%% BioMed_Central_Bib_Style_v1.01

\begin{thebibliography}{43}
% BibTex style file: bmc-mathphys.bst (version 2.1), 2014-07-24
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\csname PreBibitemsHook\endcsname

%%% 1
\bibitem{digabel1978iterative}
\begin{bchapter}
\bauthor{\bsnm{Digabel}, \binits{H.}},
\bauthor{\bsnm{Lantu{\'e}joul}, \binits{C.}}:
\bctitle{Iterative algorithms}.
In: \bbtitle{Proc. 2nd European Symp. Quantitative Analysis of Microstructures
  in Material Science, Biology and Medicine},
vol. \bseriesno{19},
p. \bfpage{8}
(\byear{1978}).
\bcomment{Riederer Verlag}
\end{bchapter}
\endbibitem

%%% 2
\bibitem{vincent1991watersheds}
\begin{barticle}
\bauthor{\bsnm{Vincent}, \binits{L.}},
\bauthor{\bsnm{Soille}, \binits{P.}}:
\batitle{Watersheds in digital spaces: an efficient algorithm based on
  immersion simulations}.
\bjtitle{IEEE Transactions on Pattern Analysis \& Machine Intelligence}
\bvolume{13}(\bissue{6}),
\bfpage{583}--\blpage{598}
(\byear{1991})
\end{barticle}
\endbibitem

%%% 3
\bibitem{arbelaez2010contour}
\begin{barticle}
\bauthor{\bsnm{Arbelaez}, \binits{P.}},
\bauthor{\bsnm{Maire}, \binits{M.}},
\bauthor{\bsnm{Fowlkes}, \binits{C.}},
\bauthor{\bsnm{Malik}, \binits{J.}}:
\batitle{Contour detection and hierarchical image segmentation}.
\bjtitle{IEEE Transactions on Pattern Analysis and Machine Intelligence}
\bvolume{33}(\bissue{5}),
\bfpage{898}--\blpage{916}
(\byear{2010})
\end{barticle}
\endbibitem

%%% 4
\bibitem{couprie1997topological}
\begin{bchapter}
\bauthor{\bsnm{Couprie}, \binits{M.}},
\bauthor{\bsnm{Bertrand}, \binits{G.}}:
\bctitle{Topological gray-scale watershed transformation}.
In: \bbtitle{Vision Geometry VI},
vol. \bseriesno{3168},
pp. \bfpage{136}--\blpage{146}
(\byear{1997}).
\bcomment{SPIE}
\end{bchapter}
\endbibitem

%%% 5
\bibitem{bertrand2005topological}
\begin{barticle}
\bauthor{\bsnm{Bertrand}, \binits{G.}}:
\batitle{On topological watersheds}.
\bjtitle{Journal of Mathematical Imaging and Vision}
\bvolume{22}(\bissue{2}),
\bfpage{217}--\blpage{230}
(\byear{2005})
\end{barticle}
\endbibitem

%%% 6
\bibitem{cousty2009watershed}
\begin{barticle}
\bauthor{\bsnm{Cousty}, \binits{J.}},
\bauthor{\bsnm{Bertrand}, \binits{G.}},
\bauthor{\bsnm{Najman}, \binits{L.}},
\bauthor{\bsnm{Couprie}, \binits{M.}}:
\batitle{Watershed cuts: Minimum spanning forests and the drop of water
  principle}.
\bjtitle{IEEE Transactions on Pattern Analysis and Machine Intelligence}
\bvolume{31}(\bissue{8}),
\bfpage{1362}--\blpage{1374}
(\byear{2009})
\end{barticle}
\endbibitem

%%% 7
\bibitem{cousty2009collapses}
\begin{bchapter}
\bauthor{\bsnm{Cousty}, \binits{J.}},
\bauthor{\bsnm{Bertrand}, \binits{G.}},
\bauthor{\bsnm{Couprie}, \binits{M.}},
\bauthor{\bsnm{Najman}, \binits{L.}}:
\bctitle{Collapses and watersheds in pseudomanifolds}.
In: \bbtitle{International Workshop on Combinatorial Image Analysis}.
\bsertitle{Lecture Notes in Computer Science},
vol. \bseriesno{5852},
pp. \bfpage{397}--\blpage{410}
(\byear{2009}).
\bcomment{Springer}
\end{bchapter}
\endbibitem

%%% 8
\bibitem{cousty2014collapses}
\begin{barticle}
\bauthor{\bsnm{Cousty}, \binits{J.}},
\bauthor{\bsnm{Bertrand}, \binits{G.}},
\bauthor{\bsnm{Couprie}, \binits{M.}},
\bauthor{\bsnm{Najman}, \binits{L.}}:
\batitle{Collapses and watersheds in pseudomanifolds of arbitrary dimension}.
\bjtitle{Journal of Mathematical Imaging and Vision}
\bvolume{50}(\bissue{3}),
\bfpage{261}--\blpage{285}
(\byear{2014})
\end{barticle}
\endbibitem

%%% 9
\bibitem{forman1995discrete}
\begin{bchapter}
\bauthor{\bsnm{Forman}, \binits{R.}}:
\bctitle{A {D}iscrete {Morse} {T}heory for cell complexes}.
In: \beditor{\bsnm{Yau}, \binits{S.-T.}} (ed.)
\bbtitle{Geometry, Topology for Raoul Bott}.
\bpublisher{International Press},
\blocation{Somerville, MA, USA}
(\byear{1995})
\end{bchapter}
\endbibitem

%%% 10
\bibitem{scoville2019discrete}
\begin{bbook}
\bauthor{\bsnm{Scoville}, \binits{N.A.}}:
\bbtitle{Discrete {M}orse {T}heory}
vol. \bseriesno{90}.
\bpublisher{American Mathematical Soc.},
\blocation{Providence, RI, USA}
(\byear{2019})
\end{bbook}
\endbibitem

%%% 11
\bibitem{najman2013mathematical}
\begin{bbook}
\bauthor{\bsnm{Najman}, \binits{L.}},
\bauthor{\bsnm{Talbot}, \binits{H.}}:
\bbtitle{Mathematical {M}orphology: from Theory to Applications}.
\bpublisher{John Wiley \& Sons},
\blocation{Hoboken, NJ, USA}
(\byear{2013})
\end{bbook}
\endbibitem

%%% 12
\bibitem{boutry2019equivalence}
\begin{bchapter}
\bauthor{\bsnm{Boutry}, \binits{N.}},
\bauthor{\bsnm{G{\'e}raud}, \binits{T.}},
\bauthor{\bsnm{Najman}, \binits{L.}}:
\bctitle{An equivalence relation between {M}orphological {D}ynamics and
  {P}ersistent {H}omology in 1{D}}.
In: \bbtitle{International Symposium on {M}athematical {M}orphology}.
\bsertitle{Lecture Notes in Computer Science Series},
vol. \bseriesno{11564},
pp. \bfpage{57}--\blpage{68}
(\byear{2019}).
\bcomment{Springer}
\end{bchapter}
\endbibitem

%%% 13
\bibitem{boutry2021equivalence}
\begin{bchapter}
\bauthor{\bsnm{Boutry}, \binits{N.}},
\bauthor{\bsnm{G{\'e}raud}, \binits{T.}},
\bauthor{\bsnm{Najman}, \binits{L.}}:
\bctitle{An equivalence relation between morphological dynamics and persistent
  homology in $n$-{D}}.
In: \bbtitle{International Conference on Discrete Geometry and Mathematical
  Morphology},
pp. \bfpage{525}--\blpage{537}
(\byear{2021}).
\bcomment{Springer}
\end{bchapter}
\endbibitem

%%% 14
\bibitem{boutry:hal-03676854}
\begin{barticle}
\bauthor{\bsnm{Boutry}, \binits{N.}},
\bauthor{\bsnm{Najman}, \binits{L.}},
\bauthor{\bsnm{G{\'e}raud}, \binits{T.}}:
\batitle{{Some equivalence relation between persistent homology and
  morphological dynamics}}.
\bjtitle{Journal of Mathematical Imaging and Vision}
\bvolume{64},
\bfpage{807}--\blpage{824}
(\byear{2022}).
\doiurl{10.1007/s10851-022-01104-z}
\end{barticle}
\endbibitem

%%% 15
\bibitem{grimaud1992new}
\begin{bchapter}
\bauthor{\bsnm{Grimaud}, \binits{M.}}:
\bctitle{New measure of contrast: the dynamics}.
In: \bbtitle{Image Algebra and Morphological Image Processing III},
vol. \bseriesno{1769},
pp. \bfpage{292}--\blpage{306}
(\byear{1992}).
\bcomment{International Society for Optics and Photonics}
\end{bchapter}
\endbibitem

%%% 16
\bibitem{edelsbrunner2008persistent}
\begin{barticle}
\bauthor{\bsnm{Edelsbrunner}, \binits{H.}},
\bauthor{\bsnm{Harer}, \binits{J.}}:
\batitle{Persistent {H}omology - {A} survey}.
\bjtitle{Contemporary mathematics}
\bvolume{453},
\bfpage{257}--\blpage{282}
(\byear{2008})
\end{barticle}
\endbibitem

%%% 17
\bibitem{tierny2017introduction}
\begin{botherref}
\oauthor{\bsnm{Tierny}, \binits{J.}}:
{Introduction to Topological Data Analysis}.
Technical report,
{Sorbonne University, LIP6, APR team},
France
(May 2017).
\url{https://hal.archives-ouvertes.fr/cel-01581941}
\end{botherref}
\endbibitem

%%% 18
\bibitem{munch2017user}
\begin{barticle}
\bauthor{\bsnm{Munch}, \binits{E.}}:
\batitle{A user's guide to {Topological Data Analysis}}.
\bjtitle{Journal of Learning Analytics}
\bvolume{4}(\bissue{2}),
\bfpage{47}--\blpage{61}
(\byear{2017})
\end{barticle}
\endbibitem

%%% 19
\bibitem{10.1007/978-3-031-19897-7_4}
\begin{bchapter}
\bauthor{\bsnm{Boutry}, \binits{N.}},
\bauthor{\bsnm{Bertrand}, \binits{G.}},
\bauthor{\bsnm{Najman}, \binits{L.}}:
\bctitle{Gradient vector fields of discrete {M}orse functions and
  watershed-cuts}.
In: \beditor{\bsnm{Baudrier}, \binits{{\'E}.}},
\beditor{\bsnm{Naegel}, \binits{B.}},
\beditor{\bsnm{Kr{\"a}henb{\"u}hl}, \binits{A.}},
\beditor{\bsnm{Tajine}, \binits{M.}} (eds.)
\bbtitle{Discrete Geometry and Mathematical Morphology},
pp. \bfpage{35}--\blpage{47}.
\bpublisher{Springer},
\blocation{Cham}
(\byear{2022})
\end{bchapter}
\endbibitem

%%% 20
\bibitem{forman1998witten}
\begin{barticle}
\bauthor{\bsnm{Forman}, \binits{R.}}:
\batitle{Witten-{M}orse theory for cell complexes}.
\bjtitle{Topology}
\bvolume{37}(\bissue{5}),
\bfpage{945}--\blpage{980}
(\byear{1998})
\end{barticle}
\endbibitem

%%% 21
\bibitem{de2013discrete}
\begin{bchapter}
\bauthor{\bsnm{De~Floriani}, \binits{L.}},
\bauthor{\bsnm{Iuricich}, \binits{F.}},
\bauthor{\bsnm{Magillo}, \binits{P.}},
\bauthor{\bsnm{Simari}, \binits{P.}}:
\bctitle{{D}iscrete {M}orse versus watershed decompositions of tessellated
  manifolds}.
In: \bbtitle{International Conference on Image Analysis and Processing}.
\bsertitle{Lecture Notes in Computer Science},
vol. \bseriesno{8157},
pp. \bfpage{339}--\blpage{348}
(\byear{2013}).
\bcomment{Springer}
\end{bchapter}
\endbibitem

%%% 22
\bibitem{delgado2014skeletonization}
\begin{barticle}
\bauthor{\bsnm{Delgado-Friedrichs}, \binits{O.}},
\bauthor{\bsnm{Robins}, \binits{V.}},
\bauthor{\bsnm{Sheppard}, \binits{A.}}:
\batitle{Skeletonization and partitioning of digital images using {D}iscrete
  {M}orse {T}heory}.
\bjtitle{IEEE Transactions on Pattern Analysis and Machine Intelligence}
\bvolume{37}(\bissue{3}),
\bfpage{654}--\blpage{666}
(\byear{2014})
\end{barticle}
\endbibitem

%%% 23
\bibitem{de2015morse}
\begin{barticle}
\bauthor{\bsnm{De~Floriani}, \binits{L.}},
\bauthor{\bsnm{Fugacci}, \binits{U.}},
\bauthor{\bsnm{Iuricich}, \binits{F.}},
\bauthor{\bsnm{Magillo}, \binits{P.}}:
\batitle{Morse complexes for shape segmentation and homological analysis:
  discrete models and algorithms}.
\bjtitle{Computer Graphics Forum}
\bvolume{34}(\bissue{2}),
\bfpage{761}--\blpage{785}
(\byear{2015}).
\bcomment{Wiley Online Library}
\end{barticle}
\endbibitem

%%% 24
\bibitem{najman1994watershed}
\begin{barticle}
\bauthor{\bsnm{Najman}, \binits{L.}},
\bauthor{\bsnm{Schmitt}, \binits{M.}}:
\batitle{Watershed of a continuous function}.
\bjtitle{Signal Processing}
\bvolume{38}(\bissue{1}),
\bfpage{99}--\blpage{112}
(\byear{1994})
\end{barticle}
\endbibitem

%%% 25
\bibitem{alexandroff1937diskrete}
\begin{barticle}
\bauthor{\bsnm{Alexandroff}, \binits{P.}}:
\batitle{Diskrete ra\"ume}.
\bjtitle{Matematicheskiĭ Sbornik}
\bvolume{2}(\bissue{3}),
\bfpage{501}--\blpage{519}
(\byear{1937})
\end{barticle}
\endbibitem

%%% 26
\bibitem{barmak2008simple}
\begin{barticle}
\bauthor{\bsnm{Barmak}, \binits{J.A.}},
\bauthor{\bsnm{Minian}, \binits{E.G.}}:
\batitle{Simple homotopy types and finite spaces}.
\bjtitle{Advances in Mathematics}
\bvolume{218}(\bissue{1}),
\bfpage{87}--\blpage{104}
(\byear{2008})
\end{barticle}
\endbibitem

%%% 27
\bibitem{whitehead1939simplicial}
\begin{barticle}
\bauthor{\bsnm{Whitehead}, \binits{J.H.C.}}:
\batitle{Simplicial spaces, nuclei and m-groups}.
\bjtitle{Proceedings of the London mathematical society}
\bvolume{2}(\bissue{1}),
\bfpage{243}--\blpage{327}
(\byear{1939})
\end{barticle}
\endbibitem

%%% 28
\bibitem{massey91}
\begin{bbook}
\bauthor{\bsnm{Massey}, \binits{W.S.}}:
\bbtitle{A Basic Course in Algebraic Topology}.
\bpublisher{Springer},
\blocation{Berlin, Germany}
(\byear{1991})
\end{bbook}
\endbibitem

%%% 29
\bibitem{BAGCHI2008327}
\begin{barticle}
\bauthor{\bsnm{Bagchi}, \binits{B.}},
\bauthor{\bsnm{Datta}, \binits{B.}}:
\batitle{Lower bound theorem for normal pseudomanifolds}.
\bjtitle{Expositiones Mathematicae}
\bvolume{26}(\bissue{4}),
\bfpage{327}--\blpage{351}
(\byear{2008})
\end{barticle}
\endbibitem

%%% 30
\bibitem{BASAK2020107035}
\begin{barticle}
\bauthor{\bsnm{Basak}, \binits{B.}},
\bauthor{\bsnm{Swartz}, \binits{E.}}:
\batitle{Three-dimensional normal pseudomanifolds with relatively few edges}.
\bjtitle{Advances in Mathematics}
\bvolume{365},
\bfpage{107035}
(\byear{2020})
\end{barticle}
\endbibitem

%%% 31
\bibitem{DBNN2008}
\begin{botherref}
\oauthor{\bsnm{Datta}, \binits{B.}},
\oauthor{\bsnm{Nilakantan}, \binits{N.}}:
Three-dimensional pseudomanifolds on eight vertices.
Int. J. Math. Mathematical Sciences
(2008)
\end{botherref}
\endbibitem

%%% 32
\bibitem{10.1007/978-3-540-31965-8_17}
\begin{bchapter}
\bauthor{\bsnm{Couprie}, \binits{M.}},
\bauthor{\bsnm{Najman}, \binits{L.}},
\bauthor{\bsnm{Bertrand}, \binits{G.}}:
\bctitle{Algorithms for the topological watershed}.
In: \beditor{\bsnm{Andres}, \binits{E.}},
\beditor{\bsnm{Damiand}, \binits{G.}},
\beditor{\bsnm{Lienhardt}, \binits{P.}} (eds.)
\bbtitle{Discrete Geometry for Computer Imagery},
pp. \bfpage{172}--\blpage{182}.
\bpublisher{Springer},
\blocation{Berlin, Heidelberg}
(\byear{2005})
\end{bchapter}
\endbibitem

%%% 33
\bibitem{cormen1999introduction}
\begin{botherref}
\oauthor{\bsnm{Cormen}, \binits{T.H.}},
\oauthor{\bsnm{Leiserson}, \binits{C.E.}},
\oauthor{\bsnm{Rivest}, \binits{R.L.}}:
Introduction to Algorithms. 23rd printing.
The MIT Press and McGraw-Hill
(1999)
\end{botherref}
\endbibitem

%%% 34
\bibitem{motwani1995randomized}
\begin{bbook}
\bauthor{\bsnm{Motwani}, \binits{R.}},
\bauthor{\bsnm{Raghavan}, \binits{P.}}:
\bbtitle{Randomized Algorithms}.
\bpublisher{Cambridge university press},
\blocation{Cambridge, UK}
(\byear{1995})
\end{bbook}
\endbibitem

%%% 35
\bibitem{vcomic2016computing}
\begin{barticle}
\bauthor{\bsnm{{\v{C}}omi{\'c}}, \binits{L.}},
\bauthor{\bsnm{De~Floriani}, \binits{L.}},
\bauthor{\bsnm{Iuricich}, \binits{F.}},
\bauthor{\bsnm{Magillo}, \binits{P.}}:
\batitle{Computing a {D}iscrete {M}orse gradient from a watershed
  decomposition}.
\bjtitle{Computers \& Graphics}
\bvolume{58},
\bfpage{43}--\blpage{52}
(\byear{2016})
\end{barticle}
\endbibitem

%%% 36
\bibitem{najman1996geodesic}
\begin{barticle}
\bauthor{\bsnm{Najman}, \binits{L.}},
\bauthor{\bsnm{Schmitt}, \binits{M.}}:
\batitle{Geodesic saliency of watershed contours and hierarchical
  segmentation}.
\bjtitle{IEEE Transactions on Pattern Analysis and Machine Intelligence}
\bvolume{18}(\bissue{12}),
\bfpage{1163}--\blpage{1173}
(\byear{1996})
\end{barticle}
\endbibitem

%%% 37
\bibitem{najman2011equivalence}
\begin{barticle}
\bauthor{\bsnm{Najman}, \binits{L.}}:
\batitle{On the equivalence between hierarchical segmentations and ultrametric
  watersheds}.
\bjtitle{Journal of Mathematical Imaging and Vision}
\bvolume{40}(\bissue{3}),
\bfpage{231}--\blpage{247}
(\byear{2011})
\end{barticle}
\endbibitem

%%% 38
\bibitem{cousty2018hierarchical}
\begin{barticle}
\bauthor{\bsnm{Cousty}, \binits{J.}},
\bauthor{\bsnm{Najman}, \binits{L.}},
\bauthor{\bsnm{Kenmochi}, \binits{Y.}},
\bauthor{\bsnm{Guimar{\~a}es}, \binits{S.}}:
\batitle{Hierarchical segmentations with graphs: quasi-flat zones, minimum
  spanning trees, and saliency maps}.
\bjtitle{Journal of Mathematical Imaging and Vision}
\bvolume{60}(\bissue{4}),
\bfpage{479}--\blpage{502}
(\byear{2018})
\end{barticle}
\endbibitem

%%% 39
\bibitem{perret2019higra}
\begin{barticle}
\bauthor{\bsnm{Perret}, \binits{B.}},
\bauthor{\bsnm{Chierchia}, \binits{G.}},
\bauthor{\bsnm{Cousty}, \binits{J.}},
\bauthor{\bsnm{Guimar{\~a}es}, \binits{S.J.F.}},
\bauthor{\bsnm{Kenmochi}, \binits{Y.}},
\bauthor{\bsnm{Najman}, \binits{L.}}:
\batitle{Higra: Hierarchical graph analysis}.
\bjtitle{SoftwareX}
\bvolume{10},
\bfpage{100335}
(\byear{2019})
\end{barticle}
\endbibitem

%%% 40
\bibitem{challa2019watersheds}
\begin{barticle}
\bauthor{\bsnm{Challa}, \binits{A.}},
\bauthor{\bsnm{Danda}, \binits{S.}},
\bauthor{\bsnm{Sagar}, \binits{B.D.}},
\bauthor{\bsnm{Najman}, \binits{L.}}:
\batitle{Watersheds for semi-supervised classification}.
\bjtitle{IEEE Signal Processing Letters}
\bvolume{26}(\bissue{5}),
\bfpage{720}--\blpage{724}
(\byear{2019})
\end{barticle}
\endbibitem

%%% 41
\bibitem{bertrand2014powerful}
\begin{barticle}
\bauthor{\bsnm{Bertrand}, \binits{G.}},
\bauthor{\bsnm{Couprie}, \binits{M.}}:
\batitle{Powerful parallel and symmetric 3d thinning schemes based on critical
  kernels}.
\bjtitle{Journal of Mathematical Imaging and Vision}
\bvolume{48}(\bissue{1}),
\bfpage{134}--\blpage{148}
(\byear{2014})
\end{barticle}
\endbibitem

%%% 42
\bibitem{bertrand1997image}
\begin{barticle}
\bauthor{\bsnm{Bertrand}, \binits{G.}},
\bauthor{\bsnm{Everat}, \binits{J.-C.}},
\bauthor{\bsnm{Couprie}, \binits{M.}}:
\batitle{Image segmentation through operators based on topology}.
\bjtitle{Journal of Electronic Imaging}
\bvolume{6}(\bissue{4}),
\bfpage{395}--\blpage{405}
(\byear{1997})
\end{barticle}
\endbibitem

%%% 43
\bibitem{forman1998morse}
\begin{barticle}
\bauthor{\bsnm{Forman}, \binits{R.}}:
\batitle{{Morse} {T}heory for cell complexes}.
\bjtitle{Advances in Mathematics}
\bvolume{134},
\bfpage{90}--\blpage{145}
(\byear{1998})
\end{barticle}
\endbibitem

\end{thebibliography}
