Current address:]Idaho State University, Pocatello, Idaho 83209

The CLAS Collaboration

# Observation of azimuth-dependent suppression of hadron pairs
in electron scattering off nuclei

S.J. Paul  University of California Riverside, 900 University Avenue,
Riverside, CA 92521, USA  S. Morán  University of California Riverside, 900
University Avenue, Riverside, CA 92521, USA  M. Arratia  University of
California Riverside, 900 University Avenue, Riverside, CA 92521, USA  Thomas
Jefferson National Accelerator Facility, Newport News, Virginia 23606  A. El
Alaoui  Universidad Técnica Federico Santa María, Casilla 110-V Valparaíso,
Chile  H. Hakobyan  Universidad Técnica Federico Santa María, Casilla 110-V
Valparaíso, Chile  W. Brooks  Universidad Técnica Federico Santa María,
Casilla 110-V Valparaíso, Chile  M.J. Amaryan  Old Dominion University,
Norfolk, Virginia 23529  W.R. Armstrong  Argonne National Laboratory, Argonne,
Illinois 60439  H. Atac  Temple University, Philadelphia, PA 19122  L. Baashen
Florida International University, Miami, Florida 33199  N.A. Baltzell  Thomas
Jefferson National Accelerator Facility, Newport News, Virginia 23606  L.
Barion  INFN, Sezione di Ferrara, 44100 Ferrara, Italy  M. Bashkanov
University of York, York YO10 5DD, United Kingdom  M. Battaglieri  INFN,
Sezione di Genova, 16146 Genova, Italy  I. Bedlinskiy  National Research
Centre Kurchatov Institute - ITEP, Moscow, 117259, Russia  B. Benkel
Universidad Técnica Federico Santa María, Casilla 110-V Valparaíso, Chile  F.
Benmokhtar  Duquesne University, 600 Forbes Avenue, Pittsburgh, PA 15282  A.
Bianconi  Università degli Studi di Brescia, 25123 Brescia, Italy  INFN,
Sezione di Pavia, 27100 Pavia, Italy  L. Biondo  INFN, Sezione di Genova,
16146 Genova, Italy  INFN, Sezione di Catania, 95123 Catania, Italy
Università degli Studi di Messina, 98166 Messina, Italy  A.S. Biselli
Fairfield University, Fairfield CT 06824  Carnegie Mellon University,
Pittsburgh, Pennsylvania 15213  M. Bondi  INFN, Sezione di Roma Tor Vergata,
00133 Rome, Italy  F. Bossù  IRFU, CEA, Université Paris-Saclay, F-91191 Gif-
sur-Yvette, France  S. Boiarinov  Thomas Jefferson National Accelerator
Facility, Newport News, Virginia 23606  K.-Th. Brinkmann  II Physikalisches
Institut der Universitaet Giessen, 35392 Giessen, Germany  W.J. Briscoe  The
George Washington University, Washington, DC 20052  D. Bulumulla  Old Dominion
University, Norfolk, Virginia 23529  V.D. Burkert  Thomas Jefferson National
Accelerator Facility, Newport News, Virginia 23606  R. Capobianco  University
of Connecticut, Storrs, Connecticut 06269  D.S. Carman  Thomas Jefferson
National Accelerator Facility, Newport News, Virginia 23606  A. Celentano
INFN, Sezione di Genova, 16146 Genova, Italy  V. Chesnokov  Skobeltsyn
Institute of Nuclear Physics, Lomonosov Moscow State University, 119234
Moscow, Russia  T. Chetry  Florida International University, Miami, Florida
33199  G. Ciullo  INFN, Sezione di Ferrara, 44100 Ferrara, Italy  Università
di Ferrara, 44121 Ferrara, Italy  P.L. Cole  Lamar University, 4400 MLK Blvd,
PO Box 10046, Beaumont, Texas 77710  Catholic University of America,
Washington, D.C. 20064  Thomas Jefferson National Accelerator Facility,
Newport News, Virginia 23606  M. Contalbrigo  INFN, Sezione di Ferrara, 44100
Ferrara, Italy  G. Costantini  Università degli Studi di Brescia, 25123
Brescia, Italy  INFN, Sezione di Pavia, 27100 Pavia, Italy  A. D’Angelo  INFN,
Sezione di Roma Tor Vergata, 00133 Rome, Italy  Università di Roma Tor
Vergata, 00133 Rome Italy  N. Dashyan  Yerevan Physics Institute, 375036
Yerevan, Armenia  R. De Vita  INFN, Sezione di Genova, 16146 Genova, Italy  M.
Defurne  IRFU, CEA, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France
A. Deur  Thomas Jefferson National Accelerator Facility, Newport News,
Virginia 23606  S. Diehl  II Physikalisches Institut der Universitaet Giessen,
35392 Giessen, Germany  University of Connecticut, Storrs, Connecticut 06269
C. Dilks  Duke University, Durham, North Carolina 27708-0305  C. Djalali  Ohio
University, Athens, Ohio 45701  University of South Carolina, Columbia, South
Carolina 29208  R. Dupre  Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405
Orsay, France  H. Egiyan  Thomas Jefferson National Accelerator Facility,
Newport News, Virginia 23606  L. El Fassi  Mississippi State University,
Mississippi State, MS 39762-5167  P. Eugenio  Florida State University,
Tallahassee, Florida 32306  S. Fegan  University of York, York YO10 5DD,
United Kingdom  A. Filippi  INFN, Sezione di Torino, 10125 Torino, Italy  G.
Gavalian  Thomas Jefferson National Accelerator Facility, Newport News,
Virginia 23606  University of New Hampshire, Durham, New Hampshire 03824-3568
Y. Ghandilyan  Yerevan Physics Institute, 375036 Yerevan, Armenia  G.P.
Gilfoyle  University of Richmond, Richmond, Virginia 23173  A.A. Golubenko
Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University,
119234 Moscow, Russia  G. Gosta  Università degli Studi di Brescia, 25123
Brescia, Italy  R.W. Gothe  University of South Carolina, Columbia, South
Carolina 29208  K.A. Griffioen  College of William and Mary, Williamsburg,
Virginia 23187-8795  M. Guidal  Université Paris-Saclay, CNRS/IN2P3, IJCLab,
91405 Orsay, France  M. Hattawy  Old Dominion University, Norfolk, Virginia
23529  T.B. Hayward  University of Connecticut, Storrs, Connecticut 06269  D.
Heddle  Christopher Newport University, Newport News, Virginia 23606  Thomas
Jefferson National Accelerator Facility, Newport News, Virginia 23606  A.
Hobart  Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France  M.
Holtrop  University of New Hampshire, Durham, New Hampshire 03824-3568  Y.
Ilieva  University of South Carolina, Columbia, South Carolina 29208  The
George Washington University, Washington, DC 20052  D.G. Ireland  University
of Glasgow, Glasgow G12 8QQ, United Kingdom  E.L. Isupov  Skobeltsyn Institute
of Nuclear Physics, Lomonosov Moscow State University, 119234 Moscow, Russia
H.S. Jo  Kyungpook National University, Daegu 41566, Republic of Korea  R.
Johnston  Massachusetts Institute of Technology, Cambridge, Massachusetts
02139-4307  K. Joo  University of Connecticut, Storrs, Connecticut 06269  S.
Joosten  Argonne National Laboratory, Argonne, Illinois 60439  D. Keller
University of Virginia, Charlottesville, Virginia 22901  A. Khanal  Florida
International University, Miami, Florida 33199  M. Khandaker  [  Norfolk State
University, Norfolk, Virginia 23504  W. Kim  Kyungpook National University,
Daegu 41566, Republic of Korea  A. Kripko  II Physikalisches Institut der
Universitaet Giessen, 35392 Giessen, Germany  V. Kubarovsky  Thomas Jefferson
National Accelerator Facility, Newport News, Virginia 23606  V. Lagerquist
Old Dominion University, Norfolk, Virginia 23529  L. Lanza  INFN, Sezione di
Roma Tor Vergata, 00133 Rome, Italy  M. Leali  Università degli Studi di
Brescia, 25123 Brescia, Italy  INFN, Sezione di Pavia, 27100 Pavia, Italy  S.
Lee  Massachusetts Institute of Technology, Cambridge, Massachusetts
02139-4307  P. Lenisa  INFN, Sezione di Ferrara, 44100 Ferrara, Italy
Università di Ferrara, 44121 Ferrara, Italy  X. Li  Massachusetts Institute of
Technology, Cambridge, Massachusetts 02139-4307  K. Livingston  University of
Glasgow, Glasgow G12 8QQ, United Kingdom  I.J.D. MacGregor  University of
Glasgow, Glasgow G12 8QQ, United Kingdom  D. Marchand  Université Paris-
Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France  V. Mascagna  Università degli
Studi di Brescia, 25123 Brescia, Italy  INFN, Sezione di Pavia, 27100 Pavia,
Italy  B. McKinnon  University of Glasgow, Glasgow G12 8QQ, United Kingdom
Z.E. Meziani  Argonne National Laboratory, Argonne, Illinois 60439  S.
Migliorati  Università degli Studi di Brescia, 25123 Brescia, Italy  INFN,
Sezione di Pavia, 27100 Pavia, Italy  R.G. Milner  Massachusetts Institute of
Technology, Cambridge, Massachusetts 02139-4307  T. Mineeva  Universidad
Técnica Federico Santa María, Casilla 110-V Valparaíso, Chile  M. Mirazita
INFN, Laboratori Nazionali di Frascati, 00044 Frascati, Italy  V.I. Mokeev
Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606
P. Moran  Massachusetts Institute of Technology, Cambridge, Massachusetts
02139-4307  C. Munoz Camacho  Université Paris-Saclay, CNRS/IN2P3, IJCLab,
91405 Orsay, France  K. Neupane  University of South Carolina, Columbia, South
Carolina 29208  D. Nguyen  Thomas Jefferson National Accelerator Facility,
Newport News, Virginia 23606  S. Niccolai  Université Paris-Saclay,
CNRS/IN2P3, IJCLab, 91405 Orsay, France  G. Niculescu  James Madison
University, Harrisonburg, Virginia 22807  M. Osipenko  INFN, Sezione di
Genova, 16146 Genova, Italy  A.I. Ostrovidov  Florida State University,
Tallahassee, Florida 32306  P. Pandey  Old Dominion University, Norfolk,
Virginia 23529  M. Paolone  New Mexico State University, PO Box 30001, Las
Cruces, NM 88003, USA  L.L. Pappalardo  INFN, Sezione di Ferrara, 44100
Ferrara, Italy  Università di Ferrara, 44121 Ferrara, Italy  R. Paremuzyan
Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606
University of New Hampshire, Durham, New Hampshire 03824-3568  E. Pasyuk
Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606
W. Phelps  Christopher Newport University, Newport News, Virginia 23606  N.
Pilleux  Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France  D.
Pocanic  University of Virginia, Charlottesville, Virginia 22901  O. Pogorelko
National Research Centre Kurchatov Institute - ITEP, Moscow, 117259, Russia
M. Pokhrel  Old Dominion University, Norfolk, Virginia 23529  J. Poudel  Old
Dominion University, Norfolk, Virginia 23529  J.W. Price  California State
University, Dominguez Hills, Carson, CA 90747  Y. Prok  Old Dominion
University, Norfolk, Virginia 23529  University of Virginia, Charlottesville,
Virginia 22901  B.A. Raue  Florida International University, Miami, Florida
33199  T. Reed  Florida International University, Miami, Florida 33199  M.
Ripani  INFN, Sezione di Genova, 16146 Genova, Italy  G. Rosner  University of
Glasgow, Glasgow G12 8QQ, United Kingdom  F. Sabatié  IRFU, CEA, Université
Paris-Saclay, F-91191 Gif-sur-Yvette, France  C. Salgado  Norfolk State
University, Norfolk, Virginia 23504  A. Schmidt  The George Washington
University, Washington, DC 20052  R.A. Schumacher  Carnegie Mellon University,
Pittsburgh, Pennsylvania 15213  Y.G. Sharabian  Thomas Jefferson National
Accelerator Facility, Newport News, Virginia 23606  E.V. Shirokov  Skobeltsyn
Institute of Nuclear Physics, Lomonosov Moscow State University, 119234
Moscow, Russia  U. Shrestha  University of Connecticut, Storrs, Connecticut
06269  P. Simmerling  University of Connecticut, Storrs, Connecticut 06269  D.
Sokhan  IRFU, CEA, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France
University of Glasgow, Glasgow G12 8QQ, United Kingdom  N. Sparveris  Temple
University, Philadelphia, PA 19122  S. Stepanyan  Thomas Jefferson National
Accelerator Facility, Newport News, Virginia 23606  I.I. Strakovsky  The
George Washington University, Washington, DC 20052  S. Strauch  University of
South Carolina, Columbia, South Carolina 29208  The George Washington
University, Washington, DC 20052  J.A. Tan  Kyungpook National University,
Daegu 41566, Republic of Korea  R. Tyson  University of Glasgow, Glasgow G12
8QQ, United Kingdom  M. Ungaro  Thomas Jefferson National Accelerator
Facility, Newport News, Virginia 23606  Rensselaer Polytechnic Institute,
Troy, New York 12180-3590  S. Vallarino  INFN, Sezione di Ferrara, 44100
Ferrara, Italy  L. Venturelli  Università degli Studi di Brescia, 25123
Brescia, Italy  INFN, Sezione di Pavia, 27100 Pavia, Italy  H. Voskanyan
Yerevan Physics Institute, 375036 Yerevan, Armenia  E. Voutier  Université
Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France  X. Wei  Thomas
Jefferson National Accelerator Facility, Newport News, Virginia 23606  R.
Wishart  University of Glasgow, Glasgow G12 8QQ, United Kingdom  M.H. Wood
Canisius College, Buffalo, NY  University of South Carolina, Columbia, South
Carolina 29208  N. Zachariou  University of York, York YO10 5DD, United
Kingdom  Z.W. Zhao  Duke University, Durham, North Carolina 27708-0305  V.
Ziegler  Thomas Jefferson National Accelerator Facility, Newport News,
Virginia 23606  M. Zurek  Argonne National Laboratory, Argonne, Illinois 60439

###### Abstract

We present the first measurement of di-hadron angular correlations in
electron-nucleus scattering. The data were taken with the CLAS detector and a
5.0 GeV electron beam incident on deuterium, carbon, iron, and lead targets.
Relative to deuterium, the nuclear yields of charged-pion pairs show a strong
suppression for azimuthally opposite pairs, no suppression for azimuthally
nearby pairs, and an enhancement of pairs with large invariant mass. These
effects grow with increased nuclear size. The data are qualitatively described
by the GiBUU model, which suggests that hadrons form near the nuclear surface
and undergo multiple-scattering in nuclei. These results show that angular
correlation studies can open a new way to elucidate how hadrons form and
interact inside nuclei.

Introduction. The quark-to-hadron transition, called hadronization, remains
poorly understood in part due to the great challenge it poses to first-
principle calculations in quantum chromodynamics. Studying how hadronization
occurs inside large nuclei provides a way to perturb the process to
potentially reveal its mechanisms and timescales Accardi  _et al._ (2009,
2016); Barabanov  _et al._ (2021); Brooks and López (2021). It also represents
a way to probe the transport properties of nuclei Baier  _et al._ (1997); Guo
and Wang (2000); Liu  _et al._ (2015); Dupré and Scopetta (2016); Song  _et
al._ (2018); Ru  _et al._ (2021); Bai and Duan (2021); Guiot and Kopeliovich
(2020), and tune models needed to interpret neutrino experiments Alvarez-Ruso
_et al._ (2018); Mosel (2019).

Scattering experiments with electron beams can help elucidate hadron
production by providing control over the energy, $\nu$, and momentum,
$\vec{q}$, transferred in the reaction, which is determined from the scattered
electron. Previous studies by HERMES Airapetian  _et al._ (2001, 2003, 2007,
2010a, 2011) and CLAS Daniel  _et al._ (2011); Morán  _et al._ (2022)
experiments revealed that the production of hadrons is strongly suppressed in
nuclei, with a complex dependence on the hadron’s energy, transverse momentum,
and type. These data agree with various models that include either gluon
bremsstrahlung, hadron re-scattering and absorption, or a mixture of these
Accardi  _et al._ (2009).

Di-hadron measurements can complement single-hadron studies by providing more
kinematic variables and higher sensitivity to nuclear effects such as multiple
scattering Xing  _et al._ (2012); Cougoulic and Peigné (2018); Liang  _et al._
(2008); Schäfer and Zhou (2013); Boer  _et al._ (2015); Zhang  _et al._
(2019); Alrashed  _et al._ (2021). Such variables include angular
correlations, which were measured in hadron-collider and fixed-target
experiments to probe cold and hot nuclear matter (see Refs. Accardi  _et al._
(2009); Connors  _et al._ (2018) for reviews). No analogous study has been
done with electron beams.

Given the strong absorption of hadrons in nuclei Airapetian  _et al._ (2001,
2003, 2007, 2010a, 2011); Daniel  _et al._ (2011); Morán  _et al._ (2022), it
is expected that most observed hadrons correspond to those that were created
near the nuclear surface Fialkowski and Wit (2007) and have their momentum
directed away from the center of the nucleus. Detailed modelling of such
geometrical effects remains a challenge Liu  _et al._ (2015). Di-hadron
azimuthal correlations offer a way to test this hypothesis. When hadron pairs
are produced near the surface and off-axis from the nuclear center, the
shortest path lengths through the nucleus are obtained when both hadrons’
transverse momenta are directed away from the center of the nucleus relative
to their production positions. When averaging over possible initial-production
positions in the nucleus, this favors events in which the azimuthal separation
between the hadrons is small, while suppressing those with large azimuthal
separation (see Fig. 1). Such a “surface bias” has been observed in hadron
collisions and has been exploited as a tool to study cold and hot nuclear
matter Connors  _et al._ (2018).

Figure 1: Diagram illustrating di-pion production in a nucleus. Top: side-
view, illustrating that the momentum-transfer axis is used to define the
azimuthal separation, $\Delta\phi$. Bottom: same reaction, as viewed from the
direction of the momentum transfer.

The di-hadron measurements at HERMES Airapetian  _et al._ (2006) revealed
hints of nuclear suppression, although with limited precision; moreover, those
studies did not explore angular dependence nor did they include hadron
identification, which was crucial to elucidate single-hadron studies
Airapetian  _et al._ (2003, 2007, 2011). Di-hadron measurements were also
performed in the SKAT experiment Agababyan  _et al._ (2011), which used a
neutrino beam incident on heavy nuclei.

We build upon the HERMES results by studying di-hadron production with a much
higher precision and with identified hadrons; in addition, we measure for the
first time the di-hadron suppression as a function of the azimuthal separation
and the invariant mass. In particular, we study the reaction

$eA\rightarrow e^{\prime}\pi^{+}\pi^{-}X,$ (1)

where $X$ represents other particles in the event.

Experimental setup. The data presented here were collected at the Continuous
Electron Beam Accelerator Facility (CEBAF) Large Acceptance Spectrometer
(CLAS) with a 5.0 GeV electron beam incident on a dual-target system Hakobyan
(2008) consisting of a liquid ^2H target cell and a ^C, ^Fe, or ^Pb foil
target.

The CLAS Mecking  _et al._ (2003) detector was based on a six-fold symmetric
toroidal magnet, which defined six sectors instrumented with drift chambers
(DC), time-of-flight scintillation counters (TOF), Cherenkov counters (CC),
and an electromagnetic calorimeter (EC). Following Refs. El Fassi  _et al._
(2012); Morán  _et al._ (2022), electrons were identified by matching
negatively charged tracks measured in the DC with hits in the TOF and EC.
Background from $\pi^{-}$ was suppressed to the $<1\%$ level using the CC and
the EC. Charged-pions were identified with TOF hits consistent with charged
pions with momentum determined in the DCs. The selection for $\pi^{+}$ with
momentum above 2.7 GeV was further refined with the CC to suppress proton
background. Fiducial cuts on momentum and angles were used in order to avoid
regions with steeply varying acceptance or low resolution.

Event selection and observables. The data were selected with a trigger that
required at least one electron candidate with momentum $p>500$ MeV. Similar to
Ref. Morán  _et al._ (2022), we selected events with $Q^{2}>1$ GeV2, $W>2$ GeV
and 2.2$<\nu<$4.2 GeV. Here, $Q^{2}$ is the square of the four-momentum
transfer, $W=\sqrt{2m_{p}\nu+m_{p}^{2}-Q^{2}}$ where $m_{p}$ is the mass of a
proton, $\nu=E-E^{\prime}$ is the energy transfer, and $E$ and $E^{\prime}$
are the beam- and scattered-electron energies.

Following Ref. Airapetian  _et al._ (2006), we selected events with a
“leading” pion, defined as having fractional energy $z_{1}=E_{h}/\nu>0.5$,
where $E_{h}$ is the energy of the pion; we then measured all the other
(“secondary”) pions in the event with charge opposite that of the leading pion
in the fractional-energy range $0.05<z_{2}<0.45$. In addition, we removed
kinematically forbidden events by requiring $|p_{1}|+|p_{2}|<\nu$, where
$p_{1}$ and $p_{2}$ are the momenta of the pion candidates, in order to
suppress proton background. The selection included both resonant and non-
resonant di-pion production, including exclusive processes, as well as
secondary hadrons arising from hadron re-scattering and other nuclear
interactions.

We selected particles arising from scattering from either the deuterium or
nuclear targets by using the longitudinal vertex position defined by
intersecting their trajectories with the beamline. The resulting vertex
resolution ensured negligible ambiguity in the target tagging Morán  _et al._
(2022).

We used the electron, the leading pion, and the sub-leading pion variables to
measure the conditional modification factor, $R_{2h}$, defined Airapetian  _et
al._ (2006) as:

$R_{2h}(z_{2})=\frac{(dN_{2h}^{A}(z_{2})/dz_{2})/N_{h}^{A}}{(dN_{2h}^{D}(z_{2})/dz_{2})/N_{h}^{D}}.$
(2)

Here, $(dN_{2h}(z_{2})/dz_{2})/N_{h}$ is the ratio of the differential number
of selected events with a secondary hadron with energy fraction $z_{2}$, a
leading pion, and an electron, to the total number of selected events with an
electron and a leading pion. In other words, $R_{2h}$ is the nuclear-to-
deuterium ratio of the average number of secondary pions per leading pion. The
superscript indicates that the term is calculated for a nuclear ($A$) or
deuterium ($D$) target. Likewise, we also measured $R_{2h}$ in this work as a
function of the azimuthal separation between the pions, $|\Delta\phi|$, and
the di-pion invariant mass, $m_{\pi\pi}$.

Uncertainties. By construction, $R_{2h}$ is a double ratio that benefits from
the cancellation of various corrections for detector effects and thus
minimizes the associated systematic uncertainties. Moreover, we exploited the
dual-target system Hakobyan  _et al._ (2008), which by design minimizes
systematic uncertainties related to variations in detector response over time
by exposing the deuterium and heavier nuclear targets at the same time. This
feature of the dual target has been exploited in various studies Daniel  _et
al._ (2011); El Fassi  _et al._ (2012); Hen  _et al._ (2013, 2014); Duer  _et
al._ (2019a); Cohen  _et al._ (2018); Duer  _et al._ (2019b); Schmookler  _et
al._ (2019); Korover  _et al._ (2020); Schmidt  _et al._ (2020); Morán  _et
al._ (2022) which used the same data set as this work.

We performed studies on various possible sources of systematic uncertainties
using data and simulation studies. For the simulation studies we used the
Pythia 6.319 event generator and the GSIM package Wolin (1995), which is based
on Geant3 Brun  _et al._ (1994), to simulate the response of the CLAS detector
and dual-target setup Hakobyan (2008). The simulation was tuned to provide a
reasonable description of the data. The possible sources of systematic
uncertainties studied include acceptance effects, event selection, particle
mis-identification, and radiative effects. Other sources of systematic
uncertainty, such as cross contamination between bins, beam luminosity,
trigger efficiency, Coulomb effects, and time-dependent effects, were found to
be negligible.

The systematic uncertainties from different sources were added in quadrature,
and totaled to 2.5-3.0% for most bins. However, for some bins, in particular
at high $m_{\pi\pi}$, they reached 8.6%. In this region, the large systematic
uncertainty is largely due to momentum-dependent variations in the efficiency
of the CC, which we used to distinguish between high-momentum $\pi^{+}$ and
protons. For most bins, the systematic uncertainty dominated over the
statistical uncertainty, which ranged from 1.1-12%, with a median value of
2.6%.

Results and discussion. Figure 2(a) shows results for $R_{2h}$ as a function
of the fractional energy of the sub-leading pion of the pair, $z_{2}$. The
CLAS data show a suppression for almost all of the bins, with stronger
suppression for heavier nuclei. $R_{2h}$ depends weakly on $z_{2}$ except at
the first and last bins. The values of $R_{2h}$ for Fe and Pb appear close;
however, a $\chi^{2}$ test reveals that their differences are significant at
the 99% CL111For this test, only the statistical uncertainties were
considered, since the systematic uncertainties were assumed to be fully
correlated between the different nuclei for any given bin.. In the
$0.1<z_{2}<0.4$ range, the average values of $R_{2h}$ are $0.836\pm 0.007\pm
0.024$, $0.738\pm 0.005\pm 0.021$, and $0.698\pm 0.008\pm 0.020$ for ^C, ^Fe,
and ^Pb, respectively (where the first uncertainty is statistical and the
second is systematic).

Our data in Fig 2(a) are compared with existing $eA$ and $\nu A$ data from the
HERMES Airapetian  _et al._ (2006) and SKAT Agababyan  _et al._ (2011)
experiments, respectively. The average kinematics for our results are
$\langle\nu\rangle=3.3$ GeV and $\langle Q^{2}\rangle=1.6$ GeV2, whereas the
HERMES results were at $\langle\nu\rangle=17.7$ GeV and $\langle
Q^{2}\rangle=2.4$ GeV2 Airapetian  _et al._ (2006). The SKAT data were taken
at $\langle\nu\rangle=5.8$ GeV and $\langle Q^{2}\rangle=2.7$ GeV2 Agababyan
_et al._ (2011). The significant differences observed suggest that the change
of kinematics has a strong impact on the nuclear effects. Unlike HERMES, our
results show significant evidence for a dependence on the nuclear mass.

Furthermore, the differences between the HERMES and CLAS results may be
explained by the smaller energy transfer in the latter, causing the hadron-
formation length to be shorter. This increases the distance that the hadrons
have to travel to escape, increasing the probability of their absorption. In
the HERMES case, there is an increased probability of pions forming outside of
the nucleus, due to longer hadron-formation lengths compared to the CLAS case.

\begin{overpic}[width=424.94574pt]{plots/z2.pdf} \put(17.0,65.0){\large{(a)}}
\end{overpic}\begin{overpic}[width=424.94574pt]{plots/dphi.pdf}
\put(17.0,65.0){\large{(b)}}
\end{overpic}\begin{overpic}[width=424.94574pt]{plots/mass.pdf}
\put(17.0,65.0){\large{(c)}} \end{overpic}

Figure 2: Conditional suppression factor, $R_{2h}$, as a function of (a) sub-
leading hadron $z$, (b) the azimuthal separation $|\Delta\phi|$, and (c) the
invariant mass of the pion pair. Points are slighted shifted horizontally for
visibility. The gray open symbols in (a) represent results by the HERMES
Airapetian  _et al._ (2006) and SKAT Agababyan  _et al._ (2011) experiments.
Horizontal bars represent the systematic uncertainties, while the vertical
bars represent the total systematic and statistical uncertainty (added in
quadrature). The values of $R_{2h}$, statistical and systematic uncertainties,
and bin edges are tabulated in the Supplementary Material sup . Curves
represent the calculations from the GiBUU model Buss  _et al._ (2012).

We compare our data with with the GiBUU Monte-Carlo event generator Buss  _et
al._ (2012) (using the 2019 default parameters), which incorporates treatment
of final-state interactions, absorption, and production mechanisms with
elastic and inelastic channels. The GiBUU model described reasonably well the
single-hadron data from CLAS Morán  _et al._ (2022) and HERMES Airapetian  _et
al._ (2003, 2007, 2011). While the GiBUU calculations reproduce some of the
qualitative features of the data in this work, there are significant
differences, for instance it predicts an uptick only at low $z_{2}$, while the
data have an uptick at both the lowest and the highest $z_{2}$ bins. The
low-$z_{2}$ uptick was also observed in the HERMES and SKAT data, which were
at very different kinematics, suggesting that this effect does not depend
strongly on $Q^{2}$ or $\nu$. In the GiBUU model, the uptick in $R_{2h}$ at
low $z_{2}$ is produced as a consequence of the interaction between hadrons
produced in the primary electron-nucleon interaction with other hadrons as
they propagate through nuclei. The uptick at high $z_{2}$ is consistent with
unity and also exists in the HERMES results. This high-$z_{2}$ uptick, which
is not reproduced by the GiBUU model, may be due to coherent production in the
$z_{1}+z_{2}\rightarrow 1$ limit; coherent production in general is not
included in the GiBUU model Buss  _et al._ (2012).

Figure 2(b) shows $R_{2h}$ as a function of the azimuthal separation,
$\Delta\phi$, between the two pions, as measured around the direction of the
momentum transfer (see Fig. 1). The data show significant dependence on
$\Delta\phi$ for all nuclei. For all three nuclei, the deviation of $R_{2h}$
from unity is smallest when $\Delta\phi$ is near 0 and drops off with
increasing $|\Delta\phi|$, with a steeper slope for heavier nuclei. For
azimuthally opposite pairs ($|\Delta\phi|$ near $\pi$), $R_{2h}$ is $0.789\pm
0.013\pm 0.024$, $0.671\pm 0.010\pm 0.020$, and $0.620\pm 0.015\pm 0.026$ for
^C, ^Fe, and ^Pb, respectively. This is qualitatively described by the GiBUU
model; however, the data show a more pronounced $\Delta\phi$ dependence.

We also present $R_{2h}$ as a function of the di-pion invariant mass,
$m_{\pi\pi}$, in Fig. 2(c). The data show a negative slope in the
$0.4<m_{\pi\pi}<1.1$ GeV region, and an enhancement at higher $m_{\pi\pi}$. We
also observe that within the region of negative slope, the dependence appears
to be smooth and no abrupt behavior is observed in $R_{2h}$ near the
$\rho^{0}(770)$ mass. The data are qualitatively described by GiBUU, including
the uptick at high mass. In the GiBUU model, this is a product of the re-
scattering of hadrons, which leads to larger transverse momentum of hadrons
and higher pair invariant mass. The qualitative behavior of the data is
reminiscent of the enhancement of hadrons with high-transverse momentum
reported in Refs. Airapetian  _et al._ (2010b, 2001, 2003, 2007, a, 2011);
Morán  _et al._ (2022).

Hadron-absorption effects in the GiBUU model can be investigated through
looking at the distribution of the hadron-production points of the final-state
pions. We observe that in the GiBUU simulations, a larger fraction of the
total final-state pions are formed near the surface of the nucleus than would
be expected if their production points were distributed uniformly. Further, we
observe that this effect is stronger for larger nuclei than for smaller ones.
The effect is also stronger in the di-pion case than for the single-pion case.
The latter effect can be explained by the fact that we require the survival of
not only the secondary pion but also the leading one as well, biasing the
sample further towards the surface. Such an interpretation is consistent with
Ref. Fialkowski and Wit (2007), which argued that an absorption model coupled
with geometrical biases caused by survivor selection could explain both the
single and double-hadron data from HERMES without resorting to other effects
such as gluon bremsstrahlung Majumder and Wang (2008); Majumder (2012).

Summary and conclusions. In summary, we have presented a measurement of di-
pion production in electron scattering off nuclei using the CLAS detector,
which includes the first study on the azimuthal separation and invariant mass.
The data show a strong suppression for azimuthally opposite pairs, no
suppression for pairs that are close in azimuthal angle, and an enhancement of
pairs with large invariant mass. This is qualitatively consistent with the
predictions from the GiBUU model, wherein it can be attributed to an increased
probability of absorption of hadrons in azimuthally opposite pairs due to the
increased path length compared to azimuthally nearby pairs; however, the
measured suppression is stronger than in the predictions.

We also measured the dependence of the nuclear-to-deuterium ratio on the
secondary pion’s fractional energy, and on the di-pion invariant mass. We
compared our measurement of the dependence on the former with results from
HERMES and found both to be qualitatively comparable; however, our measurement
shows a stronger nuclear dependence than the HERMES results, which suggests a
strong kinematic dependence of the observed effects. Further, we note that the
di-hadron suppression is stronger in heavier nuclei, although the effect
appears to saturate for higher nuclear masses.

Overall, the data show evidence that nuclear effects not only modify the
hadron distributions, but also modify the correlations between multiple
hadrons in the event, relative to the correlations that exist in the deuteron
case due to momentum conservation and limited phase space.

Our studies show how kinematic variables that depend on both hadrons, such as
azimuthal separation and pair mass, can be used as a powerful tool for
studying hadron production in electron scattering off nuclei. Given that these
data cover a poorly explored kinematic domain where the hadron-formation
length is expected to be similar to the nuclear size, future comparisons to
models (similar to those of Refs. Gallmeister and Mosel (2008); Larionov and
Strikman (2020)) might shed light on hadronization timescales and mechanisms.

These results provide a reference for planned di-hadron measurements in future
experiments with higher beam energies at the Jefferson Laboratory Burkert
(2018); Burkert  _et al._ (2020); Arrington  _et al._ (2021), and future
electron-ion colliders in the USA Accardi  _et al._ (2016); Abdul Khalek  _et
al._ (2021) and China Anderle  _et al._ (2021).

Acknowledgements. The authors acknowledge the staff of the Accelerator and
Physics Divisions at the Thomas Jefferson National Accelerator Facility who
made this experiment possible. We thank Kai Gallmeister for help in setting up
the GiBUU event generator. This work was supported in part by the Chilean
Agencia Nacional de Investigacion y Desarollo (ANID), by ANID PIA grant
ACT1413, by ANID PIA/APOYO AFB180002, by ANID FONDECYT No. 1161642 and No.
1201964 and No. 11181215 and No. 1151248, by the ANID-Millennium Science
Initiative Program - ICN2019_044, by the U.S. Department of Energy, the
Italian Instituto Nazionale di Fisica Nucleare, the French Centre National de
la Recherche Scientifique, the French Commissariat à l’Energie Atomique, the
United Kingdom Science and Technology Facilities Council (STFC), the Scottish
Universities Physics Alliance (SUPA), the National Research Foundation of
Korea, the National Science Foundation (NSF), the HelmholtzForschungsakademie
Hessen für FAIR (HFHF), the Ministry of Science and Higher Education of the
Russian Federation, and the Office of Research and Economic Development at
Mississippi State University. This work has received funding from the European
Research Council (ERC) under the European Union’s Horizon 2020 research and
innovation programme (Grant agreement No. 804480). The Southeastern
Universities Research Association operates the Thomas Jefferson National
Accelerator Facility for the United States Department of Energy under Contract
No. DE-AC05-06OR23177.

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*

## Supplemental Material

The values of $R_{2h}$, shown in Fig. 2, are listed in Tables 1, 2, and 3,
along with the edges of the bins, and the statistical and systematic
uncertainties.

Table 1: Values of $R_{2h}$ obtained for each target and each $z_{2}$ bin $\pm$ the statistical uncertainty for each data point $\pm$ the systematic uncertainty for each data point. These data correspond to those shown in Fig. 2(a) $z_{2}$ |  $R_{2h}$(C, $z_{2}$) |  $R_{2h}$(Fe, $z_{2}$) |  $R_{2h}$(Pb, $z_{2}$)
---|---|---|---
0.05–0.10 | 0.982$\pm$0.017$\pm$0.036 | 0.917$\pm$0.015$\pm$0.034 | 0.824$\pm$0.020$\pm$0.030
0.10–0.15 | 0.819$\pm$0.010$\pm$0.026 | 0.732$\pm$0.008$\pm$0.024 | 0.696$\pm$0.013$\pm$0.022
0.15–0.20 | 0.823$\pm$0.014$\pm$0.021 | 0.724$\pm$0.011$\pm$0.019 | 0.694$\pm$0.017$\pm$0.018
0.20–0.25 | 0.870$\pm$0.018$\pm$0.023 | 0.757$\pm$0.014$\pm$0.020 | 0.700$\pm$0.021$\pm$0.018
0.25–0.30 | 0.840$\pm$0.022$\pm$0.022 | 0.752$\pm$0.018$\pm$0.020 | 0.702$\pm$0.026$\pm$0.019
0.30–0.35 | 0.941$\pm$0.035$\pm$0.027 | 0.769$\pm$0.026$\pm$0.022 | 0.713$\pm$0.038$\pm$0.021
0.35–0.40 | 0.911$\pm$0.050$\pm$0.033 | 0.749$\pm$0.036$\pm$0.027 | 0.712$\pm$0.057$\pm$0.026
0.40–0.45 | 1.163$\pm$0.108$\pm$0.049 | 0.955$\pm$0.074$\pm$0.040 | 0.934$\pm$0.112$\pm$0.039
Table 2: Values of $R_{2h}$ obtained for each target and each $|\Delta\phi|$ bin $\pm$ the statistical uncertainty for each data point $\pm$ the systematic uncertainty for each data point. These data correspond to those shown in Fig. 2(b) $|\Delta\phi|$ [rad] |  $R_{2h}$(C, $|\Delta\phi|$) |  $R_{2h}$(Fe, $|\Delta\phi|$) |  $R_{2h}$(Pb, $|\Delta\phi|$)
---|---|---|---
0.00–0.39 | 1.019$\pm$0.031$\pm$0.043 | 0.968$\pm$0.026$\pm$0.041 | 0.944$\pm$0.039$\pm$0.035
0.39–0.79 | 0.962$\pm$0.028$\pm$0.030 | 0.908$\pm$0.023$\pm$0.029 | 0.878$\pm$0.035$\pm$0.028
0.79–1.18 | 0.976$\pm$0.027$\pm$0.026 | 0.895$\pm$0.021$\pm$0.023 | 0.878$\pm$0.033$\pm$0.023
1.18–1.57 | 0.944$\pm$0.022$\pm$0.024 | 0.890$\pm$0.018$\pm$0.022 | 0.827$\pm$0.026$\pm$0.021
1.57–1.96 | 0.876$\pm$0.018$\pm$0.022 | 0.775$\pm$0.014$\pm$0.020 | 0.802$\pm$0.023$\pm$0.021
1.96–2.35 | 0.841$\pm$0.016$\pm$0.021 | 0.724$\pm$0.012$\pm$0.018 | 0.675$\pm$0.018$\pm$0.020
2.35–2.75 | 0.812$\pm$0.014$\pm$0.021 | 0.705$\pm$0.011$\pm$0.019 | 0.611$\pm$0.015$\pm$0.022
2.75–3.14 | 0.789$\pm$0.013$\pm$0.024 | 0.671$\pm$0.010$\pm$0.020 | 0.620$\pm$0.015$\pm$0.026
Table 3: Values of $R_{2h}$ obtained for each target and each $m_{\pi\pi}$ bin $\pm$ the statistical uncertainty for each data point $\pm$ the systematic uncertainty for each data point. These data correspond to those shown in Fig. 2(c) $m_{\pi\pi}$ [GeV] |  $R_{2h}$(C, $m_{\pi\pi}$) |  $R_{2h}$(Fe, $m_{\pi\pi}$) |  $R_{2h}$(Pb, $m_{\pi\pi}$)
---|---|---|---
0.30–0.44 | 1.021$\pm$0.057$\pm$0.035 | 0.914$\pm$0.041$\pm$0.031 | 0.836$\pm$0.066$\pm$0.030
0.44–0.58 | 0.962$\pm$0.030$\pm$0.046 | 0.896$\pm$0.023$\pm$0.043 | 0.874$\pm$0.037$\pm$0.042
0.58–0.72 | 0.920$\pm$0.019$\pm$0.023 | 0.813$\pm$0.015$\pm$0.021 | 0.798$\pm$0.023$\pm$0.020
0.72–0.86 | 0.878$\pm$0.013$\pm$0.023 | 0.782$\pm$0.010$\pm$0.020 | 0.782$\pm$0.016$\pm$0.020
0.86–1.00 | 0.831$\pm$0.014$\pm$0.023 | 0.721$\pm$0.011$\pm$0.020 | 0.670$\pm$0.016$\pm$0.018
1.00–1.14 | 0.769$\pm$0.015$\pm$0.021 | 0.685$\pm$0.012$\pm$0.019 | 0.604$\pm$0.017$\pm$0.017
1.14–1.28 | 0.834$\pm$0.018$\pm$0.026 | 0.725$\pm$0.015$\pm$0.023 | 0.647$\pm$0.021$\pm$0.020
1.28–1.42 | 0.913$\pm$0.028$\pm$0.035 | 0.782$\pm$0.023$\pm$0.030 | 0.734$\pm$0.033$\pm$0.028
1.42–1.56 | 0.952$\pm$0.049$\pm$0.046 | 0.913$\pm$0.043$\pm$0.044 | 0.716$\pm$0.054$\pm$0.041
1.56–1.70 | 1.410$\pm$0.116$\pm$0.095 | 1.173$\pm$0.089$\pm$0.079 | 1.092$\pm$0.124$\pm$0.094


# Sketch2Model: View-Aware 3D Modeling from Single Free-Hand Sketches

Song-Hai Zhang Yuan-Chen Guo Qing-Wen Gu
BNRist corresponding author. Department of Computer Science and Technology
Tsinghua University  Beijing
<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

We investigate the problem of generating 3D meshes from single free-hand
sketches, aiming at fast 3D modeling for novice users. It can be regarded as a
single-view reconstruction problem, but with unique challenges, brought by the
variation and conciseness of sketches. Ambiguities in poorly-drawn sketches
could make it hard to determine how the sketched object is posed. In this
paper, we address the importance of viewpoint specification for overcoming
such ambiguities, and propose a novel view-aware generation approach. By
explicitly conditioning the generation process on a given viewpoint, our
method can generate plausible shapes automatically with predicted viewpoints,
or with specified viewpoints to help users better express their intentions.
Extensive evaluations on various datasets demonstrate the effectiveness of our
view-aware design in solving sketch ambiguities and improving reconstruction
quality.

##  1 Introduction

Sketch-based 3D modeling has been studied for decades, intended to free people
from the tedious and time-consuming modeling process. With the widespread
usage of portable touch screens and emergence of VR/AR technologies, the need
of 3D content creation for novice users is increasing [37]. However, existing
sketch-based 3D modeling techniques either require precise line-drawings from
multiple views or simply retrieve from existing models, both failing to
provide easy-to-use interface and customizability at the same time. We aim at
fast and intuitive 3D modeling for people without professional drawing skills,
and investigate the problem of mesh generation from a single free-hand sketch.
It is in general a single-view reconstruction problem, but has its unique
challenges due to the characteristics of free-hand sketches. Unlike real
images, free-hand sketches can be poorly-drawn with drastic simplifications
and geometric distortions, and lack important visual cues like textures or
shading. This makes it difficult, sometimes even impossible, for algorithms to
understand sketches correctly. One tricky scenario results from the “camera-
shape ambiguity” [21], as shown in Fig. 1. Subjectivity of sketch creation
could lead to different explanation of the same sketch, like which side being
the front of the car (left). Furthermore, a recent study shows that existing
single-view reconstruction approaches mainly rely on the recognition of input
images, rather than actually performing geometry reconstruction. Therefore,
they can be hard to generalize to unseen data and perform worse on hand-drawn
sketches, which are created with barely any constraint, showing more diverse
in appearance.

Figure 1: Ambiguities in free-hand sketches. It could be hard to determine how
the sketched object is posed.

Recall how human cognitive system works for the task of 3D reconstruction.
Human relies on visual memory and visual rules to recover 3D geometry from
imagery [28]. Visual memory contains priors gained from daily life, like what
an object of a certain class might look like, while visual rules act like a
regularizer, requiring that an object should match what it looks like from a
certain viewpoint. When seeing a sketch, we search our visual memory and try
to find a solution that also obeys visual rules. However, this search process
may not go well when (1) we could not figure out how the sketched object is
posed, thus finding difficulty applying visual rules; (2) multiple solutions
exist due to the ambiguity of the sketch. Both problems result from the lack
of details in sketches, and we address that viewpoint specification can be
essential to the above problems. If we are told which viewpoint the object is
sketched from, search space can be easily reduced, which lowers search
difficulty and may eliminate ambiguities.

Based on the above observations, we think that explicitly specified viewpoints
can directly guide the reconstruction algorithm to find the correct shape
described by the user. Moreover, viewpoints offer extra information for the
understanding of hand-drawn sketches, which can improve generalization ability
for out-of-distribution data. To utilize view information, we propose a view-
aware sketch-based 3D reconstruction method, which explicitly conditions the
generation process on a given viewpoint. We extend the traditional encoder-
decoder architecture used in some recent works [20, 22]. In the encoder, image
features are decomposed to a latent view code and a latent shape code. The
latent view code is used to predict viewpoint for the input sketch, and the
latent shape code is combined with a latent view code to generate the output
shape. Just like other disentangling problems, the network would take a short
path and fail to decompose certain properties if no other constraints are
made. To ensure that only view information is contained in the latent view
space, a view auto-encoder is learned to transform viewpoints to latent view
space and vice versa. To force the decoder network to depend on the given view
code, we propose a simple but effective random view reinforced training
strategy, where random views along with ground truth views are fed to the
decoder, forcing the network to learn how to match the input sketch from
different viewpoints. We use synthetic sketch data for training, due to the
lack of paired sketch-3D dataset, and apply domain adaptation technique to
bridge the gap between synthetic sketches and real sketches. In the inference
stage, our method can generate 3D mesh based on a single free-hand sketch
automatically using the predicted viewpoint, or semi-automatically using a
user-specified viewpoint.

Extensive experiments are conducted to demonstrate the effectiveness of our
design. We first perform case studies to show characteristics of our view-
aware architecture, and how specified views can be used to eliminate
ambiguities. To evaluate how our method performs on free-hand sketches and
inspire further research, we collect a ShapeNet-Sketch dataset based on the
ShapeNet dataset, which contains 1,300 sketch-shape pairs. Results on various
datasets show that our method can generate higher-quality shapes and better
convey user’s intentions comparing to alternative baselines, which
demonstrates the advantages of introducing viewpoint specification. Ablation
studies are performed to show the necessity of serveral parts of our method.

To summarize, our contributions are as follows:

  * •

We are the first to investigate the problem of generating 3D mesh from a
single free-hand sketch, which provides a fast and easy-to-use 3D content
creation solution for novice users.

  * •

We address the importance of viewpoint specification in the sketch-based
reconstruction task, and design a view-aware generation architecture to
condition the generation process explicitly on viewpoints. Quantitative and
qualitative evaluations on various datasets demonstrate our method can
generate promising shapes that well convey user’s intentions and generalize
better on free-hand sketches.

Figure 2: Network architecture of (a) baseline methods [20, 22] and (b) our
method. Purple and blue blocks denote inputs and trainable parameters
respectively. $\mathcal{R}$ is the differentiable rendering module. Our method
extends the encoder-decoder model by decomposing image features into shape
space $\mathcal{S}$ and view space $\mathcal{V}$. We train a view encoder
$E_{v}$ and a view decoder $D_{v}$ to ensure only view-related information is
contained in view space, and force the decoder $D$ to use view information by
training with an additional random view $V_{r}$. Shape quality is preserved by
a shape discriminator $D_{s}$.

##  2 Related Work

###  2.1 Single-View 3D Reconstruction

Recovering 3D geometry from a single image is an ill-posed problem. Early
approaches utilize perceptual cues, such as shading [14] and texture [39], to
get a clue about surface orientations. With the emergence of online 3D model
collections and large-scale 3D model datasets [1], data-driven approaches are
developed to infer category-specific shapes directly from image features [16,
4, 10, 8, 38, 24, 3, 29], in the form of voxel [4, 10], point cloud [8],
triangle mesh [16, 38, 29], and implicit function [24, 3]. Recently,
differentiable rendering techniques [40, 33, 20, 22, 27] are proposed to relax
the need for ground truth 3D models in training, which enables supervision
with solely 2D images. Our method is based on the single-view reconstruction
process of [22]. We extend the original approach by disentangling image
features into a latent shape space and a latent view space, and achieve view-
aware generation by applying special designed training strategy. Note that no
3D information is needed in our training process.

###  2.2 Sketch-Based 3D Modeling

3D modeling based on sketches, has been studied for a long time. Olsen et al.
[28] categorized traditional sketch-based modeling techniques into evocative
[9, 2, 34] and constructive [17, 26, 19, 25] ones. Evocative approaches create
models from template primitives or retrieve objects from model collections,
while constructive ones directly map the input strokes to a 3D model,
providing free-form modeling abilities. Either of the two paradigms has its
shortcomings: evocative methods are confined to generate certain shapes or
primitives, and the lack of prior knowledge in constructive methods often
requires large efforts to get the desired shape. Deng et al. [6] proposed to
extract free-form shapes from single images in an interactive way, inspired by
the lofting technique in CAD systems. By utilizing deep learning techniques,
several works [23, 15, 11, 32, 5, 36, 31, 35, 12] have achieved to gain priors
from existing 3D models, while being able to leverage user inputs. However,
very few of them focuses on reconstruction from free-hand sketches [36, 35],
instead of precise line drawings. Wang et al. [36] proposed a retrieval-based
apporach to generate 3D voxels from free-hand sketches. The work most similar
to ours is that of Wang et al. [35], where point cloud is generated according
to a single free-hand sketch, and rotated to a canonical view by predicted
viewpoint to match the ground truth. Different from their work, we regard
viewpoint as an additional input to the generation process, and rely on them
to interpret sketches. The authors proposed sketch standardization steps to
synthesize sketches from edge maps, while we try to bridge the domain gap in
feature space.

##  3 Method

To generate 3D mesh from a single free-hand sketch, we first propose a
baseline approach, that works the same way as single-view reconstruction for
real images. Then we extend the baseline architecture by decomposing image
features into a latent view space and a latent shape space, and condition the
generation process on the choice of viewpoint.

###  3.1 View-Aware Generation

Given an input sketch $I$, we wish to generate a 3D mesh $M$, under the
constraint that the sketch represents the object seen from a specific
viewpoint $V$.

As a basis of our method, the single-view mesh reconstruction framework
proposed in [20, 22] is built upon a simple encoder-decoder architecture,
shown in Fig.2(a). The encoder $E$ is a convolutional neural network, which
extracts image features from input image $I$ and outputs a compact feature
vector $z=E(I)$. The decoder $D$ calculates from $z$ the vertex offsets of a
template mesh, and deforms it to get the output mesh $M=D(z)$. By
approximating gradients of the rasterization process in the differentiable
rendering module $\mathcal{R}$, the network can be end-to-end trained by
comparing rendered silhouettes and ground truth ones, without the need for
ground truth 3D shapes.

To explicitly condition the generation process on viewpoints, we design a
novel view-aware architecture, shown in Fig.2(b). In our encoder, the image
feature vector $z$ is further mapped to a latent view space $\mathcal{V}$ and
a latent shape space $\mathcal{S}$. The decoder takes a latent view code
$z_{v}$ and a shape code $z_{s}$, and get a deformed mesh $M$. Denote the
image space and mesh space to be $\mathcal{I}$ and $\mathcal{M}$, our encoder
and decoder can be expressed as:

$\displaystyle E$
$\displaystyle:\mathcal{I}\rightarrow\mathcal{V}\times\mathcal{S}$ (1)
$\displaystyle D$
$\displaystyle:\mathcal{V}\times\mathcal{S}\rightarrow\mathcal{M}$ (2)

We also introduce a view auto-encoder, denoted as $E_{v}$ and $D_{v}$, to
encode an arbitrary viewpoint to the latent view space and vice versa:

$\displaystyle D_{v}(E_{v}(V))$ $\displaystyle=V$ (3) $\displaystyle E_{v}(V)$
$\displaystyle\in\mathcal{V}$ (4)

such that only view-related information are held in the latent view space. We
predict the viewpoint for the input sketch from the latent view code $z_{v}$
given by the encoder:

$\hat{V}=D_{v}(z_{v})$ (5)

Intuitive as it seems, it is not straightforward to ensure that shapes are
generated by taking the latent view code $z_{v}$ into consideration. A common
degradation could happen, that $M$ is directly generated from $z_{s}$, totally
ignoring $z_{v}$, if trained without any other constraint. We propose a random
view reinforced training strategy to solve this problem. In addition to the
ground truth viewpoint $V$, we feed a random viewpoint $V_{r}$ to the decoder
network and generate a mesh $M_{r}$. By forcing consistency between the
projected silhouette of $M_{r}$ under $V_{r}$ and the input silhouette, the
network will learn to match the input sketch under any given viewpoint.
However, interpreting input sketches with an arbitrary viewpoint is not
feasible. This will cause the network to generate distorted shapes, which only
satisfy the silhouette constraint, but are not meaningful objects. To avoid
distortions as much as possible, we introduce a shape discriminator $D_{s}$,
which is trained jointly with the encoder and decoder in an adversarial
manner. The random view reinforced training and the shape discriminator work
as a balance between view-awareness and shape quality. The network may not
produce shapes strictly matching the input silhouette under $V_{r}$, but still
be aware of the impacts of viewpoints to the generation results.

###  3.2 Training and Inference

##### Domain adaptation.

Due to the lack of paired sketch-shape data, we use synthetic sketches of
ShapeNet objects as training data, which are precise line-drawings of objects,
and have different appearances from free-hand sketches. Performance drop
occurs when the model trained on synthetic sketches is tested on hand-drawn
ones. To bridge the gap between them, previous works mostly try to mimic hand-
drawn sketches when generating synthetic data by hand-crafted rules or image
translation techniques. We first propose to bridge this gap in feature space
instead of image space, inspired by existing domain adaptation approaches. Our
intention is to make image features of synthetic and hand-drawn sketches
indistinguishable. To do this, we learn a domain discriminator to separate
features coming from the two domains, and train it with the encoder
adversarially.

##### Optimization objectives.

Our loss functions consist of five parts: silhouette loss $\mathcal{L}_{s}$
between projected and ground truth silhouettes, geometry regularizations
$\mathcal{L}_{r}$ for generated shapes, view prediction loss $\mathcal{L}_{v}$
between predicted and ground truth viewpoints, classification loss
$\mathcal{L}_{sd}$ and $\mathcal{L}_{dd}$ for shape discriminator and domain
discriminator.

For input and rasterized silhouettes, we adopt IoU loss as in [20, 22]. Let
$S_{1}$ and $S_{2}$ be two binary silhouettes, IoU loss $\mathcal{L}_{iou}$ is
defined as:

$\mathcal{L}_{iou}(S_{1},S_{2})=1-\frac{||S_{1}\otimes
S_{2}||_{1}}{||S_{1}\oplus S_{2}-S_{1}\otimes S_{2}||_{1}}$ (6)

Denote $P(\cdot,\cdot)$ as the differentiable rasterization function, which
takes a mesh $M$ and a viewpoint $V$, and output the rasterized silhouette of
$M$ under $V$. Our silhouette loss is expressed as:

$\begin{split}\mathcal{L}_{s}&=\mathcal{L}_{iou}(S,P(D(z_{s},E_{v}(V)),V))\\\
&+\lambda_{r}\mathcal{L}_{iou}(S,P(D(z_{s},E_{v}(V_{r})),V_{r}))\end{split}$
(7)

where $V$ and $S$ is the ground truth viewpoint and silhouette respectively.
Note that we use the latent code for ground truth viewpoint $E_{v}(V)$ in
training, instead of the predicted $z_{v}$, because we observe negative
impacts for training by utilizing inaccurate predictions. Most existing works
compute IoU loss on low resolution silhouettes like $64\times 64$, which
ignores fine structures. Considering computational efficiency, we adopt a
multi-scale progressive training strategy, leveraging silhouettes of different
resolutions. Let $L_{s}^{i}$ be the silhouette loss on the i-th level of the
silhouette pyramid, $N$ be the number of levels, we adopt a progressive
silhouette loss $\mathcal{L}_{sp}$:

$\mathcal{L}_{sp}=\sum_{i=1}^{N}\lambda_{s_{i}}\mathcal{L}_{s}^{i}$ (8)

In early stage of training, only low resolution silhouettes are used for loss
calculation. Higher resolution ones are used for shape refinement as the
training progresses.

To improve visual quality of generated meshes, we apply flatten loss and and
laplacian loss as regularizations for mesh structures, as in [20, 22, 38]. We
denote the shape regularization loss as $\mathcal{L}_{r}$.

For the representation of viewpoint, we assume fixed distance to camera and
represent viewpoints as Euler angles. We adopt L2 loss for predicted and
ground truth views:

$\mathcal{L}_{v}=||V-\hat{V}||_{2}=||V-D_{v}(z_{v})||_{2}$ (9)

To train the view encoder, we adopt a view reconstruction loss
$\mathcal{L}_{vr}$ between original and reconstructed views:

$\displaystyle\mathcal{L}_{vr}=||V-D_{v}(E_{v}(V))||_{2}$ (10)

Figure 3: Illustrations for effectiveness of our view-aware design. When
giving the same sketch as input but specifying different viewpoints, our model
can synthesize different results trying to match the input shape from the
corresponding point of view. For each example, the first row shows synthesized
results from a fixed viewpoint, and the second row shows projections onto the
given viewpoint overlapped with the input sketch. The fine property of our
view-aware design allows solving ambiguity problems with minimal user input.

To ease the training process, we apply a gradient reversal layer before shape
discriminator and domain discriminator. The gradient reversal layer reverses
the sign of the gradient that passes it, which achieves adversarial training
in a single pass. For the shape discriminator, we expect it to output 1 for
$M$ and 0 for $M_{r}$, and for the domain discriminator, 1 for synthetic
sketches and 0 for hand-drawn sketches, which lead to the following losses:

$\begin{split}\mathcal{L}_{sd}=&-\mathbb{E}_{M}[log(D_{s}(M))]\\\
&-\mathbb{E}_{M_{r}}[1-log(D_{s}(M_{r}))]\end{split}$ (11)
$\begin{split}\mathcal{L}_{dd}=&-\mathbb{E}_{S_{s}}[log(D_{d}(S_{s}))]\\\
&-\mathbb{E}_{S_{h}}[1-log(D_{d}(S_{h}))]\end{split}$ (12)

where $S_{s}$ and $S_{h}$ denote synthetic sketches and hand-drawn sketches
respectively.

Our overall loss function is the weighted sum of the above objectives:

$\begin{split}\mathcal{L}&=\mathcal{L}_{sp}+\mathcal{L}_{r}+\lambda_{v}\mathcal{L}_{v}+\lambda_{vr}\mathcal{L}_{vr}\\\
&+\lambda_{sd}\mathcal{L}_{sd}+\lambda_{dd}\mathcal{L}_{dd}\end{split}$ (13)

During inference, shapes can be generated from an input free-hand sketch
automatically or semi-automatically, depending on the choice of latent view
code $z_{v}$. Users can use the predicted viewpoint $\hat{V}$ to get the
output mesh $\hat{M}=D(z_{s},E_{v}(\hat{V}))$, or provide a specified
viewpoint $\tilde{V}$ to get $\tilde{M}=D(z_{s},E_{v}(\tilde{V}))$.

|  Voxel IoU ($\uparrow$)
---|---
Category | airplane | bench | cabinet | car | chair | display | lamp | loudspeaker | rifle | sofa | table | telephone | watercraft | mean
Retrieval | 0.513 | 0.380 | 0.518 | 0.667 | 0.346 | 0.385 | 0.325 | 0.468 | 0.475 | 0.483 | 0.311 | 0.622 | 0.422 | 0.455
SoftRas | 0.576 | 0.467 | 0.663 | 0.769 | 0.496 | 0.541 | 0.431 | 0.629 | 0.605 | 0.613 | 0.512 | 0.706 | 0.556 | 0.582
Ours (pred) | 0.618 | 0.477 | 0.667 | 0.746 | 0.515 | 0.550 | 0.463 | 0.624 | 0.606 | 0.620 | 0.470 | 0.673 | 0.569 | 0.584
Ours (gt) | 0.624 | 0.481 | 0.701 | 0.751 | 0.522 | 0.604 | 0.472 | 0.641 | 0.612 | 0.622 | 0.478 | 0.719 | 0.586 | 0.601
|  Chamfer Distance ($\downarrow$)
Category | airplane | bench | cabinet | car | chair | display | lamp | loudspeaker | rifle | sofa | table | telephone | watercraft | mean
Retrieval | 0.856 | 1.384 | 1.941 | 0.767 | 1.878 | 1.967 | 3.017 | 2.468 | 0.731 | 2.056 | 2.151 | 1.042 | 1.130 | 1.645
SoftRas | 0.531 | 0.944 | 2.271 | 0.947 | 1.703 | 1.762 | 3.272 | 2.234 | 0.495 | 2.161 | 1.662 | 1.307 | 0.872 | 1.551
Ours (pred) | 0.493 | 1.003 | 1.867 | 0.812 | 1.488 | 1.637 | 3.300 | 2.021 | 0.604 | 1.944 | 1.790 | 1.120 | 1.018 | 1.469
Ours (gt) | 0.470 | 0.974 | 1.561 | 0.790 | 1.457 | 1.228 | 3.263 | 1.884 | 0.574 | 2.011 | 1.744 | 0.928 | 0.897 | 1.368
Table 1: Comparisons of mean voxel IoU and Chamfer Distance on ShapeNet-Synthetic test set. Our method with either ground truth viewpoins (gt) or predicted viewpoints (pred) surpasses baseline methods on most of the classes on voxel IoU score, and achieves the best overall performance regarding to Chamfer Distance.  Figure 4: Ablation studies for random view reinforced training strategy (RVR) and shape discriminator (SD). Without applying random view reinforced training, the network would fail to generate meaningful objects under given viewpoints (first row). Without shape discriminator, the output shape may not resemble real objects (second row). We successfully achieve view-aware generation by adopting both techniques (third row). RVR | SD | MS | airplane | bench | cabinet | car | chair | display | lamp
---|---|---|---|---|---|---|---|---|---
|  |  | 0.557 (0.565) | 0.345 (0.460) | 0.597 (0.579) |  0.747 (0.753) | 0.499 (0.508) |  0.457 (0.577) | 0.290 (0.421)
✓ |  |  | 0.587 (0.469) | 0.407 (0.435) | 0.674 (0.641) | 0.753 (0.736) | 0.514 (0.505) | 0.525 (0.504) | 0.454 (0.451)
✓ | ✓ |  | 0.588 (0.582) | 0.459 (0.455) | 0.690 (0.658) |  0.756 (0.749) | 0.510 (0.504) | 0.591 (0.540) | 0.461 (0.453)
✓ | ✓ | ✓ |  0.624 (0.618) |  0.481 (0.477) |  0.701 (0.667) | 0.751 (0.746) |  0.522 (0.515) |  0.604 (0.550) |  0.472 (0.463)
RVR | SD | MS | loudspeaker | rifle | sofa | table | telephone | watercraft | mean
|  |  | 0.584 (0.614) | 0.500 (0.576) |  0.624 (0.643) | 0.406 (0.427) |  0.522 (0.705) |  0.574 (0.575) | 0.516 (0.569)
✓ |  |  | 0.605 (0.598) | 0.570 (0.444) | 0.613 (0.612) | 0.431 (0.427) | 0.651 (0.590) | 0.570 (0.551) | 0.566 (0.536)
✓ | ✓ |  | 0.606 (0.598) | 0.565 (0.560) |  0.633 (0.632) | 0.429 (0.424) | 0.698 (0.638) | 0.550 (0.551) | 0.580 (0.565)
✓ | ✓ | ✓ |  0.641 (0.624) |  0.612 (0.606) | 0.622 (0.620) |  0.478 (0.470) |  0.719 (0.673) |  0.586 (0.569) |  0.601 (0.584)
Table 2: Quantitative ablation studies for random view reinforced training (RVR), shape discriminator (SD) and multi-scale progressive training (MS). Numbers outside and inside parenthesis are mean voxel IoU scores on ShapeNet-Synthetic test set for ground truth and predicted viewpoints respectively. By adopting all three strategies, we can achieve the highest IoU scores in most cases with or without groud truth views. Figure 5: Some representative results on our ShapeNet-Sketch dataset. Each model is rendered from a fixed viewpoint, and the projection on the ground truth viewpoint is given on the bottom right corner of each example for comparison. Our method can generate promising shapes with hand-drawn sketches. Note that the results shown here use predicted viewpoints for generation. More results are shown in the supplementary material. Category | airplane | bench | cabinet | car | chair | display | lamp | loudspeaker | rifle | sofa | table | telephone | watercraft | mean
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
Retrieval | 0.411 | 0.219 | 0.409 | 0.626 | 0.238 | 0.338 | 0.223 | 0.365 | 0.413 | 0.431 | 0.232 | 0.536 | 0.369 | 0.370
SoftRas | 0.469 | 0.347 | 0.545 | 0.648 | 0.361 | 0.472 | 0.328 | 0.533 | 0.541 | 0.534 | 0.359 | 0.537 | 0.456 | 0.472
Ours (pred) | 0.479 | 0.357 | 0.547 | 0.649 | 0.383 | 0.435 | 0.336 | 0.526 | 0.510 | 0.528 | 0.361 | 0.551 | 0.450 | 0.470
Ours (gt) | 0.487 | 0.366 | 0.568 | 0.659 | 0.393 | 0.479 | 0.338 | 0.544 | 0.534 | 0.534 | 0.357 | 0.554 | 0.466 | 0.483
Ours + DA (pred) | 0.515 | 0.362 | - | 0.659 | 0.385 | - | - | - | 0.511 | 0.533 | 0.360 | - | - | 0.475
Ours + DA (gt) | 0.526 | 0.367 | - | 0.679 | 0.398 | - | - | - | 0.535 | 0.548 | 0.357 | - | - | 0.489
Table 3: Mean voxel IoU on ShapeNet-Sketch dataset. We apply domain adaptation (DA) on 7 of the classes, which have considerable amount of sketches in the Sketchy database [30] and Tu-Berlin dataset [7]. Our method with domain adaptation achieves the highest IoU score, and shows significant improvement on airplane, car and sofa. Category | airplane | bench | cabinet | car | chair | display | lamp | loudspeaker | rifle | sofa | table | telephone | watercraft | mean
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
SoftRas | 0.584 | 0.687 | 0.835 | 0.793 | 0.728 | 0.765 | 0.599 | 0.762 | 0.568 | 0.773 | 0.720 | 0.802 | 0.690 | 0.716
Ours (pred) | 0.647 | 0.620 | 0.857 | 0.864 | 0.724 | 0.777 | 0.652 | 0.807 | 0.654 | 0.808 | 0.703 | 0.848 | 0.726 | 0.745
Ours (gt) | 0.644 | 0.673 | 0.868 | 0.866 | 0.737 | 0.807 | 0.631 | 0.822 | 0.614 | 0.817 | 0.735 | 0.855 | 0.735 | 0.754
Table 4: Comparison of 2D silhouette IoU score on ShapeNet-Sketch dataset. The
generated shapes are projected to the ground truth view and we calculate the
IoU score between the projected silhouette and the ground truth silhouette.
Our method achieves significantly higher results than baseline methods. It
demonstrates that our method can generate shapes better match the input
sketches. Figure 6: Qualitative comparisons with two baseline methods on
sketches from the Sketchy database [30] and Tu-Berlin dataset [7]. The
reconstructed mesh is projected on our predict viewpoint, to compare with the
given sketch. Our method generates meshes that align better with the given
sketch, and performs well on rare shapes (bottom right) and poorly-drawn
sketches (bottom left). Figure 7: Ablation study for domain adaptation.
Without domain adaptation, some distinctive features might be lost, like the
tail of the airplane (left). Shapes generated after domain adaptation tend to
have sharper boundaries (middle, right).

##  4 Experiments

We first perform case studies to show the effectiveness of our view-aware
design and how specified viewpoints can be used to solve the ambiguity
problem. Quantitative and qualitative evaluations on both synthetic and hand-
drawn sketches show that our method generates shapes better matching the given
sketch comparing to alternative baselines.

###  4.1 Datasets

##### ShapeNet-Synthetic.

We use synthetic sketches to train our model. We create the synthetic dataset
using rendered images provided by Kar et al. [18]. It contains object
renderings of 13 categories from ShapeNet [1]. Images from 20 different views
of each object are rendered in 224x224 resolution. We extract the edge map of
each rendered image using canny edge detector, which does not require 3D
ground truth comparing to extracting contours from 3D shapes. We directly use
the edge maps as synthetic sketches, and use this dataset for training and
evaluation, under the same train/test split as in [22].

##### ShapeNet-Sketch.

To quantitatively evaluate our method on free-hand sketches and benefit
further research, we collect a paired dataset of 3D shape and hand-drawn
sketches, which we call ShapeNet-Sketch. We randomly choose 100 rendered
images for each of the 13 ShapeNet categories from Kar’s dataset [18], and ask
people of different drawing skills to sketch the object based on the rendered
image on a touch pad. Our ShapeNet-Sketch dataset contains in total 1,300
free-hand sketches and their corresponding ground truth 3D models. We use this
dataset for evaluations only.

##### Existing sketch datasets.

We use some existing sketch datasets designed for other sketch-related tasks
to qualitatively evaluate our method, and demonstrate the advantages of our
method in dealing with poorly-drawn sketches. In detail, we use sketches of 7
categories that overlap with the ShapeNet classes, from Sketchy database [30]
and Tu-Berlin dataset [7].

###  4.2 Implementation Details

We use ResNet-18 [13] as our image feature extractor and SoftRas [22] for
differentiable rendering of generated meshes. Detailed network architecture is
described in the supplementary material. We assume a canonical view for
objects in each class and use elevation and azimuth angles to represent
viewpoints. The canonical view is 0 in elevation and 0 in azimuth, and the
distance to camera is fixed. We use Adam optimizer with learning rate $1e-4$,
and train a separate model for each class. Hyper-parameters are set to
$\lambda_{r}=\lambda_{sd}=\lambda_{dd}=0.1$, $\lambda_{v}=\lambda_{vr}=10$.

###  4.3 Effectiveness of View-Aware Design

As is illustrated in Sec.3.1, our generation result relies on both input
sketch image and a viewpoint. With different viewpoints, the network is
expected to generate different shapes to match the input sketch. Examples in
Fig.3 show how the generated shape changes with the change of elevation and
azimuth angle. For each example, the second row shows how well the generated
model matches the input sketch from the given view. In the vehicle example
(top right), the choice of azimuth angle, which represents which side the
vehicle is looking from, influences the output model to be a van (left, -90 in
azimuth) or a truck (right, 90 in azimuth). For the badly-drawn table (bottom
left), the height of the table and the thickness of the table top are
determined by the elevation angle.

Fig.4 shows the importance of the proposed random view reinforced training
strategy and shape discriminator to the generation results. If only normal
views are used in training, the network fails to learn the dependency on input
viewpoint, and could get confused on given views. Without shape discriminator,
the output mesh may get distorted and not resemble a real object. Under the
influence of both, we can get view-aware property with promising shape
quality.

###  4.4 Comparisons and Evaluations

We compare our method with the traditional encoder-decoder architecture in
Fig. 2(a) and a retrieval-based approach. For the former, we adopt SoftRas
[22] as the differentiable rendering module, and denote it as “SoftRas” for
simplicity. We also train a separate model for each category for fair
comparison. Retrieval is a widely-adopted apporach to get 3D shape from a
single sketch input. Instead of using traditional image features, we use
features from a pre-trained sketch classification network, which is
demonstrated to be more powerful than hand-crafted features in many sketch-
related works [41, 30]. For each input sketch, we find its nearest neighbor in
training edge maps and take the corresponding 3D shape as the retrieval
result. For quantitative comparisons, we use voxel IoU score, as in [20, 22].

####  4.4.1 Comparisons on ShapeNet-Synthetic Dataset

Comparison results on ShapeNet-Synthetic test set is shown in Table.1. We
evaluate our method using both the predicted viewpoint (pred) and the ground
truth viewpoint (gt), which serves as the lower and upper bound for our view-
aware design. Our method outperforms the two baselines on most of the
categories, especially when the ground truth view is given. This implies that
view information plays an essential role in reconstruction, and generation
quality should be improved by specifying correct views. We perform ablation
studies on several designs of our approach in Table.2. RVR, SD, MS denotes for
random view reinforced training, shape discriminator and multi-scale
progressive training respectively. Without using any of the three techniques,
the method performs well on predicted viewpoints, but fails on given ground
truth views, since it is not trained to fit arbitrary viewpoints. Adopting
random view reinforced training without shape discriminator will lead to poor
results on predicted views, because the shapes may get distorted given
inaccurate view predictions. By applying multi-scale progressive training, the
performance can be further improved.

####  4.4.2 Comparisons on ShapeNet-Sketch Dataset

We show voxel IoU score on our collected ShapeNet-Sketch dataset in Table.3,
and further demonstrate the effectiveness of our domain discriminator. We
observe significant performance improvement after applying domain adaptation
in some of the classes (airplane, car, sofa), indicating that large domain
gaps exist. For comparison, we also tried to create fake sketches by utilizing
CycleGAN and use them as training data, but no significant improvement is
observed. Some reconstruction results using predicted views on ShapeNet-Sketch
dataset is shown in Fig.5. Fig.7 visualizes the effects of domain adaptation.
Shapes without domain adaptation can be too smooth and lack distinctive
features, like the tail of the airplane (left).

We also compare projected silhouettes of generated meshes with ground truth
silhouettes, and show the results in Table.4. It shows our model is more
powerful at matching input sketches, which provides evidence for the
effectiveness of our view-aware design.

####  4.4.3 Evaluations on Free-Hand Sketches

Finally, we qualitatively evaluate our method on hand-drawn sketches from the
Sketchy database [30] and Tu-Berlin dataset [7]. Some representative results
are shown in Fig.6. It can be seen that our method can better align the
boundary of the generated mesh with the input sketch, benefit from the view-
aware design. Our method balance well between sketch alignment and shape
realism when handling out-of-distribution shapes, like the airplane on the top
left and the table on the bottom left. Results here are all generated
automatically using predicted viewpoints, and users should be able to control
the output shape by specifying new viewpoints, like is illustrated in Sec.4.3.
This makes our method more flexible and practical than existing view-agnostic
methods.

##  5 Conclusion

We investigate the problem of generating 3D mesh from a single free-hand
sketch, aiming for fast content generation for novice users. A view-aware
architecture is proposed, to condition the generation process explicitly on
viewpoints, which improves generation quality and brings controllability to
the output shape. Our method can generate promising shapes on several free-
hand sketch datasets, well balancing user intentions and shape qualities,
especially for poorly-drawn sketches. We hope the view-aware paradigm can
inspire further researches in single view 3D reconstruction and sketch-related
areas.

##### Acknowledgements.

We thank all reviewers for their thoughtful comments. This work was supported
by the National Key Technology R&D Program (Project Number 2017YFB1002604),
the National Natural Science Foundation of China (Project Numbers 61772298,
61521002), Research Grant of Beijing Higher Institution Engineering Research
Center, and Tsinghua–Tencent Joint Laboratory for Internet Innovation
Technology.

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