost $\tau$ is needed to deliver
the product to the customer. This cost leads to the Marshallian externality
that firms want to be close to their customers and customers want to be close
to their suppliers [21, 22].

The firm will optimally decide how to share tasks between workers. The key
trade-off is economizing on the cost of communication while exploiting the
division of labor [20]. Let $n$ denote the number of workers involved in the
production process. Because workers are symmetric, each works on $Z=1/n$ range
of tasks before passing the work to the next worker. Production involves $n-1$
“contacts” (instances of communication) and there is an additional contact
with the customer.

Fig 1 illustrates the division of labor between workers. Horizontal movement
represents production along a range of tasks ($Z=1/n$), vertical movement
represents interaction ($\tau$). We note three potential interpretations of
our model. First, when workers work in teams, they can efficiently divide
labor among themselves (panel A). The benefit of a larger team is better
specialization. Second, communication may involve the customer (panel B). The
benefit of more frequent interaction with the customer is a product or service
that is better suited to their needs. Third, workers may need access to a key
physical resource, such as a machine, vehicle or an oil well (panel C). In
this case, even if they do not communicate, they may be subject to social
distancing measures. The key assumption behind all three interpretations is
that frequent interaction increases productivity, whether happening between
workers, between workers and customers, or between workers and machines.

W1W2W3…$1/n$$1/n$$1/n$$0$(A)$1$

WC$1/n$$1/n$$1/n$$1/n$$0$(B)$1$

RW1W2…$1/n$$1/n$$1/n$$1/n$$0$(C)$1$

Figure 1: Patterns of interaction in the workplace. Horizontal movement
represents production, vertical movement represents interaction. (A) Each
worker W works on a range $1/n$ of tasks, passing work $n-1$ times. (B) Worker
W and customer C engage in frequent interactions. (C) Each worker W needs
physical access to a key resource R.

The firm’s cost minimization problem can then be written as a function of the
number of contacts alone,

$c(\tau)=\min_{n}n\tau+\frac{1}{\gamma}n^{-\gamma},$ (1)

where total communication costs are $n\tau$ and production costs are
$nZ^{1+\gamma}/\gamma$ with $Z=1/n$.

Given the strict convexity of this cost function, and ignoring integer
problems, the first-order condition is necessary and sufficient for the
optimum,

$n^{*}(\tau)=\tau^{-1/(1+\gamma)}.$ (2)

The number of worker contacts is decreasing in the cost of communication,
expressed relative to worker wage. When the division of labor is important,
$\gamma$ is high, and the number of contacts does not depend very strongly on
communication costs.

The total cost of producing one good can be calculated by substituting in (2)
into (1),

$c(\tau)=\tau^{\chi}/\chi,$ (3)

where $\chi=\gamma/(1+\gamma)\in(0,1)$ measures the importance of division of
labor. This unit cost function is the same as if workers and communication
were substitutable in the production function in a Cobb-Douglas fashion.
Indeed, $\chi$ captures the share of costs associated with communication and
can be calibrated accordingly.

### The cost of communication

Businesses may differ in $\chi$, how important communication is in their
production process. Another source of heterogeneity is the cost of
communication between workers, which we specify further as follows.

When workers meet face to face, communication costs depend inversely on the
population density in the neighborhood of the firm, $\tau=d^{-\varepsilon}$
with $\varepsilon>0$. This captures the Marshallian externality of knowledge
spillovers [21], which happen more easily in densely populated areas [15, 23,
24, 16]. Contacts will be more frequent in dense areas,

$n^{*}(d)=d^{\varepsilon(1-\chi)}.$ (4)

The unit cost of production is

$c(d)=d^{-\varepsilon\chi}/\chi.$ (5)

Firms in dense areas face lower unit costs [25], but this agglomeration
benefit may be offset by higher wages and land rents in places with high
population density [26, 27, 28]. In spatial equilibrium (not modeled here),
firms with high communication needs will choose to locate in high-density
areas [16].

### Social distancing measures

We study the effect of a social distancing intervention that puts an upper
limit $N$ on the number of face-to-face contacts. Firms can mitigate the
disruption from this measure by moving communication online, but this is more
costly per contact than face-to-face communication.

The optimal number of contacts without social distancing is given by Eq (4).
Firms with $n^{*}>N$ are limited by social distancing. Without moving
communication online, their unit cost will increase to
$c^{\prime}=Nd^{-\varepsilon}+N^{-\gamma}/\gamma$, which is greater than the
optimal cost,

$\frac{c^{\prime}(d)}{c(d)}=\chi\frac{N}{n^{*}(d)}+(1-\chi)\left(\frac{N}{n^{*}(d)}\right)^{-\gamma}>1.$
(6)

The first term of the weighted average is less than one, representing a
reduction in communication costs once the number of contacts is limited. The
second term is greater than one due to the fact that every worker has to
complete a wider range of tasks than before, and they lose the benefit of
specialization. Because $n^{*}$ is the cost-minimizing communication choice of
the firm, the second term dominates, and production costs increase with social
distancing.

If the firm chooses to use telecommunication, the cost per contact will be
$T>d^{\varepsilon}$ (otherwise the firm would have used telecommunication
before). The proportional increase in production costs in this case is given
by

$\frac{c^{\prime\prime}(d)}{c(d)}=T^{\chi}d^{\varepsilon\chi}>1.$ (7)

In both cases, the cost increase is highest for communication-intensive firms
(large $\gamma$ and $\chi$) and those operating in a high-density area (high
$d$ and hence high $n^{*}$).

Fig 2 displays the ratio of production costs under social distancing to the
optimal production costs as a function of density. Firms in low-density areas
are unaffected by social distancing since they do not have many contacts
anyway. Those in intermediate-density areas would suffer less of a cost
increase by switching to telecommunication. Firms in the highest-density areas
will stick to face-to-face communication, which is still the more efficient
form of communication despite restrictions. However, they will suffer the
greatest cost increase.

$c^{\prime}/c$density$1$social distancingtelecommunication Figure 2: Both
social distancing and telecommunication hurt firms in dense areas more. See Eq
(6) and Eq (7) for the relative production costs under the two interventions.

## Data and methodology

To estimate the potential disruptions from social distancing, we need a
measure of the importance of worker interaction (corresponding to $\chi$ in
the model) and its cost (captured by population density $d$).

Let $\xi_{o}$ denote an indicator equal to one if occupation $o$ is
interaction-intensive and zero otherwise. For industry $i$,
$\chi_{i}=\sum_{o}s_{io}\xi_{o}$ measures the fraction of workers in affected
occupations, with $s_{io}$ denoting the employment share of occupation $o$ in
industry $i$.

We use the Occupational Information Network (O*NET) [17] to measure the
characteristics of a given occupation, similarly to previous studies [29, 30,
31]. The O*NET dataset contains detailed standardized descriptions on almost
1,000 occupations along eight dimensions. We focus on job characteristics that
are related to recent social distancing measures, while prior work focused
mainly on measuring offshorability of the given tasks [29, 30].

Social distancing interventions limit the interaction between people and
regulate physical proximity between individuals. We thus focus on three
related job characteristics based on work context and work activity described
in O*NET. The first two indicators capture how communication-intensive the job
is. Communication can be of two types: internal communication with co-workers
(_teamwork_) or external communication directly with customers (_customer-
facing_). The third indicator takes into consideration the possibility that
workers may need to be in physical proximity of one another even if they do
not communicate. We create an index that shows how important _physical
presence_ is to perform a given job. Table 1 details the specific O*NET
indexes that contribute to each of our three measures. As social distancing
measures only limit personal communication, for communication indexes, we
require that the necessary face-to-face communication happens at least several
times a week. In teamwork, face-to-face meetings can often be substituted by
more structured communication, for which working from home is not as
disruptive. To allow for this possibility, we only classify occupations as
teamwork-intensive where both emails and letters and memos are less frequent
forms of communication than face-to-face meetings. This excludes most managers
and certain business services. Similarly, for physical presence, we require at
least a certain degree of proximity to other workers which corresponds to
working in a shared office.

Table 1:  Definition of social distancing indexes.

Index | Tasks | Context
---|---|---
Teamwork  | Work With Work Group or Team | Face-to-face
| Provide Consultation and Advice to Others | discussions
| Coordinating the Work and Activities of Others | several times a week
| Guiding Directing and Motivating Subordinates | & more often than
| Developing and Building Teams | emails, letters, memos
Customer  | Deal With External Customers | Face-to-face
| Performing for or Working Directly with the Public | discussions
| Assisting and Caring for Others | several
| Provide Consultation and Advice to Others | times a week
| Establishing and Maintaining Interpersonal Relationships |
Presence  | Handling and Moving Objects | Density of
| Operating Vehicles, Mechanized Devices or Equipment | co-workers
| Repairing and Maintaining Electronic Equipment | like shared
| Repairing and Maintaining Mechanical Equipment | office or more
| Inspecting Equipment, Structures, or Material |

Each social distancing index (column 1) is created as an arithmetic average of
the component indexes (column 2). To be classified an affected occupation, the
average has to exceed 62.5 and the work context index has to exceed the
threshold in column 3.

We aggregate the measures to 6-digit occupation codes (Standard Occupational
Classification; 2010-SOC). We have information on the relevance of teamwork,
customer contact and physical presence for 809 occupations in SOC 2010 codes.

Teamwork and customer contacts are highly correlated (Fig 3), but they are
conceptually different. While all medical occupations require teamwork and
customer contact, supervisors in general are working in teams but do not often
communicate directly with customers. Machine operators and production workers
in general are at the bottom of both of the distributions. As managers can
substitute personal communication with emails, they are not considered in
general as teamwork-intensive occupations according to our definition. Given
the high correlation between the two types of communication, we often refer to
_communication-intensive_ occupations that are either teamwork-intensive or
customer-facing.

Figure 3: Teamwork and customer contact are highly correlated. Each circle
represents an occupation. Teamwork and customer contact indexes are
constructed as explained in main text.

As a next step, we calculate for each sector the share of workers whose job
requires a high level of teamwork, customer contact and physical presence. We
use the same sectoral breakdown as the Current Employment Statistics (CES)
[32]. As all the indexes are an absolute value running from 0 to 100, we use
62.5 as a cutoff to define a job to be teamwork-intensive, customers contact-
intensive or job that require physical presence from the worker. The
occupation structure of the industries are retrieved from the official
industry-occupation matrix [33], we use the employment statistics by
occupation-industry for February 2020.

Based on the share of relevant occupations in industry employment, the most
teamwork-intensive sectors are, for example “Hospitals,” “Accommodation” and
“Motion picture and sound recording industries.” In contrast, teamwork is not
important in sectors like “Forestry and logging” and “Fishing, hunting and
trapping.” Customer contact is relevant in sectors like “Hospitals” and
“Retail”, while it is not relevant is sectors line “Truck transportation,” and
“Forestry and logging.” Physical presence is relevant in sectors like “Truck
transportation,” “Repair and maintenance,” mining in general, while it is not
relevant in finance and information technology sectors.

“Hospitals” score high on all three measures because communication in health
care teams and with patients is important, and doctors and nurses work in
close physical proximity to others. We nonetheless remove this sector from the
analysis because of its inevitable direct role in combating the epidemic which
is not captured well in a simple model of communication.

To measure the heterogeneity in the cost of communication, we measure
population density in the neighborhood of businesses. The assumption in the
model is that communication costs are lower in dense areas. This is consistent
with the fact that communication-intensive sectors such as business services
and advertising, together with central administrative offices of production
firms tend to be concentrated in high-density areas [34].

The location of sectors comes from the County Business Patterns (CBP) data for
2017 [18]. For a finer spatial resolution, we use the data tabulated by ZIP-
Code Tabulation Areas. The CBP lists the number of establishments of a certain
size for each ZIP-code and NAICS industry code. Because establishment sizes
are given in bins (e.g., 1–4 employees), we take the midpoint of each bin as
our estimated employment (e.g., 2.5 employees). In small industries and ZIP
codes, the Census omits some size categories to protect the confidentiality of
businesses. We impute employment in these plants from the national size
distribution of plants in the same NAICS industry. Our estimated industry-
level employment is a very good approximation to official employment
statistics [32]. The correlation between our estimates based on CBP and the
employment reported in CES is 0.98.

To understand the heterogeneity across regions, we average the share of
workers in teamwork-intensive, customer-facing and physical presence
occupations across industries active in each ZIP code. For each of the three
occupation groups, let $\xi_{og}$ denote the indicator whether occupation $o$
belongs to group $g$. The industry share of workers in the occupation group is
given by $\sum_{o}s_{io}\xi_{og}$. We compute the regional share of the
occupation group as an employment-weighted average across industries,
$\sum_{i}l_{ir}\sum_{o}s_{io}\xi_{og}/\sum_{i}l_{ir}$, where $l_{ir}$ is the
estimated employment of industry $i$ in region (ZIP code) $r$. Because we only
have industry but not occupation data by location, we have assumed that the
occupation distribution within the sector, $s_{io}$, does not vary across
locations. The fact that the CBP tabulates employment by establishments rather
than firms makes this a good approximation. For example, a sporting good
producer may also have an administrative office and a retail store in
different locations, but these will be classified in their respective NAICS
sectors rather than in sporting good manufacturing.

We use population density to measure how locations differ in the costs of
communication. We also experimented with using employment densities instead of
population densities. Results were very similar, as the two measures are
highly correlated with the exception of very high employment-density urban
centers where population is more sparse [35].

### Counterfactual calculations

To gauge the magnitude of the effect of social distancing, we calibrate the
parameters of the model and compute the effect of a policy that limits the
number of worker contacts. At the same time, we let the government introduce a
proportional wage subsidy $\lambda$ to help offset the costs from lower
interaction. With this subsidy, the cost of labor will be $(1-\lambda)$. We
ask what level of $\lambda$ would compensate businesses for the communication
disruption caused by social distancing. Using the cost change in Eq 6, we can
express

$\lambda_{ir}=1-\frac{1-\chi_{i}}{1-\chi_{i}N/n_{ir}^{*}}\left(\frac{N}{n_{ir}^{*}}\right)^{\gamma_{i}}>0.$
(8)

The compensating wage subsidy increases in the importance of communication
$\chi_{i}$ and the optimal number of contacts $n^{*}_{ir}$, and decreases in
the number of allowed contacts $N$. The subscripts note that communication
share is industry specific and the optimal number of contacts is both industry
and region specific.

We calibrate the upper limit on personal contacts $N$ such that the overall
number of contacts in the economy, when averaged across ZIP codes and
industries, is reduced by half,
$\sum_{i,r}l_{ir}\min\\{N,n_{ir}^{*}\\}=0.5\sum_{i,r}l_{ir}n_{ir}^{*}$. Due to
the inherent nonlinearity of the model, other interventions will have
different effects.

To calibrate the importance of communication $\chi_{i}$, note that it is the
cost share of communication, and can be correspondingly calibrated to the
employment share of communication-intensive occupations in industry $i$. Here
we take all occupations that are either teamwork intensive or customer facing.

Population density in region $r$ can be measured directly in the data, as
explained above. The only remaining parameter to calibrate is the elasticity
of the communication externality $\varepsilon$. We rely on previous estimates
of agglomeration effects that capture the elasticity of total factor
productivity with respect to population density [25]. In our model, the
elasticity of unit costs (which can be construed as the inverse of
productivity) with respect to density is $-\varepsilon\chi$ (Eq (5)). We
calibrate $\varepsilon=0.02$ so that, across all ZIP codes and industries, a
regression of log model-implied productivity ($\varepsilon\chi_{i}\ln d_{r}$)
on log population density $\ln d_{r}$ yields an elasticity of 0.04 [25, page
60].

Given these parameter values, we compute the compensating wage subsidy for
each industry in each ZIP code using Eq 8. We report employment-weighted
averages of this across sectors and across locations.

## Results

Table 2 displays the top five and the bottom five industries by 2-digit NAICS
industries as sorted by the percentage of workers in communication-intensive
occupations, excluding hospitals and clinics. Across industries, retail trade,
accommodation and food services, arts, entertainment, and recreation, other
services and educational services have the highest share of communication-
intensive workers, exceeding 35 percent. Transportation, production,
construction and agricultural industries are less reliant on face-to-face
communication. This heterogeneity across industries is important to understand
the effect of social distancing measures.

Table 2:  Retail, professional services, finance and restaurants are the most
communication intensive.

| Communication |
---|---|---
Industry | Teamw. | Custom. |  Overall | Presence
Retail trade  | 13 | 67 | 68  | 5
Accommodation & food services  | 8 | 50 | 51  | 1
Arts, Entertainment, and Recreation  | 12 | 40 | 42  | 2
Other Services (except Public Admin.)  | 12 | 38 | 41  | 12
Educational Services  | 15 | 35 | 37  | 1
…  |  |  |  |
Wholesale Trade  | 8 | 16 | 20  | 12
Transportation and Warehousing  | 8 | 10 | 16  | 32
Manufacturing  | 7 | 6 | 11  | 10
Construction  | 15 | 5 | 18  | 28
Agri., forestry, fishing & hunting  | 4 | 4 | 7  | 23

“Teamw.” and “Custom.” show the percentage of workers in teamwork-intensive
and customer-facing occupations, respectively. “Overall” shows the percentage
of workers in communication-intensive occupations that are either teamwork-
intensive or customer-facing. It is less than the sum of the two indexes
because some occupations rely on both types of communication. “Presence” shows
the percentage of workers whose jobs require physical presence in close
proximity to others.

Fig 4 plots the share of workers in the three affected occupation groups
across ZIP codes by population density. Customer-facing occupations are
overrepresented in dense areas. In the highest population density ZIP codes,
43 percent of workers are employed in customer-facing occupations. Teamwork-
intensive occupations are broadly distributed in space.

Figure 4: Urban areas employ more workers in customer-facing occupations, less
in occupations requiring physical presence. Locally weighted polynomial
regression of average share of teamwork-intensive occupations, customer-facing
occupations and occupations requiring physical presence across sectors within
the ZIP code (bandwidth $=0.5$).

In the calibrated model, a social distancing policy that puts a cap on
interactions per worker such that the total number of interactions drops by
half nationwide is compensated a 12.2 percent wage subsidy. The distribution
of the compensating wage subsidy is, however, unequal over space and across
industries. New York City, with a population density about 20 times the
average U.S. city, would require a 13.3 percent wage subsidy. By contrast, the
compensating wage subsidy in agriculture, transportation and manufacturing
would be less than 6 percent (Table 3).

Table 3:  The five most affected sectors require more than 20 percent wage
subsidy.

Industry | Wage subsidy | Employment
---|---|---
Retail Trade  | 22.1 | 15,659
Accommodation and Food Services  | 17.7 | 14,379
Arts, Entertainment, and Recreation  | 15.1 | 2,494
Other Services (except Public Admin.)  | 14.5 | 5,939
Educational Services  | 13.8 | 3,838
…  |  |
Wholesale Trade  | 7.7 | 5,936
Construction  | 6.8 | 7,646
Transportation and Warehousing  | 5.9 | 5,523
Manufacturing  | 4.5 | 12,861
Agriculture, Forestry, Fishing and Hunting  | 2.6 | 55
Average | 12.2 | 116,496

“Wage subsidy” displays the percentage decrease in labor costs necessary to
compensate businesses when worker contacts are reduced by half. “Employment”
is the February 2020 employment of the sector in thousands [32]. The last row
shows the employment-weighted average wage subsidy. Table excludes hospitals,
clinics, and government establishments which are not present in CBP.

## Discussion and conclusions

The main cost of social distancing in our model is insufficient division of
labor. This mechanism is motivated by [19] and captures the same trade-off as
[20]. Our contribution is specifying the cost function in such a way that can
be easily mapped to the data.

More broadly, our argument is that frequent interaction increases productivity
irrespective whether it is happening between workers, between workers and
customers, or between workers and machines. In the main part of the empirical
analysis, we focused only on the first two types of interactions, while we
were silent about the third. But social distancing measures also affect
sectors where workers need to be in physical proximity of one another even if
they do not communicate, for example, to operate machinery or access key
resources. This is relevant in sectors like “Mining, Quarrying, and Oil and
Gas Extraction” and “Transportation” while it is not relevant in sectors like
“Finance and Insurance” and “Professional, Scientific, and Technical
Services.” As can be seen from Fig 4, occupations requiring physical presence
have the highest share in less dense areas where production and mining plants
are located. (Farms are not included in the CBP.) The share of these
occupations in the most dense areas is only 3 percent.

To a greater or lesser extent, all sectors will be affected by social
distancing. Some sectors are hit by the intervention due to restricted face-
to-face communication, others are hit due to restricting physical proximity of
people. Some sectors are less affected across all dimensions. Examples include
“Fishing, hunting and trapping,” “Printing and related support activities,”
and manufacturing in general.

We see four avenues for further research. The first concerns the demand side
of the economy, which we have mostly neglected by focusing on the production
function. The employment response to a production disruption greatly depends
on the elasticity of demand. We hypothesize that sectors like schooling and
health care have inelastic demand and will continue to employ many workers
despite significant disruptions. However, personal services, small grocery
stores and restaurants may face more elastic demand and respond to large
production cost increases by laying off a significant fraction of their work
force.

The second direction concerns the interaction between sectors and regions.
Whenever productivity in any business drops, this shock can propagate to its
buyers and suppliers. The aggregate consequences of the epidemic will hence be
modulated by input-output linkages between sectors, regions and countries [36,
37, 38].

The third and forth directions concern the long-run response of businesses as
they try to become more resilient to such shocks in the future. Whether the
share of telecommunication remains large in the long run depends crucially on
how easily it substitutes for face-to-face interaction. In our model, the two
are perfect substitutes with the only distinction that the efficiency of face-
to-face meetings improves with population density, whereas telecommunication
does not depend on agglomeration [23, 24, 16]. Previous work has found face-
to-face communication to be more effective in high-intensity communication
which is particularly helpful to overcome incentive problems in joint
production [39, 40]. Data on internet flows suggests that telecommunication is
not a good substitute for face-to-face meetings [41]. None of these papers
discuss disruptions from social distancing measures. Further study of the
modes of communication in the O*NET occupation survey can shed light on
whether telecommunication can act as a low-cost substitute for face-to-face
meetings.

Fourth, businesses may change their location in response to perceived threats
and disruptions. As we discussed, epidemics have a disproportionate effect on
cities. So it is conceivable that in a post-pandemic spatial equilibrium (not
modeled here, but see [16]), the agglomeration premium falls and firms find it
less attractive to locate in cities. A poignant point of comparison is the
increased threat of terrorism in major cities following devastating attacks on
New York, Washington, London, Paris, Madrid, Moscow and Mumbai. The general
conclusion about terror threat is that cities have remained resilient and a
robust attractor of businesses [42, 43]. We speculate that epidemics and
social distancing can be more detrimental to cities than terror threats,
because they tear apart the very fabric of urban life. However, we have
limited data to make further predictions.

## Supporting information

#### S1 Full table of sectors.

Social distancing exposure by sector. Available at
https://github.com/ceumicrodata/social-
distancing/blob/master/data/derived/industry-index.csv.

#### S2 Full table of ZIP-codes.

Social distancing exposure by location. Available at
https://github.com/ceumicrodata/social-
distancing/blob/master/data/derived/location-index.csv.

#### S3 Data repository.

Replication code and data. Replication code and data are available at
https://github.com/ceumicrodata/social-distancing.

## Acknowledgments

We thank Gábor Békés, Péter Harasztosi, Péter Karádi, Balázs Lengyel, Dávid
Krisztián Nagy, and Andrea Weber for comments.

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# ArcAid: Analysis of Archaeological Artifacts using Drawings

Offry Hayon
Technion, Israel
Stefan Münger
U. of Bern, Switzerland
Ilan Shimshoni
U. of Haifa, Israel
Ayellet Tal
Technion, Israel

###### Abstract

Archaeology is an intriguing domain for computer vision. It suffers not only
from shortage in (labeled) data, but also from highly-challenging data, which
is often extremely abraded and damaged. This paper proposes a novel semi-
supervised model for classification and retrieval of images of archaeological
artifacts. This model utilizes unique data that exists in the domain—manual
drawings made by special artists. These are used during training to implicitly
transfer the domain knowledge from the drawings to their corresponding images,
improving their classification results. We show that while learning how to
classify, our model also learns how to generate drawings of the artifacts, an
important documentation task, which is currently performed manually. Last but
not least, we collected a new dataset of stamp-seals of the Southern Levant.
The dataset and the code will be released upon acceptance.

##  1 Introduction

Archaeology benefits society through understanding of the past and is
acknowledged worldwide as a major research field. Advances in computer vision
may be harnessed to the task in order to automatize some aspects of the study
of archaeological findings (artifacts). For instance, a core task in the
domain is to look for similar artifacts, which may reveal relations, commerce
and connections between countries and cultures. The current practice is to
leaf through thousands of pages in site reports. Instead, performing this task
(and others) utilizing vision methods could take minutes. These methods are
essential not only because the number of artifacts is large and the number of
experts is small, but also because datasets are distributed all over the
world.

This, however, is an intriguing task, as the archaeological domain exposes the
limits of current computer vision techniques, due to several unique
properties. First, there is a shortage of labeled data, since labelling must
be performed by archaeological experts. Second, many archaeological artifacts
are preserved in poor state of condition, eroded or broken, which differs from
that of standard natural images. Third, since the artifacts are hand crafted,
the consistency between different items of the same class is relatively weak.

A major task in archaeology is to classify artifacts by different criteria.
The few classification methods in the domain exhibit good results, however
they mostly focus on classes that have small variety within each class (for
instance, similar coins with varied state of preservation) [38, 13, 34, 10, 2,
8, 6]. Our goal is broader: classifying a given artifact, where the images in
each class may vary greatly. This is either because they were produced in
different periods or by different artists (e.g. considerably different lions
and ibexes shown in Figure LABEL:fig:teaser(b)) or because they are clustered
by periods, even though the appearance of the shapes from the same period
inherently differ (Figure LABEL:fig:teaser(c)).

Since we do not have access to the real artifacts, which are often kept in
museum storage and store rooms of archaeological services, we focus on the
visual documentation of these artifacts. One obvious such documentation is
images, which is our input. Oftentimes, the images of the artifacts are
accompanied by illustrations, made by trained drafts persons. Though the
drawings and the photos are not necessarily aligned and the drawings are not
exact depictions of the images, some features of the artifacts look clearer
and more enhanced in the drawings. Thus, we propose to use them during
training.

We introduce a novel semi-supervised approach for classifying archaeological
artifacts. During training we utilize unlabeled pairs of drawings and images,
together with a smaller number of labeled pairs. At inference, however, only
an image is given as input. Our approach addresses the unique domain’s
challenges—a small dataset, the poor state, the lack of consistency between
artifacts in the same class, and similar objects in different classes (which
require expertise). Furthermore, we show that our approach is general and
enables us to classify the same artifact into various classification types.
Specifically, as demonstrated in Figure LABEL:fig:teaser(b)-(c), our model
classifies both by shape and by period. In these examples, the given image (at
inference) is not ideal in terms of quality. Yet, our model classifies the
images correctly according to both classification types.

Our method is based on a key observation that although the drawings are not
exact edge detections of the photos, utilizing them during training is
beneficial. This is so since they both represent the same main features of the
artifact, so the global features found in both are similar, but clearer to
detect in a drawing due to the state of the artifact (Figure 1). Forcing
similarity between the embeddings of images and drawings contributes to the
representation learning.

During training we solve an additional task—drawing generation—with unlabeled
image-drawing pairs. Currently, since drawing generation requires special
artists, it is done for very few selected artifacts, rather than to the whole
data. We present SoTA results in classification, retrieval, and image-to-
drawing generation in our domain.

Last but not least, we present a novel dataset, Corpus of the Stamp-seals of
the Southern Levant (CSSL). It contains scarabs and other seal types from
Egypt and the Southern Levant ($1750$-$330$ BCE), as well as their
impressions. The scarabs are classified by experts both by shape and by
period. This is an important contribution, since archaeological datasets are
rare in general, and in particular datasets of paired images and drawings.

Hence, this paper makes three contributions.

  1. 1.

It presents a semi-supervised method for multi-modal learning of paired
drawings & photos in archaeology.

  2. 2.

It introduces a model for image classification and retrieval of scarabs, with
respect to the shape or the period, jointly with the ability for drawing
generation.

  3. 3.

We collected a new dataset of images and drawings of decorated scarabs,
together with classifications and retrieval benchmarks according to both shape
and period.

|  |  |
---|---|---|---
|  |  |
(a) Bird | (b) Lion | (c) Ibex | (d) Beetle
Figure 1: Input to training. The edges of the drawings are clear and complete,
comparable to their counterpart in the images. Moreover, the details differ
and the pairs are misaligned.

##  2 Related work

Computer vision for archaeology. Most of the papers that develop vision
techniques for the archaeological domain address one of three tasks: (1)
documentation, where the goal is to either generate 3D curves [29, 30] or to
extract reliefs [12, 11, 51, 35]; (2) restoration, where the attempt is to
restore the way the artifact looked before it was damaged, such as in hole
completion [43, 32, 45], or in reassembly [15, 7, 37, 48]; (3) location, where
the attempt is to locate the artifact in time and space through classification
[6, 38, 2, 34, 24, 4, 13, 42] or retrieval [38, 44, 26, 3, 22, 42].

Our focus in this paper is on classification and retrieval of images of
archaeological artifacts. In [2] a new architecture, CoinNet, is presented,
which performs classification by shape (decoration). Results are presented on
a Roman coins dataset. In [6] the GlyphNet architecture is introduced, which
presents classification results on Hieroglyphs. In [38] classification is done
both by period and by site, utilizing multiple CNNs and inferring with a
voting ensemble approach. Their dataset contains images of archaeological
tools and artifacts, mostly found in good preservation conditions. We compare
our results to those of the recent models of [2, 6] and to those of the
backbone model of [38], which work on 2D data and made their code available.

To generate drawings from 3D archaeological data, in [28, 18, 49] the sought-
after curves are mathematically defined, and based on this definition nice
results are produced for a few available 3D shapes. Since 3D archaeological
data is even scarcer than 2D data, we (are the first to) address the problem
in 2D.

2D archaeological datasets. A dataset of $4,310$ grayscale images of
hieroglyphs is presented in [17]. The artifacts are not well-preserved,
however the variety in each class is relatively low. A dataset that comprises
photographs of $6,770$ artifacts of different types is presented in [38]. Most
of the artifacts are relatively well-preserved, however the variation within
each class is high. The released version of the dataset is in a much lower
resolution than that of the original dataset, and therefore we do not
experiment on it. The dataset published in [2] contains $18,225$ images of
ancient Roman coins. The artifacts are well-preserved and the variety within
each class is low. We present a new dataset, which is not only the first to
contain labeled pairs of images and drawings, but also contains challenging
artifacts in terms both of preservation and of class variety.

##  3 Method

Our goal is to design a model which, given only an image of a 3D decorated
archaeological artifact, will output an embedding vector representation that
can be used for analysis applications, in particular classification or
retrieval. Such images differ from natural images in several manners. First,
they are monochromatic. Second, the quality of the artifacts is poor, missing
some contours, while others are created due to noise. Finally, the photos are
often in poor condition.

Sometimes, these images are associated with drawings, created by special
archaeological artists, as shown in Figure 1. These drawings consist of clear
edges and their quality is superior to the quality of the corresponding
photographs, for a couple of reasons: Due to the artists’ vast experience,
they can draw parts of the contours, even if they are abraded. In addition,
the artist may have access to the real artifact when drawing it and can see
the 3D features that are unclear in the image. Hence, these drawings
encapsulate the important domain knowledge in them. However, the drawings and
the images are not necessarily aligned to each other, in terms of the actual
geometric alignment of the edges, additional edges, missing edges, and missing
damages. We will show that despite these drawbacks, when paired images and
drawings are available during training, image representation is improved, in
comparison to learning only from images. Our problem can thus be considered as
multi-modal learning, which learns shared knowledge between different domains
[19, 36, 33, 27, 31, 23, 9, 50].

Figure 2: Training with and without drawings. When training only using images
(top), the model focuses on the torso of the ibex, which leads to
misclassification as a lion. Conversely, thanks to the drawing, our model
focuses on the horns and the head (bottom), and classifies the image
correctly.  Figure 3:  Model. This figure illustrates the processing of a
batch of image-drawing pairs ($3$ in this example), where some of them are
unlabeled and some are. The image and its corresponding drawing are encoded,
where $\theta_{Enc_{Draw}}$ and $\theta_{Enc_{Im}}$ represent the parameters
of their encoders, respectively. The FC components represent the classifiers.
The image decoder, whose parameters are $\theta_{Dec_{Im}}$, generates the
reconstructed drawing. The loss $\mathcal{L}$ consists of three components:
$\mathcal{L}_{CE}$ for classification, $\mathcal{L}_{Gen}$ for image-to-
drawing generation and $\mathcal{L}_{S}im$, whose goal is to maximize the
similarity between pair embeddings. In case of an unlabeled pair, the
classification component is ignored. Thus, we freeze $\theta_{Enc_{Draw}}$ and
update the other components. In case of a labeled pair, $\theta_{Enc_{Draw}}$
is updated due to $\mathcal{L}_{CE}$; $\theta_{Enc_{Im}}$ is updated due to
all the components of the loss function; and $\theta_{Dec_{Im}}$ is updated
via $\mathcal{L}_{Gen}$.

We propose to utilize the drawings during training to improve image
representation. During inference, however, images are the sole input, since in
most cases drawings are unavailable. Intuitively, a drawing of an object can
be considered as an augmentation of the photo, one which expresses the
object’s shape as an edge map and makes it easier to extract features that are
difficult to obtain from the image. This is demonstrated in Figure 2, where
the drawing enables our model to differentiate between engravings of ibexes
and lions. Using only images, the localization map [41] focuses on a region
(torso) in which the ibex and the lion engravings are hardly distinguishable,
whereas when trained with our method, the model’s focus is on the horns, which
distinguishes between the two classes. This intuition is reinforced in our
experiments in Section 6. Interestingly, since training is performed also for
drawings, it enables our model to be used for a generative task—drawing an
artifact, i.e. image-to-drawing in the archaeological domain.

Since in archaeology labeled data is scarce, we propose a training process
that utilizes both labeled and unlabeled data, which exists in much larger
numbers. We show that the mere existence of image-drawing pairs, even when
unlabeled, helps. In particular, Section 6 shows that by training in this
semi-supervised manner, we achieve better results than by using just the
labeled data. Only classes that are unknown to the model appear in the
unlabeled data.

The model. As shown in Figure 3, both labeled and unlabeled pairs of images
and drawings are received as input, randomly in each batch, where most of the
pairs are naturally unlabeled. The key idea is to optimize image embedding for
classification, by maximizing the similarity between paired images and
drawings. This is since training a network for drawing classification is
easier than for images, as the shape is much clearer in drawings. Thus, we
assume that the feature map of a drawing, represented by an embedding vector,
is more informative than that of its corresponding image. Under this
assumption, making an image embedding similar to its paired drawing embedding,
contributes significantly to improve image representation.

Our model, which realizes this idea, consists of two encoders, $Enc_{Draw}$
and $Enc_{Im}$, whose inputs are drawings, $D$, and the corresponding images,
$I$. Two fully-connected layers of the same structure are trained for
classification. The output of the image encoder is fed into a decoder,
$Dec_{Im}$, whose goal is to reconstruct drawings from images. Let us denote
the parameters of the drawing encoder by $\theta_{Enc_{Draw}}$ and of the
image encoder and image-to-drawing decoder by $\theta_{Enc_{Im}}$ and
$\theta_{Dec_{Im}}$, respectively.

Our method is general and may train using many types of encoder/decoder
backbone architectures. We will show in Section 5 that our method
significantly improves the results irrespective of the chosen backbone.

Losses. Two losses use the outputs of the encoders, the similarity loss
($\mathcal{L}_{Sim}$) whose goal is to maximize the embedding similarity
between the drawing and the matching image, and the cross-entropy loss
($\mathcal{L}_{CE}$) whose goal is to minimize classification errors. The
output of the image decoder, jointly with the original drawing, are used for
yet another loss function, the generation loss ($\mathcal{L}_{Gen}$).

In the unsupervised case, when a label is not given, we would still like to
train the two encodings to be similar, by modifying the image encoding to be
similar to the drawing encoding, which is kept fixed. In addition, the
reconstructed drawing should be close to the original drawing. Thus, the
gradients of $\mathcal{L}_{Sim}$ and $\mathcal{L}_{Gen}$ are used to update
$\theta_{Enc_{Im}}$, the gradient of $\mathcal{L}_{Gen}$ is used to update
$\theta_{Dec_{Im}}$, and $\theta_{Enc_{Draw}}$ is frozen. Freezing
$\theta_{Enc_{Draw}}$ means that drawings affect and improve images embedding,
but not the opposite, in a way that might harm drawings embedding.

In the supervised case, the classifier components are also used. Thus, in
addition to the above, the gradients of the two $\mathcal{L}_{CE}$ losses
update their respective encoders. Only in this case $\theta_{Enc_{Draw}}$ is
updated.

Our image encoder loss is a sum of the three losses:

$\mathcal{L}=\gamma_{1}\cdot\mathcal{L}_{Sim}+\gamma_{2}\cdot\mathcal{L}_{CE}+\gamma_{3}\cdot\mathcal{L}_{Gen}.$
(1)

The weights, $\gamma_{i}$, are hyper-parameters, chosen by trial and error and
their values are $\gamma_{1}=0.8$, $\gamma_{2}=0.05$ and $\gamma_{3}=0.15$. We
hereby elaborate on the losses.

|  |  |  |  |  |  |  |  |  |
---|---|---|---|---|---|---|---|---|---|---
|  |  |  |  |  |  |  |  |  |
(a) Ankh | Anthrop. | Bands | Beetle | Bird | Circles | Cross | Ibex | Lion | Sa |
(b) $152$ | $130$ | $81$ | $152$ | $95$ | $89$ | $71$ | $101$ | $120$ | $75$ |
Figure 4: Shape classes. (a) shows a single instance of an image-drawing pair
for each of the $10$ classes. (b) is the number of labeled pairs.

To maximize the similarity in the latent space between the image embedding
$z_{I}$ and its corresponding drawing embedding $z_{D}$, we minimize a
negative cosine similarity loss:

$\mathcal{L}_{Sim}=-\frac{z_{I}\cdot
z_{D}}{\left\|z_{I}\right\|_{2}\cdot\left\|z_{D}\right\|_{2}}.$ (2)

Thus, by maximizing the similarity, we force the image embedding to be closer
to the drawings embedding, updating only $\theta_{Enc_{Im}}$ (and not
$\theta_{Enc_{Draw}}$).

We train the FC layers for classification with a CE loss, $\mathcal{L}_{CE}$,
one for drawings and the other for images. The goal is to improve both drawing
and image embedding by updating $\theta_{Enc_{Draw}}$ and $\theta_{Enc_{Im}}$
for classification. The CE loss is computed only for the labeled pairs in the
batch.

The generation loss takes into account the distance between the reconstructed
drawing and the original drawing, using both the $\mathcal{\ell}_{2}$ norm and
a perceptual loss, $\mathcal{L}_{P}$, similarly to [25]. While
$\mathcal{\ell}_{2}$ aims to minimize mismatches between pixels of a drawing
and a generation, the use of the perceptual loss encourages a similar feature
representation. Because the pairs of drawings and images are misaligned, a
full pixel-wise match is not possible. Hence, the combination of
$\mathcal{\ell}_{2}$ and $\mathcal{L}_{P}$ enables the model to learn a better
visually-similar generation. $\mathcal{L}_{Gen}$ is thus defined as

$\mathcal{L}_{Gen}=\alpha\cdot\left\|\tilde{D}-D\right\|_{2}+\beta\cdot\mathcal{L}_{P}.$
(3)

Here, $\tilde{D}$ is the reconstructed drawing, $D$ is the original drawing,
and $\alpha$ & $\beta$ are weights. In our implementation, $\alpha=0.3$ and
$\beta=0.7$; they were chosen via grid search.

##  4 Our new dataset - CSSL

A major contribution of our paper is a novel dataset of pairs of images &
drawings of ancient Egyptian scarabs, called the Corpus of the Stamp-seals of
the Southern Levant (CSSL). This is the first dataset that contains paired
images and drawings of any class of archaeological artifacts. The data was
collected by seven different archaeologists for their own archaeological
research. Thus, images might be centered and aligned differently between the
archaeologists. Each artifact was classified by an expert archaeologist and
was drawn by a trained drafts person. Despite the archaeological significance
of these findings to their owners, we managed to get permission from all the
involved parties to make this data available to the computer vision community.

CSSL contains $6,636$ pairs, out of which $1,020$ pairs are classified into
$10$ classes of scarab shapes and $5,616$ pairs are unclassified. The classes
and the number of objects per class are shown in Figure 4. The supplemental
material contains additional images of the various classes.

This dataset has a secondary classification into three periods and five sub-
periods. In particular, $955$ pairs are labeled into Middle Bronze (MB), Late
Bronze (LB) and Iron ages and $65$ of the labeled data do not have a period
label. The Middle Bronze age and the Iron age are divided into two sub-periods
each. Thus, $820$ pairs are labeled into sub-periods. Figure 5 illustrates the
difficulty of classification into periods, as lion-decorated scarabs, which
are relatively similar to a non-expert, are related to different periods.

|  |  |  |
---|---|---|---|---
|  |  |  |
(a) M.Bronze | M.Bronze | L.Bronze | Iron | Iron
(b) Early | Late |  | Early | Late
(c) 144 | 374 | 217 | 43 | 44
Figure 5: Sub-period classes. All the findings are decorated by lions. They
differ in shape and are dated to different periods (a) and sub-periods (b).
The bottom row (c) shows the number of labeled pairs in each sub-period (not
just for lions).

Figures 4-5 demonstrate why Archaeological datasets might be very challenging
for computer vision techniques. The artifacts are eroded, causing the shapes
to be hard to discern. In addition, the artifacts were made over a period of
hundreds of years, which naturally resulted in the shapes of the objects from
the same class to vary significantly.

##  5 Experimental results

Experimental setup. We evaluated our results using a variety of backbones as
encoders: Resnet101 [20], DenseNet161 [21], EfficientNetB3 [47] (used in
[38]), CoinNet [2], pretrained on ImageNet [14], and Glyphnet [6, 1]. The
latter two models are designed for archaeological data. For each encoder, we
implemented a decoder, such that the encoder/decoder model is similar to that
of UNet [39]. We show that for each backbone and task, our method
significantly improves the results, demonstrating its generality.

We present the average result obtained for a two-fold cross-validation
process, 50% train and 50% test. We use the accuracy measure for
classification and _mean average precision (mAP)_ for retrieval, both are the
most-commonly used measures. For mAP, we evaluate P@1 and P@10.

Classification and retrieval. Table 1 shows that our method indeed improves
the shape classification accuracy of each of the five models on CSSL by
$7.1\%$-$18.3\%$, and the mAP score by $0.03$-$0.22$.

Model | Class. | P@1 | P@10
---|---|---|---
DenseNet161 [21] | 80.8% | 0.78 | 0.77
DenseNet161 [21]+ours | 90.5% | 0.90 | 0.89
Resnet101 [20] | 82.5% | 0.78 | 0.77
Resnet101 [20]+ours | 89.6% | 0.86 | 0.86
EfficientNetB3 [47] | 72.9% | 0.64 | 0.61
EfficientNetB3 [47]+ours | 87% | 0.85 | 0.84
Architectures for Archaeology
CoinNet[2] | 79.6% | 0.77 | 0.76
CoinNet[2]+ours | 90.8% | 0.80 | 0.80
Glyphnet[6] | 55.4% | 0.43 | 0.43
Glyphnet[6]+ours | 73.7% | 0.65 | 0.64
Table 1: Shape classification and retrieval on our dataset. Our method is
general and can utilize a variety of backbones. It outperforms all previous
methods when compared on the same backbone. The best classification and
retrieval results are obtained when using our method on top of DenseNet161 and
CoinNet respectively.

Table 2 shows the results of classification by period. We trained our model
first on shape classification and then fine-tuned it for period
classification. For each backbone, our method improves the results of
$3$-period classification by $0.3\%$-$5.1\%$ and of $5$-period by
$0.06\%$-$9.0\%$. For classification to $3$ periods, the best results
($83.9\%$) are obtained when using our method on top of CoinNet. For
$5$-period classification, the best results ($71.9\%$) are obtained when using
our method on top of DenseNet161.

Model | 3 Periods | 5 Periods
---|---|---
DenseNet161 [21] | 81.3% | 71.3%
DenseNet161 [21]+ours | 83.7% | 71.9%
Resnet101 [20] | 81.1% | 68.9%
Resnet101 [20]+ours | 82.0% | 70.2%
EfficientNetB3 [47] | 77.3% | 66.6%
EfficientNetB3 [47]+ours | 82.4% | 71.6%
Architectures for Archaeology
CoinNet[2] | 83.6% | 70.2%
CoinNet[2]+ours | 83.9% | 71.1%
Glyphnet[6] | 72.2% | 56.6%
Glyphnet[6]+ours | 75.6% | 65.6%
Table 2: Period classification on our dataset. Our method improves all models.
The best results are obtained when using our model on top of CoinNet and
DenseNet161.

Next, we experimented with the hieroglyphs dataset of [17]. The artifacts are
not well-preserved, similarly to our dataset. Thus, we assumed that paired
drawings (during training) could improve the classification results. However,
this dataset does not contain drawings. Instead, we utilized general
illustrations of the hieroglyph types from [40, 5, 16]. During training we
paired each image to a random sample of hieroglyph drawing of the same type;
they differ in style and small features. We used $2$-$7$ drawings for each
class. In contrast to our dataset, here all pairs are labeled.

We compare our results to those of [6]. They use a train, test and validation
split of $70\%$, $15\%$ and $15\%$ respectively. Most of the dataset is
released, but not all, thus we re-split the released subset with the same
ratios. Table 3 compares the results presented in [6] on the full dataset to
the results attained when training it on the released sub-set, with and
without our model. It is shown that our results outperform [6]’s. Thus, we
show that even though the drawings are not accurate matches to the images,
using them during training improves the classification results. We note that
the diversity within each class in this dataset is low, which makes
classification easier than it is for our dataset.

Model | Dataset | Classification
---|---|---
Glyphnet[6] | Full [6] | 97.6%
Glyphnet[6] | Released [17] | 99.2%
Glyphnet[6]+ours | Released [17] | 99.4%
Table 3: Hieroglyphs classification on [17]. Our results are better than those
reported in [6] on the full dataset and those attained on the released subset,
when using the same backbone.

Since this dataset is relatively easy, to further evaluate the benefit of our
model, we applied it to a small training set. We split the released dataset
into $20\%$ train and $80\%$ test. Table 4 compares the results on several
backbones. The classification accuracy improves by $0.5\%$ by our method,
which is quite significant for this specific dataset.

Model | Classification
---|---
Resnet50 [20] | 94.5%
Resnet50 [20]+Ours | 95.0%
Densnet161 [21] | 96.0%
Densnet161 [21]+Ours | 96.5%
Glyphnet[6] | 96.2%
Glyphnet[6]+Ours | 96.7%
Table 4: Hieroglyphs classification on [17]. Our method outperforms all
backbones. All the backbones are trained from scratch; similar results are
obtained for pre-trained backbones.

Image-to-drawing generation. We strive to create an informative drawing from a
given image of an archaeological artifact. This task differs from that of
classical edge detection for a couple of reasons. First, unlike natural
images, artifacts might be eroded and highly noisy, and edges are expected to
be also in the eroded parts. Second, the drawings are not fully aligned with
the image. Recall that the second challenge is handled by $\mathcal{L}_{P}$,
which aims to maximize similar feature maps, rather than full pixel-wise
match.

|  |  |
---|---|---|---
anthropomorphic
|  |  |
cross
|  |  |
ibex
|  |  |
sa
(a) Input | (b) Manual | (c) Ours | (d) [46]
Figure 6: Image-to-drawing generation. Our results are more similar to the
manual drawings than those of [46] in generating delicate textures and in
completing faint edges. Additional results are given in the supplemental
materials.

Figure 6 demonstrates our results qualitatively. Since there is no previous
work that generates drawings in our domain, to allow comparison we trained a
SoTA supervised edge detector, DexiNed [46] on CSSL, considering the paired
drawings as edge maps. A main challenge is to deal with noise, existing in the
images but not in the drawings, caused as a result of the quality of the
images, erosion of the artifacts, and the ability of the artist to complete
the missing lines. In addition, each artifact has defects, some of which also
present in our generations. DexiNed’s results miss the delicate textures and
drawing features, such as the texture on the ibex’s torso. DexiNed also
generates thick edges, in accordance with the image itself. Conversely, our
method generates the delicate textures, nicely completes the faint edges, and
uses edge thickness as learned from the manual drawings. A couple of
archaeologists we consulted with consider the generated drawings as useful.

Table 5 quantitatively compares our results to DexiNed [46]’s, using common
edge detecting metrics: F-measure of Optimal Dataset Scale (ODS), Optimal
Image Scale (OIS) and Average Precision (AP). In this experiment we consider
the manual drawings as ground truth edge maps. Our results outperforms
DexiNed’s in all metrics.

We note that our model is even able to generate accurate drawings from photos
of objects it was not trained on, such as artistic reliefs, sculptures and a
variety of archaeological artifacts. We show qualitative results in the
supplementary.

Training method | ODS | OIS | AP
---|---|---|---
Our drawings | 0.38 | 0.39 | 0.29
DexiNed [46]’s drawings | 0.28 | 0.28 | 0.25
Table 5: Image-to-drawing generation quantitative results. Our model
outperforms DexiNed [46]’s in common metrics for edge detection, considering
the manual drawings as ground truth.

##  6 Ablation study

This section evaluates the benefits of the different components of our method.
In particular, we evaluate the contribution of the drawings for the training,
the benefit of jointly solving classification and drawing generation, and the
contribution of training with both labeled and unlabeled data. In all the
cases, we also examine the benefit of our method when the amount of labeled
data is low, which is likely to be the case for future archaeological
datasets. For that sake, we use three different sizes of labeled pairs during
two-fold cross validation training: full dataset ($507$,$513$), half dataset
($256$,$259$) and a quarter of the dataset ($129$,$132$). The size and split
of the test set remains the same, $507$ & $513$ pairs. In all the experiments
we use the Resnet101 backbone. Similar results are obtained for other
backbones.

The contribution of the drawings for the training. In this experiment, we
trained our model with and without drawings. Recall that the input at
inference is always images, as this is the prevalent available data. Table 6
shows that, as expected, training with pairs is indeed preferable. Moreover
the more data, the better. Finally, the less available data during training,
the more important it is to use paired data.

Input type / size | Full set |  $1/2$ set |  $1/4$ set
---|---|---|---
Ours: drawings & photos | 89.6% | 86.5% | 78.0%
Photos only | 82.5% | 72.0% | 60.3%
Table 6:  Training with different inputs. The classification results, when
training with paired images & drawings, outperform the results when using only
images during training. Furthermore, the less data available, the more
important it is to use these pairs.

The benefit of jointly solving all tasks. We evaluate the impact on
classification of image-drawing similarity and of drawing generation. Toward
this end, we checked the impact of $\mathcal{L}_{Sim}$ and
$\mathcal{L}_{Gen}$. Specifically, we trained the classification model without
$\mathcal{L}_{Gen}$ and then a model that solves generation without forcing
the similarity embedding $\mathcal{L}_{Sim}$ (Equation 1). Table 7 shows that,
as expected, $\mathcal{L}_{Sim}$ is crucial for classification. Furthermore,
adding $\mathcal{L}_{Gen}$ improves classification as well, while providing
drawings that are important for documentation.

Training set size | Full set |  $1/2$ set |  $1/4$ set
---|---|---|---
Full method | 89.6% | 86.5% | 78.0%
w/o $\mathcal{L}_{Sim}$ | 82.2% | 72.1% | 61.8%
w/o $\mathcal{L}_{Gen}$ | 87.8% | 84.1% | 73.9%
Table 7: Impact of $\mathcal{L}_{Sim}$ and $\mathcal{L}_{Gen}$ on
classification. Both $\mathcal{L}_{Sim}$ $\mathcal{L}_{Gen}$ are crucial for
the accuracy of solving classification.

Semi-supervised vs. fully supervised. This experiment studies the impact of
using unlabeled data. To do it, we trained two models, one only with the
available labeled data (fully supervised) and the other also with the
unlabeled data. Specifically, in the full-set case we used $1,020$ labeled
pairs, and in the semi-supervised training we used the additional available
$5,616$ unlabeled pairs.

Table 8 shows that for all sizes of training sets, the results achieved by the
semi-supervised training outperforms those of the supervised training. Thus,
additional input, even if unlabeled, should be used. Furthermore, the fewer
the labeled data is, the more beneficial semi-supervision is. This is so since
when having fewer labeled pairs, but the same number of unlabeled pairs, their
influence grows.

Hyper-parameters. These are quite robust. Specifically, in the loss function,
if we change the most important $\gamma_{1}$ (similarity), which is $0.8$, at
the expense of $\gamma_{2}$ or $\gamma_{3}$, the accuracy change will not be
significant. Increasing $\alpha$ over $\beta$ affects the generation; however
changing their values from $(0.3,0.7)$ to $(0.4,0.6)$ for instance, the impact
will be almost invisible. More details are given in the supplementary.

Training | Full set |  $1/2$ set |  $1/4$ set
---|---|---|---
Ours: labeled+unlabeled | 89.6% | 86.5% | 78.0%
Ours: only labeled | 83.8% | 75.8% | 64.8%
Table 8: Supervised vs. semi-supervised training. This experiment shows that
unlabeled data is beneficial and improves the results. Since we do not expect
to have much labeled data in this domain, this is very important.

Limitations. Figure 8 shows some cases where our model fails to classify the
objects correctly. In all these cases, the artifacts are worn out and the
method erroneously classified the artifacts into related classes.

Figure 8 shows cases where our generated drawings do not succeed to generate
the delicate textures. It can be seen though, that our drawings are still
better than those of [46].

|  |
---|---|---
(a) lion | (b) beetle | (c) ibex

Figure 7: Classification limitation. These three worn-out artifacts are
classified erroneously: the lion as as anthropomorphic (a), the beetle as ankh
(b) and the ibex as lion (c).

|  |  |
---|---|---|---
|  |  |
Input | Manual | Ours | [46]

Figure 8: Image-to-drawing limitation. Our method might fail to draw some fine
details, such as the buckles on the anthropomorphic belt and some decorations
on the lion’s body and tail. Still, our results preserve most of the original
details, compared to [46].

##  7 Conclusions

In archaeology, artifacts are studied using their photographs. For a subset of
them, drawings are made by trained drafts people. These are experts in their
field and are able to complete features that are not visible due to the eroded
condition of the artifacts. The challenge addressed in this paper is how such
a dataset can be used to solve classification in the case of a small damaged
dataset. We show that implicit knowledge obtained from the drawing is
transferred to the image, guiding it to the more important features.
Furthermore, we show that performing the training in a semi-supervised way,
takes advantage of unlabelled image-drawing pairs.

In addition, our model generates from the image a drawing of the object. This
is challenging since the image and the drawing are not exactly aligned and
what is transferred is the approximate position of the image features. The
resulting model is able to mimic with high accuracy the knowledge and the
drawing expertise of the artist, as well as the knowledge of the
archaeologist. Our method can be generalized to objects of reliefs, either
archaeological or artistic.

Last but not least, we created a relatively large and challenging dataset of
scarabs. We intend to make both that dataset and our code public, so they can
be used in future research projects.

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