EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

CERN-PH-EP-2011-212 LHCb-PAPER-2011-026 December 20, 2011

Observation of $\overline{B}_{s}^{0}\rightarrow J/\psi f^{\prime}_{2}(1525)$
in $J/\psi K^{+}K^{-}$ final states
The LHCb Collaboration†††Authors are listed on the following pages.

The decay $\overline{B}_{s}^{0}\rightarrow J/\psi K^{+}K^{-}$ is investigated
using 0.16 fb-1 of data collected with the LHCb detector using 7 TeV $pp$
collisions. Although the $J/\psi\phi$ channel is well known, final states at
higher $K^{+}K^{-}$ masses have not previously been studied. In the
$K^{+}K^{-}$ mass spectrum we observe a significant signal in the
$f^{\prime}_{2}(1525)$ region as well as a non-resonant component. After
subtracting the non-resonant component, we find
${{\cal{B}}\left(\overline{B}_{s}^{0}\rightarrow J/\psi
f^{\prime}_{2}(1525)\right)}/{{\cal{B}}\left(\overline{B}_{s}^{0}\rightarrow
J/\psi\phi\right)}=(26.4\pm 2.7\pm 2.4)$%.

Keywords: LHC, $C\\!P$ violation, $B$ decays
PACS: 13.25.Hw, 14.40.Nd, 14.40.Be
Submitted to Physical Review Letters

The LHCb Collaboration

R. Aaij23, C. Abellan Beteta35,n, B. Adeva36, M. Adinolfi42, C. Adrover6, A.
Affolder48, Z. Ajaltouni5, J. Albrecht37, F. Alessio37, M. Alexander47, G.
Alkhazov29, P. Alvarez Cartelle36, A.A. Alves Jr22, S. Amato2, Y. Amhis38, J.
Anderson39, R.B. Appleby50, O. Aquines Gutierrez10, F. Archilli18,37, L.
Arrabito53, A. Artamonov 34, M. Artuso52,37, E. Aslanides6, G. Auriemma22,m,
S. Bachmann11, J.J. Back44, D.S. Bailey50, V. Balagura30,37, W. Baldini16,
R.J. Barlow50, C. Barschel37, S. Barsuk7, W. Barter43, A. Bates47, C. Bauer10,
Th. Bauer23, A. Bay38, I. Bediaga1, S. Belogurov30, K. Belous34, I.
Belyaev30,37, E. Ben-Haim8, M. Benayoun8, G. Bencivenni18, S. Benson46, J.
Benton42, R. Bernet39, M.-O. Bettler17, M. van Beuzekom23, A. Bien11, S.
Bifani12, T. Bird50, A. Bizzeti17,h, P.M. Bjørnstad50, T. Blake37, F. Blanc38,
C. Blanks49, J. Blouw11, S. Blusk52, A. Bobrov33, V. Bocci22, A. Bondar33, N.
Bondar29, W. Bonivento15, S. Borghi47,50, A. Borgia52, T.J.V. Bowcock48, C.
Bozzi16, T. Brambach9, J. van den Brand24, J. Bressieux38, D. Brett50, M.
Britsch10, T. Britton52, N.H. Brook42, H. Brown48, A. Büchler-Germann39, I.
Burducea28, A. Bursche39, J. Buytaert37, S. Cadeddu15, O. Callot7, M.
Calvi20,j, M. Calvo Gomez35,n, A. Camboni35, P. Campana18,37, A. Carbone14, G.
Carboni21,k, R. Cardinale19,i,37, A. Cardini15, L. Carson49, K. Carvalho
Akiba2, G. Casse48, M. Cattaneo37, Ch. Cauet9, M. Charles51, Ph.
Charpentier37, N. Chiapolini39, K. Ciba37, X. Cid Vidal36, G. Ciezarek49,
P.E.L. Clarke46,37, M. Clemencic37, H.V. Cliff43, J. Closier37, C. Coca28, V.
Coco23, J. Cogan6, P. Collins37, A. Comerma-Montells35, F. Constantin28, A.
Contu51, A. Cook42, M. Coombes42, G. Corti37, G.A. Cowan38, R. Currie46, C.
D’Ambrosio37, P. David8, P.N.Y. David23, I. De Bonis4, S. De Capua21,k, M. De
Cian39, F. De Lorenzi12, J.M. De Miranda1, L. De Paula2, P. De Simone18, D.
Decamp4, M. Deckenhoff9, H. Degaudenzi38,37, L. Del Buono8, C. Deplano15, D.
Derkach14,37, O. Deschamps5, F. Dettori24, J. Dickens43, H. Dijkstra37, P.
Diniz Batista1, F. Domingo Bonal35,n, S. Donleavy48, F. Dordei11, A. Dosil
Suárez36, D. Dossett44, A. Dovbnya40, F. Dupertuis38, R. Dzhelyadin34, A.
Dziurda25, S. Easo45, U. Egede49, V. Egorychev30, S. Eidelman33, D. van
Eijk23, F. Eisele11, S. Eisenhardt46, R. Ekelhof9, L. Eklund47, Ch.
Elsasser39, D. Elsby55, D. Esperante Pereira36, L. Estève43, A.
Falabella16,14,e, E. Fanchini20,j, C. Färber11, G. Fardell46, C. Farinelli23,
S. Farry12, V. Fave38, V. Fernandez Albor36, M. Ferro-Luzzi37, S. Filippov32,
C. Fitzpatrick46, M. Fontana10, F. Fontanelli19,i, R. Forty37, M. Frank37, C.
Frei37, M. Frosini17,f,37, S. Furcas20, A. Gallas Torreira36, D. Galli14,c, M.
Gandelman2, P. Gandini51, Y. Gao3, J-C. Garnier37, J. Garofoli52, J. Garra
Tico43, L. Garrido35, D. Gascon35, C. Gaspar37, N. Gauvin38, M. Gersabeck37,
T. Gershon44,37, Ph. Ghez4, V. Gibson43, V.V. Gligorov37, C. Göbel54, D.
Golubkov30, A. Golutvin49,30,37, A. Gomes2, H. Gordon51, M. Grabalosa
Gándara35, R. Graciani Diaz35, L.A. Granado Cardoso37, E. Graugés35, G.
Graziani17, A. Grecu28, E. Greening51, S. Gregson43, B. Gui52, E. Gushchin32,
Yu. Guz34, T. Gys37, G. Haefeli38, C. Haen37, S.C. Haines43, T. Hampson42, S.
Hansmann-Menzemer11, R. Harji49, N. Harnew51, J. Harrison50, P.F. Harrison44,
T. Hartmann56, J. He7, V. Heijne23, K. Hennessy48, P. Henrard5, J.A. Hernando
Morata36, E. van Herwijnen37, E. Hicks48, K. Holubyev11, P. Hopchev4, W.
Hulsbergen23, P. Hunt51, T. Huse48, R.S. Huston12, D. Hutchcroft48, D.
Hynds47, V. Iakovenko41, P. Ilten12, J. Imong42, R. Jacobsson37, A. Jaeger11,
M. Jahjah Hussein5, E. Jans23, F. Jansen23, P. Jaton38, B. Jean-Marie7, F.
Jing3, M. John51, D. Johnson51, C.R. Jones43, B. Jost37, M. Kaballo9, S.
Kandybei40, M. Karacson37, T.M. Karbach9, J. Keaveney12, I.R. Kenyon55, U.
Kerzel37, T. Ketel24, A. Keune38, B. Khanji6, Y.M. Kim46, M. Knecht38, P.
Koppenburg23, A. Kozlinskiy23, L. Kravchuk32, K. Kreplin11, M. Kreps44, G.
Krocker11, P. Krokovny11, F. Kruse9, K. Kruzelecki37, M. Kucharczyk20,25,37,j,
T. Kvaratskheliya30,37, V.N. La Thi38, D. Lacarrere37, G. Lafferty50, A.
Lai15, D. Lambert46, R.W. Lambert24, E. Lanciotti37, G. Lanfranchi18, C.
Langenbruch11, T. Latham44, C. Lazzeroni55, R. Le Gac6, J. van Leerdam23,
J.-P. Lees4, R. Lefèvre5, A. Leflat31,37, J. Lefran$c$cois7, O. Leroy6, T.
Lesiak25, L. Li3, L. Li Gioi5, M. Lieng9, M. Liles48, R. Lindner37, C. Linn11,
B. Liu3, G. Liu37, J. von Loeben20, J.H. Lopes2, E. Lopez Asamar35, N. Lopez-
March38, H. Lu38,3, J. Luisier38, A. Mac Raighne47, F. Machefert7, I.V.
Machikhiliyan4,30, F. Maciuc10, O. Maev29,37, J. Magnin1, S. Malde51, R.M.D.
Mamunur37, G. Manca15,d, G. Mancinelli6, N. Mangiafave43, U. Marconi14, R.
Märki38, J. Marks11, G. Martellotti22, A. Martens8, L. Martin51, A. Martín
Sánchez7, D. Martinez Santos37, A. Massafferri1, Z. Mathe12, C. Matteuzzi20,
M. Matveev29, E. Maurice6, B. Maynard52, A. Mazurov16,32,37, G. McGregor50, R.
McNulty12, M. Meissner11, M. Merk23, J. Merkel9, R. Messi21,k, S.
Miglioranzi37, D.A. Milanes13,37, M.-N. Minard4, J. Molina Rodriguez54, S.
Monteil5, D. Moran12, P. Morawski25, R. Mountain52, I. Mous23, F. Muheim46, K.
Müller39, R. Muresan28,38, B. Muryn26, B. Muster38, M. Musy35, J. Mylroie-
Smith48, P. Naik42, T. Nakada38, R. Nandakumar45, I. Nasteva1, M. Nedos9, M.
Needham46, N. Neufeld37, C. Nguyen-Mau38,o, M. Nicol7, V. Niess5, N.
Nikitin31, A. Nomerotski51, A. Novoselov34, A. Oblakowska-Mucha26, V.
Obraztsov34, S. Oggero23, S. Ogilvy47, O. Okhrimenko41, R. Oldeman15,d, M.
Orlandea28, J.M. Otalora Goicochea2, P. Owen49, B. Pal52, J. Palacios39, A.
Palano13,b, M. Palutan18, J. Panman37, A. Papanestis45, M. Pappagallo47, C.
Parkes50,37, C.J. Parkinson49, G. Passaleva17, G.D. Patel48, M. Patel49, S.K.
Paterson49, G.N. Patrick45, C. Patrignani19,i, C. Pavel-Nicorescu28, A. Pazos
Alvarez36, A. Pellegrino23, G. Penso22,l, M. Pepe Altarelli37, S.
Perazzini14,c, D.L. Perego20,j, E. Perez Trigo36, A. Pérez-Calero Yzquierdo35,
P. Perret5, M. Perrin-Terrin6, G. Pessina20, A. Petrella16,37, A.
Petrolini19,i, A. Phan52, E. Picatoste Olloqui35, B. Pie Valls35, B.
Pietrzyk4, T. Pilař44, D. Pinci22, R. Plackett47, S. Playfer46, M. Plo
Casasus36, G. Polok25, A. Poluektov44,33, E. Polycarpo2, D. Popov10, B.
Popovici28, C. Potterat35, A. Powell51, J. Prisciandaro38, V. Pugatch41, A.
Puig Navarro35, W. Qian52, J.H. Rademacker42, B. Rakotomiaramanana38, M.S.
Rangel2, I. Raniuk40, G. Raven24, S. Redford51, M.M. Reid44, A.C. dos Reis1,
S. Ricciardi45, K. Rinnert48, D.A. Roa Romero5, P. Robbe7, E. Rodrigues47,50,
F. Rodrigues2, P. Rodriguez Perez36, G.J. Rogers43, S. Roiser37, V.
Romanovsky34, M. Rosello35,n, J. Rouvinet38, T. Ruf37, H. Ruiz35, G.
Sabatino21,k, J.J. Saborido Silva36, N. Sagidova29, P. Sail47, B. Saitta15,d,
C. Salzmann39, M. Sannino19,i, R. Santacesaria22, C. Santamarina Rios36, R.
Santinelli37, E. Santovetti21,k, M. Sapunov6, A. Sarti18,l, C. Satriano22,m,
A. Satta21, M. Savrie16,e, D. Savrina30, P. Schaack49, M. Schiller24, S.
Schleich9, M. Schlupp9, M. Schmelling10, B. Schmidt37, O. Schneider38, A.
Schopper37, M.-H. Schune7, R. Schwemmer37, B. Sciascia18, A. Sciubba18,l, M.
Seco36, A. Semennikov30, K. Senderowska26, I. Sepp49, N. Serra39, J. Serrano6,
P. Seyfert11, M. Shapkin34, I. Shapoval40,37, P. Shatalov30, Y. Shcheglov29,
T. Shears48, L. Shekhtman33, O. Shevchenko40, V. Shevchenko30, A. Shires49, R.
Silva Coutinho44, T. Skwarnicki52, A.C. Smith37, N.A. Smith48, E. Smith51,45,
K. Sobczak5, F.J.P. Soler47, A. Solomin42, F. Soomro18, B. Souza De Paula2, B.
Spaan9, A. Sparkes46, P. Spradlin47, F. Stagni37, S. Stahl11, O. Steinkamp39,
S. Stoica28, S. Stone52,37, B. Storaci23, M. Straticiuc28, U. Straumann39,
V.K. Subbiah37, S. Swientek9, M. Szczekowski27, P. Szczypka38, T. Szumlak26,
S. T’Jampens4, E. Teodorescu28, F. Teubert37, C. Thomas51, E. Thomas37, J. van
Tilburg11, V. Tisserand4, M. Tobin39, S. Topp-Joergensen51, N. Torr51, E.
Tournefier4,49, M.T. Tran38, A. Tsaregorodtsev6, N. Tuning23, M. Ubeda
Garcia37, A. Ukleja27, P. Urquijo52, U. Uwer11, V. Vagnoni14, G. Valenti14, R.
Vazquez Gomez35, P. Vazquez Regueiro36, S. Vecchi16, J.J. Velthuis42, M.
Veltri17,g, B. Viaud7, I. Videau7, X. Vilasis-Cardona35,n, J. Visniakov36, A.
Vollhardt39, D. Volyanskyy10, D. Voong42, A. Vorobyev29, H. Voss10, S.
Wandernoth11, J. Wang52, D.R. Ward43, N.K. Watson55, A.D. Webber50, D.
Websdale49, M. Whitehead44, D. Wiedner11, L. Wiggers23, G. Wilkinson51, M.P.
Williams44,45, M. Williams49, F.F. Wilson45, J. Wishahi9, M. Witek25, W.
Witzeling37, S.A. Wotton43, K. Wyllie37, Y. Xie46, F. Xing51, Z. Xing52, Z.
Yang3, R. Young46, O. Yushchenko34, M. Zavertyaev10,a, F. Zhang3, L. Zhang52,
W.C. Zhang12, Y. Zhang3, A. Zhelezov11, L. Zhong3, E. Zverev31, A. Zvyagin37.

1Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil
2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
3Center for High Energy Physics, Tsinghua University, Beijing, China
4LAPP, Université de Savoie, CNRS/IN2P3, Annecy-Le-Vieux, France
5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-
Ferrand, France
6CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France
7LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France
8LPNHE, Université Pierre et Marie Curie, Université Paris Diderot,
CNRS/IN2P3, Paris, France
9Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
10Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
11Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
12School of Physics, University College Dublin, Dublin, Ireland
13Sezione INFN di Bari, Bari, Italy
14Sezione INFN di Bologna, Bologna, Italy
15Sezione INFN di Cagliari, Cagliari, Italy
16Sezione INFN di Ferrara, Ferrara, Italy
17Sezione INFN di Firenze, Firenze, Italy
18Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
19Sezione INFN di Genova, Genova, Italy
20Sezione INFN di Milano Bicocca, Milano, Italy
21Sezione INFN di Roma Tor Vergata, Roma, Italy
22Sezione INFN di Roma La Sapienza, Roma, Italy
23Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
24Nikhef National Institute for Subatomic Physics and Vrije Universiteit,
Amsterdam, The Netherlands
25Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraców, Poland
26AGH University of Science and Technology, Kraców, Poland
27Soltan Institute for Nuclear Studies, Warsaw, Poland
28Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
29Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
30Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
31Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
32Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN),
Moscow, Russia
33Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State
University, Novosibirsk, Russia
34Institute for High Energy Physics (IHEP), Protvino, Russia
35Universitat de Barcelona, Barcelona, Spain
36Universidad de Santiago de Compostela, Santiago de Compostela, Spain
37European Organization for Nuclear Research (CERN), Geneva, Switzerland
38Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
39Physik-Institut, Universität Zürich, Zürich, Switzerland
40NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
41Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
42H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
43Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
44Department of Physics, University of Warwick, Coventry, United Kingdom
45STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
46School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
47School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
48Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
49Imperial College London, London, United Kingdom
50School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
51Department of Physics, University of Oxford, Oxford, United Kingdom
52Syracuse University, Syracuse, NY, United States
53CC-IN2P3, CNRS/IN2P3, Lyon-Villeurbanne, France, associated member
54Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
55University of Birmingham, Birmingham, United Kingdom
56Physikalisches Institut, Universität Rostock, Rostock, Germany, associated
to 11

aP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
bUniversità di Bari, Bari, Italy
cUniversità di Bologna, Bologna, Italy
dUniversità di Cagliari, Cagliari, Italy
eUniversità di Ferrara, Ferrara, Italy
fUniversità di Firenze, Firenze, Italy
gUniversità di Urbino, Urbino, Italy
hUniversità di Modena e Reggio Emilia, Modena, Italy
iUniversità di Genova, Genova, Italy
jUniversità di Milano Bicocca, Milano, Italy
kUniversità di Roma Tor Vergata, Roma, Italy
lUniversità di Roma La Sapienza, Roma, Italy
mUniversità della Basilicata, Potenza, Italy
nLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
oHanoi University of Science, Hanoi, Viet Nam

The $\overline{B}_{s}^{0}\rightarrow J/\psi K^{+}K^{-}$ channel has previously
been studied only when the $K^{+}K^{-}$ are consistent with the decay of the
$\phi$ meson. This mode has been used to measure the $C\\!P$ violation in
$\overline{B}_{s}^{0}$ mixing, $\phi_{s}$, a key probe in the search for
physics beyond the Standard Model [1, 2, 3, 4].111Charge conjugate modes are
also considered throughout. In addition to the $\phi$ other resonant or non-
resonant final states may appear and affect the $C\\!P$ measurements,
including an S-wave contribution [5]. In this paper we study the entire
$K^{+}K^{-}$ mass spectrum, including a search for other final states that may
be useful in $C\\!P$ violation studies. These states may provide other ways of
measuring $\phi_{s}$, in decays with a different spin structure that may be
useful for revealing different aspects of $C\\!P$ violation.

We use a 0.16 fb-1 data sample collected with the LHCb detector [6] at a
center-of-mass energy of 7 TeV. The detector elements most important for this
analysis include a vertex locator, a silicon strip device that surrounds the
$pp$ interaction region in the LHC, and other downstream tracking devices
before and after a 4 Tm dipole magnet. Two ring-imaging Cherenkov detectors
are used to identify charged hadrons, while muons are identified using their
penetration through iron. This analysis is restricted to events accepted by a
di-muon trigger [7]. Subsequent selection criteria are applied that serve to
reject background, yet preserve high efficiencies, as determined by Monte
Carlo (MC) events generated using Pythia [8], and the LHCb detector simulation
based on Geant [9]. To be considered as a $J/\psi\rightarrow\mu^{+}\mu^{-}$
candidate, opposite sign tracks are required to have transverse momentum,
$p_{\rm T}$, greater than 500 MeV, be identified as muons, and give a good fit
to a common vertex.222We work in units where $c=1$. Di-muon candidates with
masses between $-48$ and +43 MeV of the $J/\psi$ peak are selected for further
analysis, where the r.m.s. resolution is 13.4 MeV. The invariant mass of the
$\mu^{+}\mu^{-}$ pair is constrained to the $J/\psi$ mass for further
analysis.

Kaon candidates are selected if their minimum distance from the closest
primary vertex is inconsistent with being produced at that vertex. They must
be positively identified based on the logarithm of the likelihood ratio
comparing two particle hypotheses (DLL). There are two criteria used; loose
corresponds to DLL($K-\pi)>0$, while tight has DLL($K-\pi)>10$ and
DLL($K-p)>-3$. We use the loose criterion for checking kaon identification
efficiencies, otherwise the tight criterion is used. In addition, the two
kaons must have the sum of the magnitudes of their $p_{\rm T}>900$ MeV.

To select $\overline{B}_{s}^{0}$ candidates we require that the $K^{+}K^{-}$
pair and the $J/\psi$ candidate give a good fit to a common secondary vertex
with a $\chi^{2}<5$ per degree of freedom. We also require that the
$\overline{B}_{s}^{0}$ candidate’s decay point must be $>$ 1.5 mm from the
primary vertex and that the negative of its momentum vector points back to the
primary.

The $\overline{B}_{s}^{0}$ candidate invariant mass is shown in Fig. 1. A
clear signal is seen, part of which comes from the previously known
$J/\psi\phi$ mode.

Figure 1: Invariant mass of $J/\psi K^{+}K^{-}$ combinations. The vertical
lines indicate the signal and sideband regions.

A check was made for possible resonant states decaying to $J/\psi K^{-}$ since
similar exotic states have been claimed [10], but no obvious structures are
visible in the invariant mass spectrum. Figure 2 shows the $K^{+}K^{-}$
invariant mass for both signal and sideband regions, where the signal region
extends $\pm$25 MeV around the $\overline{B}_{s}^{0}$ mass peak and the
sidebands extend from 35 MeV to 60 MeV on either side of the peak.

Figure 2: Invariant mass of $K^{+}K^{-}$ combinations. The histogram shows the
data in the signal region while the points (red) show the sidebands.

Apart from the large peak at the $\phi$ there is a structure near 1525 MeV. In
addition there is an excess of signal events over most of the mass range which
we refer to as non-resonant. We investigate the possibility of the peak to be
the $f^{\prime}_{2}(1525)$ resonance. The PDG quotes the mass of the
$f_{2}^{\prime}$ state as 1525$\pm$5 MeV and the width as 73${}^{+6}_{-5}$ MeV
[11]. Other states such as the $f_{2}(1270)$ and the $f_{0}(1500)$ have small
branching fractions into $K^{+}K^{-}$ of less than 5%, and are unlikely to
have large rates.

It is possible for the decay $\overline{B}^{0}\rightarrow J/\psi K^{-}\pi^{+}$
to fake our signal if the $\pi^{+}$ is misidentified as a $K^{+}$. A specific
example is given by $\overline{B}^{0}\rightarrow
J/\psi\overline{K}_{2}^{*}(1430)$ decays [12]. To examine if we are sensitive
to a reflection of this mode in the 1525 MeV di-kaon mass region, a simulation
was performed where the $\pi^{+}$ from the $\overline{K}_{2}^{*}(1430)$ was
interpreted as a $K^{+}$. Figure 3(a) shows that the reflection of this mode
does indeed peak in the di-kaon mass range around 1525 MeV. It also peaks in
the $\overline{B}_{s}^{0}$ signal region but is much wider than the
$\overline{B}_{s}^{0}$ mass peak. The region $25-200$ MeV above the
$\overline{B}_{s}^{0}$ mass peak provides a sample of misidentified
$\overline{B}^{0}\rightarrow J/\psi K^{-}\pi^{+}$ decays. By measuring the
number of $\overline{B}^{0}$ candidates in this region we can calculate the
number in the $\overline{B}_{s}^{0}$ signal region.

Figure 3: (a) The $m(K^{+}K^{-})$ distribution for simulated
$\overline{B}^{0}\rightarrow J/\psi\overline{K}_{2}^{*}(1430)$ decays where
the $\pi^{+}$ from the $\overline{K}_{2}^{*}(1430)$ decay is interpreted as a
$K^{+}$. The histogram shows $m(K^{+}K^{-})$ in the signal region of
$\overline{B}_{s}^{0}$ mass and the points in the sideband region. The
simulation corresponds to approximately 8 fb-1 of data. (b) The $m(J/\psi
K^{+}\pi^{-})$ distribution for $J/\psi K^{+}K^{-}$ data candidates $25-200$
MeV above the $\overline{B}_{s}^{0}$ mass, and with $m(K^{+}K^{-})$ within
$\pm$300 MeV of 1525 MeV, reinterpreted as $\overline{B}^{0}\rightarrow J/\psi
K^{-}\pi^{+}$ events. The fit is to a signal Gaussian whose mass and width are
allowed to vary as well as a quadratic background.

To determine the size of any $\overline{B}^{0}$ reflection in the
$f^{\prime}_{2}$ mass region we select events where the reconstructed $J/\psi
K^{+}K^{-}$ mass is in the range $25-200$ MeV above the $\overline{B}_{s}^{0}$
mass, reassign each of the two kaons in turn to the pion hypothesis, and plot
the $J/\psi K\pi$ mass. The resulting peak at the $\overline{B}^{0}$ mass has
36$\pm$10 events from the fit shown in Fig. 3(b). We calculate 37$\pm$10
events in the $\overline{B}_{s}^{0}$ signal region, using the shape from Monte
Carlo simulation, and use this number as a constraint in the fit described
below to determine the $f^{\prime}_{2}$ parameters and signal yields.

To test the $f^{\prime}_{2}$ hypothesis we perform a simultaneous fit to the
$\overline{B}_{s}^{0}$ candidate mass and the di-kaon mass. The
$f^{\prime}_{2}$ signal is parameterized by a spin-2 Breit-Wigner function
[13]. The width of the $f^{\prime}_{2}$ is fixed to the PDG value of 73 MeV
[11]. A contribution from non-resonant $K^{+}K^{-}$ is included as a linear
function in the di-kaon mass. The contribution from the $K^{-}\pi^{+}$
reflection is included using the di-kaon and $\overline{B}_{s}^{0}$ mass
shapes from the simulation, with the normalization fixed by the event yield in
Fig 3(b). The results of the fits are shown in Fig. 4. The $f_{2}^{\prime}$
mass from the fit is 1525$\pm$4 MeV and the yield is 269$\pm$26 events within
$\pm$125 MeV of the mass. If we allow the $f_{2}^{\prime}$ width to vary we
find a consistent value of 90${}^{+16}_{-14}$ MeV.

Figure 4: Projections of fits to (a) the $\overline{B}_{s}^{0}$ candidate mass
and (b) the di-kaon mass. The $f^{\prime}_{2}$ signal is parameterized by a
spin-2 Breit-Wigner function whose width is fixed to 73 MeV (dotted curve).
The combinatorial background is shown in the light shaded region, while the
darker shaded region shows the non-resonant $J/\psi K^{+}K^{-}$ component. The
long-dashed (red) line shows the misidentified $\overline{B}^{0}\rightarrow
J/\psi K^{-}\pi^{+}$ decays, and the (blue) line the total.

As we have not taken into account possible interferences between the
$f^{\prime}_{2}$ and other $J/\psi K^{+}K^{-}$ final states we do not provide
systematic uncertainties for these values. The decay angle of the $J/\psi$,
$\theta_{J/\psi}$, can test for pure spin-0, or the presence of a higher spin
state such as the spin-2 $f^{\prime}_{2}$ [11]. Here $\theta_{J/\psi}$ is
defined as the angle of the $\mu^{+}$ with respect to the
$\overline{B}_{s}^{0}$ direction in the $J/\psi$ rest frame. It is distributed
as

$f(\cos\theta_{J/\psi})=(1-p)\sin^{2}\theta_{J/\psi}+\frac{p}{2}\left(1+\cos^{2}\theta_{J/\psi}\right),$
(1)

where $1-p$ is the fraction of helicity zero and $p$ is the fraction of
helicity $\pm$1\. Shown in Fig. 5 is the background subtracted, acceptance
corrected $\cos\theta_{J/\psi}$ distribution for $K^{+}K^{-}$ masses in the
$f^{\prime}_{2}$ region. MC simulation is used to find the acceptance
correction. The points are extracted from the joint fit to the $m(J/\psi
K^{+}K^{-})$ and $m(K^{+}K^{-})$ distributions in the $K^{+}K^{-}$ mass region
within $1400-1650$ MeV for events in the peak above the non-resonant
$K^{+}K^{-}$. The fit result is $p=(0.57\pm 0.13)$, with $\chi^{2}$/number of
degrees of freedom (ndof) of 10/8 (27% probability). Fitting only with an
S-wave gives $\chi^{2}$/ndof of 27/9 (0.1% probability), showing that the data
are not likely to be pure spin-0, but are compatible with a higher spin state
consistent with an $f^{\prime}_{2}$ contribution.

Figure 5: Distribution of $\cos\theta_{J/\psi}$ for
$\overline{B}_{s}^{0}\rightarrow J/\psi f^{\prime}_{2}$ decays. The background
and non-resonant $K^{+}K^{-}$ components have been subtracted, and the data
have been corrected for acceptance. The fit to Eq. 1 is shown by the solid
line. Note that for pure S-wave the distribution would be
$\sin^{2}\theta_{J/\psi}$ ($p=0$), shown as the dotted curve, while for pure
helicity 1 ($p=1$) the data would be described by the dot-dashed curve.

The branching fraction of $\overline{B}_{s}^{0}\rightarrow J/\psi
f_{2}^{\prime}$ relative to $\overline{B}_{s}^{0}\rightarrow J/\psi\phi$ is
determined by assuming that the dominant background is S-wave and the signal
D-wave, so there is no interference between them.333Although there can be
interference as a function of the $K^{+}$ decay angle in the $f_{2}^{\prime}$
rest frame, integrating over this variable causes the net result to be zero.
The number of $J/\psi K^{+}K^{-}$ events is determined by a fit to the
$\overline{B}_{s}^{0}$ mass distribution, within $\pm$20 MeV of the $\phi$
mass. A small S-wave component in the $\phi$ mass region of (4.2$\pm$2.3)% is
subtracted [2]. Although there are the same final state particles in both
modes, the relative efficiency is (78$\pm$2)%, where the uncertainty arises
from simulation statistics. The efficiency ratio differs from unity due to the
different $p_{\rm T}$ distributions of the kaons in the final states. The kaon
identification efficiencies are corrected with respect to those given by the
MC simulation using a sample of $D^{*+}$ decays, where the kaon can be
selected without resorting to PID information. Typical corrections are on the
order of 5%.

To find the effective relative rate of $f^{\prime}_{2}$ decays we use the fit
where the width is allowed to vary. There are 320$\pm$33 $f^{\prime}_{2}$
events and 1774$\pm$42 $\phi$ events. Correcting for the relative efficiencies
and the explicit branching fractions
${\cal{B}}\left(f^{\prime}_{2}(1525)\rightarrow K^{+}K^{-}\right)=(44.4\pm
1.1)$%, and ${\cal{B}}\left(\phi\rightarrow K^{+}K^{-}\right)=(48.9\pm 0.5)$%
[11], we measure

$R\equiv\frac{{\cal{B}}\left(\overline{B}_{s}^{0}\rightarrow J/\psi
f^{\prime}_{2}(1525)\right)}{{\cal{B}}\left(\overline{B}_{s}^{0}\rightarrow
J/\psi\phi\right)}=(26.4\pm 2.7\pm 2.4)\%.$ (2)

The systematic uncertainty on $R$ has several contributions, as listed in
Table 1.

Table 1: Systematic uncertainties on $R$. Source | Change (%)
---|---
$f^{\prime}_{2}$ width | 6.3
Helicity | 4.0
Relative efficiency | 2.6
S-wave under $\phi$ | 2.3
$K^{+}K^{-}$ mass dependent efficiency | 2.3
Background shape | 1.3
$\overline{B}_{s}^{0}$ $p_{\rm T}$ distribution | 0.5
$\overline{B}_{s}^{0}$ mass resolution | 0.5
PID | 1.0
Signal shape | 1.0
${\cal{B}}\left(f^{\prime}_{2}(1525)\rightarrow K^{+}K^{-}\right)$ | 2.5
${\cal{B}}\left(\phi\rightarrow K^{+}K^{-}\right)$ | 1.0
Total | 9.2

The largest source of uncertainty is $f^{\prime}_{2}$ width. The error quoted
reflects changing the width by one standard deviation from the fitted value of
90 MeV. The helicity amplitudes of the $J/\psi f^{\prime}_{2}$ decay are
unknown, unlike the $J/\psi\phi$ amplitudes which are well measured [11]. The
difference between the values obtained using helicity zero and helicity one
$J/\psi$ MC samples is 4% compared to our central value. The S-wave
subtraction of the events in the $J/\psi\phi$ region causes a 2.3%
uncertainty. We include an uncertainty for the efficiency as a function of
$K^{+}K^{-}$ mass, as the tracking could be sensitive to the opening angle of
the kaon pair. Modifying the acceptance from a flat to linear function of mass
changes the yield by 2.3%. Varying the $\overline{B}_{s}^{0}$ $p_{\rm T}$
distribution within limits imposed by the data results in a small 0.5% change
in the rate. Changing the mass resolution by its error results in a 0.5%
change. A PID uncertainty of 1% is added to account for different momentum
distributions of the kaons in the two final states. As a check we note that
the ratio of the number of events in $J/\psi\phi$ with tight cuts to loose
cuts on the kaon identification is (61$\pm$2)% and the simulation gives a
consistent (60$\pm$1)%. Variation of the background and signal shapes makes
small differences.

In conclusion, we have made the first investigation of the $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow J/\psi K^{+}K^{-}$
final state over the entire range of $K^{+}K^{-}$ mass. There is a significant
non-resonant component that extends under the $\phi$ region which can affect
$C\\!P$ violation measurements [5]. We have also observed
$\overline{B}_{s}^{0}\rightarrow J/\psi f^{\prime}_{2}(1525)$ decays. The
branching fraction ratio relative to $J/\psi\phi$ is

$\frac{{\cal{B}}\left(\overline{B}_{s}^{0}\rightarrow J/\psi
f^{\prime}_{2}(1525)\right)}{{\cal{B}}\left(\overline{B}_{s}^{0}\rightarrow
J/\psi\phi\right)}=(26.4\pm 2.7\pm 2.4)\%,$ (3)

assuming that the background does not interfere with the signal amplitude.
This decay mode can also be used to measure $C\\!P$ violation in the
$\overline{B}_{s}^{0}$ system, although a different transversity analysis than
in $J/\psi\phi$ would be required as the final state is a combination of a
spin-1 $J/\psi$ and a spin-2 $f^{\prime}_{2}$ state. Some consideration has
been given to measuring $C\\!P$ violation in vector-tensor decays [14].

We express our gratitude to our colleagues in the CERN accelerator departments
for the excellent performance of the LHC. We thank the technical and
administrative staff at CERN and at the LHCb institutes, and acknowledge
support from the National Agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil);
CERN; NSFC (China); CNRS/IN2P3 (France); BMBF, DFG, HGF and MPG (Germany); SFI
(Ireland); INFN (Italy); FOM and NWO (the Netherlands); SCSR (Poland); ANCS
(Romania); MinES of Russia and Rosatom (Russia); MICINN, XuntaGal and GENCAT
(Spain); SNSF and SER (Switzerland); NAS Ukraine (Ukraine); STFC (United
Kingdom); NSF (USA). We also acknowledge the support received from the ERC
under FP7 and the Region Auvergne.

## References

  * [1] LHCb collaboration, R. Aaij et al., Measurement of the $C\\!P$ violating phase $\phi_{s}$ in $\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}\rightarrow J/\psi f_{0}(980)$,  Phys. Lett. B707 (2012) 497–505, [arXiv:1112.3056]
  * [2] LHCb collaboration, R. Aaij et al., Measurement of the CP-violating phase $\phi_{s}$ in the decay $B_{s}^{0}\rightarrow J/\psi\phi$, arXiv:1112.3183
  * [3] D0 collaboration, V. M. Abazov et al., Measurement of the $C\\!P$-violating phase $\phi_{s}^{J/\psi\phi}$ using the flavor-tagged decay $B_{s}^{0}\rightarrow J/\psi\phi$ in 8 fb-1 of $p\overline{p}$ collisions, arXiv:1109.3166
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# Jumpstarting Surgical Computer Vision

Deepak Alapatt Aditya Murali Vinkle Srivastav Pietro Mascagni AI4SafeChole
Consortium Nicolas Padoy ICube, University of Strasbourg, CNRS, Strasbourg,
France  IHU Strasbourg, Strasbourg, France  Fondazione Policlinico
Universitario A. Gemelli IRCCS, Rome, Italy  Azienda Ospedaliero-Universitaria
Sant’Andrea, Rome, Italy  Fondazione IRCCS Ca’ Granda Ospedale Maggiore
Policlinico, Milan, Italy  Monaldi Hospital, Naples, Italy

###### Abstract

Purpose: General consensus amongst researchers and industry points to a lack
of large, representative annotated datasets as the biggest obstacle to
progress in the field of surgical data science. Self-supervised learning
represents a solution to part of this problem, removing the reliance on
annotations. However, the robustness of current self-supervised learning
methods to domain shifts remains unclear, limiting our understanding of its
utility for leveraging diverse sources of surgical data.

Methods: In this work, we employ self-supervised learning to flexibly leverage
diverse surgical datasets, thereby learning task-agnostic representations that
can be used for various surgical downstream tasks. Based on this approach, to
elucidate the impact of pre-training on downstream task performance, we
explore 22 different pre-training dataset combinations by modulating three
variables: source hospital, type of surgical procedure, and pre-training scale
(number of videos). We then finetune the resulting model initializations on
three diverse downstream tasks: namely, phase recognition and critical view of
safety in laparoscopic cholecystectomy and phase recognition in laparoscopic
hysterectomy.

Results: Controlled experimentation highlights sizable boosts in performance
across various tasks, datasets, and labeling budgets. However, this
performance is intricately linked to the composition of the pre-training
dataset, robustly proven through several study stages.

Conclusion: The composition of pre-training datasets can severely affect the
effectiveness of SSL methods for various downstream tasks and should
critically inform future data collection efforts to scale the application of
SSL methodologies.

Keywords: Self-Supervised Learning, Transfer Learning, Surgical Computer
Vision, Endoscopic Videos, Critical View of Safety, Phase Recognition

##  1 Introduction

Over the last decade, developments in data science have had a sweeping effect
spanning almost all areas of healthcare. While this has catalyzed the
development of numerous clinically impactful applications in fields such as
pathology and radiology, the same cannot be said for surgery [14]. In 2019, a
large survey, conducted by the Surgical Data Science Initiative [13],
primarily attributed this lack of success stories to a lack of representative
annotated data [14]. On the other hand, it is also unclear whether available
datasets are being well-utilized when not directly specific to the task at
hand. For example, a recently conducted survey [6] on participant practices
across 80 biomedical image analysis competitions, revealed that only 9% of all
respondents that used deep learning utilized data outside what was provided
for the competition (excluding pre-trained models). A natural explanation may
be that available public datasets are often small, specific, and mono-centric
[14], making it unclear whether they could be leveraged to improve model
performance.

In the broader computer vision domain, one of the most effective strategies
for leveraging related datasets is transfer learning. For deep learning
models, a neural network is pre-trained on a first dataset and task, then the
resulting learned features are used as an initialization, or a “jumpstart”,
for learning the task of interest on a smaller labeled dataset. This simple
approach for visual representation learning has proven almost unreasonably
effective, contributing significantly to pushing the state of the art for a
wide range of tasks including segmentation [11], object detection [12], and
activity recognition [2]. Since then, this paradigm of pre-training and then
fine-tuning has become the de facto standard, with pre-trained initializations
for large-scale general computer vision datasets, such as ImageNet [19], now
widely available for integration into other work. We take inspiration from
these developments, hypothesizing that similar access to more appropriate (see
Fig. 1) domain-specific initializations can effectively consolidate disparate
datasets in the field and channel them toward widely enabling early
prototyping for various clinical applications and, eventually, developing more
success stories for surgical data science.

Fig. 1: Uniform Manifold Approximation and Projection (UMAP) used to visualize
the extracted representations of 2 public surgical datasets (Cholec80,
HeiChole) and 1 natural image dataset (Imagenet) using a pre-trained ImageNet
model. A wide range of natural images forms distinctive separable clusters,
while surgical images from all 3 datasets form a single intermixed cluster
(red circle). Images have been sampled in proportion to the scale of the
corresponding datasets.

One challenge precluding this development is the availability of diverse
large-scale datasets, annotated with many categorical classes, all factors
contributing significantly to effective pre-training [12, 21]. Self-Supervised
Learning (SSL) is suggestive of a seemingly natural alternative to learning
generic representations, and consequently, building generic model
initializations, without the need for large and varied annotations.

SSL methodologies in the broader computer vision domain have seen significant
developments in design, moving from early heuristic-based pre-training tasks,
such as predicting image augmentations, to more elegant strategies that
directly learn to predict latent representations specific to the content of an
image. Until recently, these shifts in design were slow to be adopted into the
surgical domain with most work focusing on hand-crafted pre-text tasks, such
as colorization [18], or leveraging intrinsically collected information such
as robot kinematics [4, 20] or the temporal order of frames [7, 16]. A large
benchmark study of state-of-the-art SSL methodologies applied to the surgical
domain attributed this to the complexity of translating and tuning newly
proposed models to the surgical domain [17]. However, in the same study, the
authors demonstrate through extensive experimentation that when applied
correctly, these methods achieve state-of-the-art results on a range of tasks,
benchmarks, and labeled-data regimes. Since then, a number of works have
explored the value of pre-training similar methods on a massive scale by
aggregating public datasets [1], utilizing large private repositories [8], or
some combination of the two [25]. All three of these works demonstrate that
large-scale pre-training on their respective datasets brings sizable boosts in
performance when performing various downstream tasks. [1] aggregate 10 public
datasets for several types of laparoscopic procedures sourced from centers
worldwide to create a pre-training dataset of about 700k images. [8] compile a
private dataset of $\sim$7900 laparoscopic procedures ($>$23M images) from 8
centers and a curated polyp image dataset generated from $\sim$14k
colonoscopies ($>$2M Images). [25] combine 6 public datasets for laparoscopy
and endoscopy along with a large private repository of endoscopic videos to
pre-train on $\sim$33k videos and $\sim$5M images. Different from these works
that aggregate laparoscopic and endoscopic video data collected from different
centers (hospitals) and different procedures to pre-train at scale, we focus
this study on better understanding and quantifying the implications of pre-
training dataset composition on pre-training efficacy.

Our contributions are threefold:

  1. 1.

We conduct extensive experimentation ($>$300 experiments) demonstrating the
sensitivity of pre-training efficacy to various factors spanning 22 pre-
training datasets, 10 surgical procedures, 7 centers (hospitals), 3 labeled-
data settings, 3 downstream tasks, and multiple runs.

  2. 2.

We robustly highlight key considerations regarding pre-training dataset
composition, which we hope could inform future data collection and application
efforts.

  3. 3.

We validate our findings at scale ($\sim$400 surgical videos) illustrating how
diverse surgical datasets can be leveraged, quantifying key considerations
when doing so.

Pre-training Dataset | # Videos | Source Center | Procedure Type
---|---|---|---
| Strasbourg | Other | Cholecystectomy | Other
StrasChole400 | 400 | 400 | 0 | 400 | 0
StrasChole200 + MultiChole2023 | 405 | 200 | 205 | 405 | 0
StrasChole200 | 200 | 200 | 0 | 200 | 0
MultiCholec2023 | 205 | 0 | 205 | 205 | 0
Laparo420 (with LC) | 420 | 420 | 0 | 45 | 375
Laparo420 (w/o LC) | 375 | 375 | 0 | 0 | 375

Table 1: Large Scale Pre-training Data Combinations

##  2 Methodology

In this section, we begin by enumerating the various datasets we use and the
downstream tasks we evaluate. Then, we describe our training procedure for
generating each model initialization and finetuning for each downstream task
and finally we describe our study stages.

###  2.1 Datasets

We use 9 different surgical computer vision datasets of minimally invasive
abdominal procedures including: AutoLaparo [24], Cholec80 [22], Endoscapes
[15], HeiChole [23], Laparo425 [9], and MultiChole2022 [10]. We also use three
unlabeled cholecystectomy datasets: MultiChole2023, StrasChole200, and
StrasChole400, containing 205, 200, and 400 randomly selected cholecystectomy
videos, respectively. StrasChole200 and StrasChole400 contain videos only from
Nouvel Hôpital Civil, Strasbourg, France while MultiChole2023, an extension of
MultiChole2022, contains 205 videos, with $\sim$50 videos from each of the 4
following centers through the AI4SafeChole Consortium: Policlinico
Universitario Agostino Gemelli, Rome; Azienda Ospedaliero-Universitaria
Sant’Andrea, Rome; Fondazione IRCCS Ca’ Granda Ospedale Maggiore Policlinico,
Milan; and Monaldi Hospital, Naples.

These datasets span 10 different surgical procedures (several cholecystectomy
datasets, 8 others in Laparo420, 1 other in AutoLaparo), and 7 centers
(several Strasbourg datasets, 4 others in MultiCholec2023, 2 aggregated in
HeiChole). Lastly, for fair experimentation, we remove 5 videos from Laparo425
that are found in the test sets for the downstream tasks, yielding Laparo420.
Using these datasets, we create our various pre-training data combinations.

###  2.2 Downstream Tasks

We consider 3 downstream tasks, each using a different dataset: phase
recognition (on both Cholec80 and AutoLaparo) and critical view of safety
(CVS) prediction (Endoscapes), thus spanning 2 procedures (cholecystectomy,
hysterectomy) and 2 centers (Strasbourg, Hong Kong). Our selected downstream
tasks are also highly diverse: CVS criteria assessment (3-class binary
classification) is one of several tasks proposed for the prevention of bile
duct injuries, all of which require fine-grained analysis. Meanwhile, phase
recognition is a widely studied and benchmarked task in surgical computer
vision, that, unlike CVS classification, requires long-range temporal
reasoning.

For each of the 2 phase recognition datasets, we consider one high-label data
regime using 100% of the available training labels (40 videos for Cholec80, 10
videos for Autolaparo) and two low-label data regimes using 5 videos and 3
videos, respectively. For the CVS task, we similarly consider 3 label settings
using 120 videos (100% of the train set), 40 videos (25% of the train set),
and 20 videos (12.5% of the train set). For every low-label setting on each
downstream task, we present results using the mean and std over 3 randomly
sub-selected splits to mitigate the effects of selection bias.

###  2.3 Training Procedure

For all experiments, we use Momentum Contrast (MoCo v2) [3] to pre-train a
ResNet-50 feature extractor. MoCo v2 is a contrastive learning method that
learns powerful image representations by minimizing differences between
embeddings of augmented views of the same image to be similar and maximizing
distance between embeddings of different images. We use MoCo v2 for all pre-
training motivated by the results in [17], where it is shown to outperform
several competing methods for surgical video analysis tasks.

This pre-training procedure results in a trained ResNet-50 backbone
parametrized by model weights $\Theta_{c}$ for each pre-training data
configuration $c$. We use each $\Theta_{c}$ to initialize a ResNet-50
classifier that we finetune separately for each downstream task while varying
the number of labeled videos. Finally, for the phase recognition downstream
tasks (Cholec80, AutoLaparo), we additionally train TeCNO [5] on top of the
finetuned ResNet-50 features to enable temporal reasoning as in [17].

###  2.4 Study Stages

Stage 1. The purpose of this stage is to establish performance baselines for
how robust SSL pre-training is to extreme domain shifts. Through these
experiments, we aim to better understand how related datasets (e.g.
laparoscopic abdominal procedure videos of a different surgery type) could be
leveraged for various tasks. To do this we perform 4 cross-over experiments
examining the added value over ImageNet initializations: (1) where the
downstream task is from the same dataset as the pre-training data (matched
finetuning), and (2) where the downstream task and dataset are different from
the pre-training dataset (unmatched finetuning). Note that both downstream
tasks are conceptually similar (surgical phase recognition); however, the two
datasets span two geographic regions (Hong Kong and France), two anatomical
targets (Gallbladder and Uterus), and likely stylistic and functional
differences in workflow and instrumentation.

We adopt this process for two datasets, Cholec80 and AutoLaparo, reporting
both matched and unmatched finetuning performance for both downstream phase
recognition tasks. We only utilized public datasets in this stage to
additionally illustrate the potential of aggregating already accessible
datasets.

Initialization | Cholec80 Phase (F1) | AutoLaparo Phase (F1)
---|---|---
Number of Labeled Videos | Number of Labeled Videos
40 | 5 | 3 | 10 | 5 | 3
Cholec80 SSL | 79.6 | 66.1 $\pm$ 4.2 | 61.7 $\pm$ 4.8 | 61.5 | 58.3 $\pm$ 2.8 | 47.7 $\pm$ 2.3
AutoLaparo SSL | 80.0 | 62.4 $\pm$ 6.0 | 54.4 $\pm$ 5.7 | 70.7 | 64.4 $\pm$ 5.1 | 59.5 $\pm$ 3.9
ImageNet Supervised | 80.3 | 62.3 $\pm$ 7.4 | 50.4 $\pm$ 3.8 | 70.1 | 57.6 $\pm$ 5.1 | 50.8 $\pm$ 6.3
Table 2: Results of Stage 1 - Cross-Over Experiments. Performance is measured
by average F1 Score across videos. For the lower data budget experiments (5
and 3 labeled videos), we report the average and standard deviation of video-
wise F1 score across three random subsets. Meanwhile, since the 40 and 10
video settings use all available labels, we do not report standard deviation.

Stage 2. In the second stage of our study, we aim to study the impact of pre-
training surgical procedure types on downstream task performance. To enable
this analysis, we separate Laparo420, which is a collection of various
laparoscopic and robotic surgical videos, into 8 different subsets by
procedure type (cholecystectomy, eventration, gastric bypass, hernia repair,
robotic gastric bypass, sigmoidectomy, sleeve gastrectomy, and nissen
fundoplication). We then evaluate Cholec80 Phase Recognition and Endoscapes
CVS Classification.

In this controlled experiment, we keep the source center for all the pre-
training datasets fixed (Nouvel Hôpital Civil) and the pre-training dataset
size fixed to $\sim$50 videos111All procedure-specific pre-training datasets
contain exactly 50 videos except for cholecystectomy, which contains 45 since
5 videos had to be removed to avoid contamination with the downstream task
test sets.; by controlling the source center and pre-training data scale in
this fashion, we aim to isolate the impact of the pre-training procedure type.
Still, confounding variables such as differences in instrumentation,
acquisition device preferences for particular procedure types or cases, etc.
do exist, which we aim to mitigate through the number of procedures considered
(8) and the number of cases per procedure ($\sim$50).

Stage 3. In the third stage of our study, we aim to study the impact of the
source center for the pre-training dataset on downstream task performance. As
has been noted by numerous works, surgical videos can vary greatly among
medical centers due to differences in instrumentation, workflow, lighting,
acquisition hardware, software, and patient characteristics. We leverage 4
subsets of MultiChole2022, which contains laparoscopic cholecystectomy videos
from four different Italian hospitals, as well as the HeiChole public train
set, combining cholecystectomy videos from 2 German hospitals. Further, we
also utilize a 25-video subset of Cholec80; thus, constructing 6 subsets of
$\sim$25 videos.

As in stage 2, this allows us to control for procedure type (cholecystectomy)
and data scale ($\sim$25 videos)222All center-specific pre-training datasets
contain exactly 25 videos except for the public HeiChole training dataset,
which contains 24 videos. and isolate the impact of source center. Note again,
confounding variables such as differences due to instrumentation, acquisition
device preferences for particular source centers or cases, etc. do exist,
which we aim to mitigate through the number of centers considered (2 from
HeiChole and 5 others) and the number of cases per center ($\sim$25). We again
measure performance through downstream performance on Cholec80 Phase
Recognition and Endoscapes CVS Classification.

Stage 4. Lastly, one of the great promises of self-supervised representation
learning is its scalability; however, there are numerous possibilities to
accomplish this scaling in the surgical domain. To name a few, only including
data from the same center and the same procedure type as the downstream task,
fixing the center and varying procedure type or vice-versa, or naively
including any and all available videos. To identify an optimal scaling
strategy, we pre-train models on a series of data combinations, enumerated in
Table 1. Finally, we pre-train one last model using the identified optimal
scaling strategy, going beyond ImageNet scale. We again consider downstream
Cholec80 Phase Recognition and Endoscapes CVS Classification as in Stages 2
and 3.

##  3 Results and Discussion

###  3.1 Stage 1: Cross-over Experiments

In this subsection, we examine if and how two public datasets (Cholec80 and
AutoLaparo) for surgical phase recognition could be leveraged using SSL-based
pre-training initializations. In Table 2, we see that for the matched pre-
trainings, i.e. performing SSL pre-training on the same dataset as the
downstream task, there are sizable boosts in performance; particularly so when
many labeled examples are not available for supervised finetuning.
Quantitatively, when using as few as 3 labeled videos, we see an 11.3% and
8.7% boost over the standard ImageNet initialization when performing matched
pre-training on Cholec80 and AutoLaparo, respectively. On the other hand,
except for the lowest labeled setting (3 labeled videos), the unmatched pre-
training experiments perform on par or worse than using just an ImageNet
initialization despite both being laparoscopic video datasets for abdominal
procedures. We hypothesize that SSL can help integrate critical
representational attributes in lower data settings that are otherwise easily
learned when more data is available. Both pairs of matched and unmatched
experiments appear largely consistent over all labeled data settings. These
results underscore the need to carefully consider available labeling and data
resources when applying SSL methodologies to leverage related datasets for
surgical computer vision.

Fig. 2: Phase Recognition and CVS assessment results when finetuning from ImageNet supervised initialization, SSL-based initializations pre-trained on the relevant procedure to the downstream task (violet line), or a different procedure as the downstream task (shaded blue region). Note that the shaded region represents the range of performance values across the 7 non-cholecystectomy procedures under consideration. Initialization | Cholec80 Phase (F1) | Endoscapes CVS (mAP)
---|---|---
Number of Labeled Videos | Number of Labeled Videos
40 | 5 | 3 | 120 | 40 | 20
StrasChole400 SSL | 82.5 | 67.4 $\pm$ 4.9 | 62.2 $\pm$ 5.1 | 52.2 | 45.2 $\pm$ 4.7 | 35.0 $\pm$ 7.4
StrasChole200 + MultiChole2023 SSL | 82.2 | 68.4 $\pm$ 1.3 | 61.1 $\pm$ 4.5 | 51.4 | 46.6 $\pm$ 3.5 | 34.2 $\pm$ 6.4
StrasChole200 SSL | 81.8 | 67.4 $\pm$ 2.6 | 58.5 $\pm$ 6.6 | 52.3 | 46.0 $\pm$ 4.8 | 35.5 $\pm$ 8.0
MultiChole2023 SSL | 81.9 | 64.9 $\pm$ 3.2 | 58.9 $\pm$ 5.1 | 51.5 | 45.6 $\pm$ 5.9 | 34.8 $\pm$ 6.4
Laparo420 (with LC) SSL | 79.1 | 63.9 $\pm$ 3.2 | 58.1 $\pm$ 6.3 | 53.3 | 44.1 $\pm$ 5.4 | 34.0 $\pm$ 6.6
Laparo420 (w/o LC) SSL | 80.5 | 64.7 $\pm$ 3.3 | 55.7 $\pm$ 5.7 | 54.5 | 41.2 $\pm$ 4.5 | 31.5 $\pm$ 2.7
ImageNet Supervised | 80.3 | 62.3 $\pm$ 7.4 | 50.4 $\pm$ 3.8 | 50.0 | 40.5 $\pm$ 7.0 | 33.8 $\pm$ 4.1
Table 3: Results of Stage 4 - Scaling Experiments. Performance is measured by
average F1 Score across videos (Phase) or mean average precision across all
frames (CVS). We report mean and standard deviation across three random
subsets for the lower data budgets. Horizontal lines separate the different
sub-studies: scaling with (1) the fewest variations (same procedure, same
center), (2) same procedure but different centers, and (3) same center but
different procedures. We report the results of using ImageNet initialization
for reference.

###  3.2 Stage 2: Cross-Procedure Experiments

In Fig. 2, in line with the results of Stage 1, we see that pre-training on
the procedure relevant to the downstream tasks (cholecystectomy) brings boosts
in performance over ImageNet initializations across the board for all labeled
data settings and for both downstream tasks/datasets. Interestingly, using the
7 initializations other than those pre-trained on the same procedure as the
downstream task delivers performance markedly worse, even lower than ImageNet
initializations at times. In Stage 4, we further investigate whether merging
subsets of data generated from procedures that are not directly relevant to
the downstream task could bring additional value.

###  3.3 Stage 3: Cross-Center Experiments

The stage 3 experiments (Fig. 3), present a number of interesting findings.
Firstly, as in the the previous stage, we see large performance boosts over
ImageNet initializations across all data settings and both downstream tasks:
for phase recognition and CVS assessment respectively, we obtain improvements
of up to 10.7$\%$ and 6.3$\%$ with Same Center SSL and up to 8.8$\%$ and
7.2$\%$ with Different Center SSL. Notably, when pre-training, domain shifts
introduced by sourcing videos from different centers appear to be much less
impactful than those introduced by varying procedure types. This effect is
resoundingly confirmed through the 7 centers (2 aggregated in HeiChole)
included in this stage. Unlike the cross-procedure experiments, each
initialization, irrespective of which center’s data it was generated using,
delivers boosts over the ImageNet initialization, at times even higher than
initializations generated using data from the same center. However, across the
considered downstream tasks and pre-training datasets, using SSL-based
initializations generated through datasets from the same center still
generally appears to be superior to those generated from other centers. These
results may suggest that access to large-scale procedure-specific
initializations, even if sourced from different centers, could enable rapid
prototyping for various downstream tasks.

Fig. 3: Phase Recognition and CVS assessment results when finetuning from
ImageNet supervised initialization, SSL-based initializations pre-trained on
the relevant center to the downstream task (violet line), or a different
center as the downstream task (shaded blue region). Note that the shaded
region represents the range of performance values across the 6 non-Strasbourg
(2 aggregated in HeiChole) centers under consideration.

###  3.4 Stage 4: Approaches to Scale

The previous 3 sections present strong evidence that pre-training dataset
composition can severely impact downstream performance and must be carefully
considered. In this final stage, we aim to validate those findings at scale,
to better understand the interplay between the different effects, and to
provide indications for how to optimally scale SSL pre-training for surgical
computer vision. In Table 3, when using initializations pre-trained on large
($\sim$ 400 videos) cholecystectomy datasets (StrasChole400 and StrasChole200
+ MultiChole2023), we see performance largely on par with the cholecystectomy-
only datasets included in previous study stages despite being an order of
magnitude larger. An important caveat to this finding, though consistent with
previous works [17], is that higher capacity models may be better suited, if
not required, to effectively leverage this scale of data for self-supervised
pre-training [8]. We also note that the two $\sim$200-video subsets,
StrasCholec200 and MultiChole2023, deliver fairly comparable boosts across
downstream tasks, splits, and labeled-data percentages, despite strictly
including or excluding videos sourced from the center relevant to the
downstream tasks. These findings echo those discussed in Stage 3 regarding the
impact of domain shifts introduced by multi-centric pre-training data on
downstream task performance. Finally, we aim to provide indications about the
impact of curating multi-procedure datasets for SSL pre-training using two
$\sim$400-video scale datasets, Laparo420 (with LC) and Laparo420 (w/o LC),
containing 45/420 and 0/375 cholecystectomy procedures, respectively. Both of
these datasets, despite being of comparable size (# videos) with StrasChole400
and StrasChole200 + MultiCholec2023, perform markedly worse, further
reinforcing the findings of Stage 2 that learning procedure-agnostic features
may require dedicated methodological design. To the best of our knowledge,
each of the 3 previous works utilizing massive scale pre-training [1, 8, 25]
only validated their pre-trained initializations on downstream tasks well-
represented in the pre-training dataset. These findings further emphasize the
need for validation to better understand how generalizable those
initializations may be for downstream tasks conducted on other surgical
procedures.

##  4 Conclusion

Recent developments in self-supervised learning for surgery allow us to learn
generic representational features, useful for a range of downstream tasks in
the domain. In this work, we build on these developments, shifting the focus
from models to data, and exploring whether pre-trained networks could be an
effective means to consolidate disparate datasets in the field of Surgical
Data Science. We illustrate that simple model initializations can indeed help
leverage these disparate datasets, helping ’jumpstart’ work on new problems in
new procedures at new clinical centers with fewer annotations.

##  5 Acknowledgments

This work was supported by French state funds managed by the ANR within the
National AI Chair program under Grant ANR-20-CHIA-0029-01 (Chair AI4ORSafety)
and within the Investments for the future program under Grant ANR-10-IAHU-02
(IHU Strasbourg), and by BPI France under reference DOS0180017/00 (project
5G-OR). It was granted access to the HPC resources of Unistra Mesocentre. This
work was granted access to the HPC resources of IDRIS under the allocations
2022-AD011011640R2, 2023-AD011013523R1, and 2023-AD011011631R3 made by GENCI.
The AI4SafeChole consortium is represented by Giovanni Guglielmo Laracca,
Ludovica Guerriero, Andrea Spota, Claudio Fiorillo, Giuseppe Quero, Segio
Alfieri, Ludovica Baldari, Elisa Cassinotti, Luigi Boni, Diego Cuccurullo,
Guido Costamagna, and Bernard Dallemagne.

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