@article {ast,
    AUTHOR = {Angenent, Sigurd and Sapiro, Guillermo and Tannenbaum, Allen},
     TITLE = {On the affine heat equation for non-convex curves},
   JOURNAL = {J.~Amer. Math. Soc.},
  FJOURNAL = {Journal of the American Mathematical Society},
    VOLUME = {11},
      YEAR = {1998},
    NUMBER = {3},
     PAGES = {601--634},
       URL = {https://doi.org/10.1090/S0894-0347-98-00262-8},
}

@article {and,
    AUTHOR = {Andrews, Ben},
     TITLE = {The affine curve-lengthening flow},
   JOURNAL = {J.~Reine Angew. Math.},
  FJOURNAL = {Journal f\"{u}r die Reine und Angewandte Mathematik. [Crelle's
              Journal]},
    VOLUME = {506},
      YEAR = {1999},
     PAGES = {43--83},
       URL = {https://doi.org/10.1515/crll.1999.008},
}

@incollection {btv,
    AUTHOR = {Bay, H. and Tuytelaars, T. and Van Gool, L.},
     TITLE = {Surf: speeded up robust features},
 BOOKTITLE = {Computer Vision~-- ECCV 2006},
    EDITOR = {Leonardis, A. and Bischof, H. and Pinz, A.},
     PAGES = {404--417},
 PUBLISHER = {Springer, Berlin~-- Heidelberg},
      YEAR = {2006},
       URL = {https://doi.org/10.1007/11744023_32},
}

@book {Blaschke,
    AUTHOR = {Blaschke, W.},
     TITLE = {Vorlesungen \"uber Differentialgeometrie und geometrische Grundlagen von Einsteins Relativit\"atstheorie. II.~Affine Differentialgeometrie},
 PUBLISHER = {Springer, Berlin},
      YEAR = {1923},
     PAGES = {ix+259},
}

@book {Cartanrm,
    AUTHOR = {Cartan, \'E.},
     TITLE = {La M\'ethode du Rep\`ere Mobile, la Th\'eorie des Groupes Continus, et les Espaces G\'en\'eralis\'es},
 PUBLISHER = {Hermann, Paris},
      YEAR = {1935},
     PAGES = {65},
}

@book {cz,
    AUTHOR = {Chou, Kai-Seng and Zhu, Xi-Ping},
     TITLE = {The curve shortening problem},
 PUBLISHER = {Chapman \& Hall/CRC, Boca Raton, FL},
      YEAR = {2001},
     PAGES = {x+255},
       URL = {https://doi.org/10.1201/9781420035704},
}

@article {chy,
    AUTHOR = {Cohen, F. S. and Huang, Z. and Yang, Z.},
     TITLE = {Invariant matching and identification of curves using B-splines curve representation},
   JOURNAL = {IEEE Trans. Image Process.},
  FJOURNAL = {IEEE Transactions on Image Processing},
    VOLUME = {4},
      YEAR = {1995},
     PAGES = {1--10},
       URL = {https://doi.org/10.1109/83.350818},
}

@incollection {drw,
    AUTHOR = {Damelin, Steven B. and Ragozin, David L. and Werman, Michael},
     TITLE = {On best uniform approximation of convex/concave real valued functions from ${\mathbb R}^k$, Chebyshev equioscillation and graphics},
 BOOKTITLE = {Excursions in Harmonic Analysis, Vol.~6, In Honor of John Benedetto's 80th Birthday},
    SERIES = {Applied and Numerical Harmonic Analysis},
      NOTE = {{t}o appear},
    EPRINT = {1812.02302},
}

@article {ds,
    AUTHOR = {Daskalopoulos, P. and Sesum, N.},
     TITLE = {Ancient solutions to geometric flows},
   JOURNAL = {Notices Amer. Math. Soc.},
  FJOURNAL = {Notices of the American Mathematical Society},
    VOLUME = {67},
      YEAR = {2020},
     PAGES = {467--474},
}

@article {dde,
    AUTHOR = {Deckelnick, Klaus and Dziuk, Gerhard and Elliott, Charles M.},
     TITLE = {Computation of geometric partial differential equations and
              mean curvature flow},
   JOURNAL = {Acta Numer.},
  FJOURNAL = {Acta Numerica},
    VOLUME = {14},
      YEAR = {2005},
     PAGES = {139--232},
       URL = {https://doi.org/10.1017/S0962492904000224},
}

@incollection {eg,
    AUTHOR = {Epstein, C. L. and Gage, Michael},
     TITLE = {The curve shortening flow},
 BOOKTITLE = {Wave Motion: Theory, Modelling, and Computation, Proceedings of a Conference in Honor of the 60th Birthday of Peter D.~Lax ({B}erkeley,
              {C}alif., 1986)},
    EDITOR = {Chorin, A. J. and Majda, A. J.},
    SERIES = {Math. Sci. Res. Inst. Publ.},
    VOLUME = {7},
     PAGES = {15--59},
 PUBLISHER = {Springer, New York},
      YEAR = {1987},
       URL = {https://doi.org/10.1007/978-1-4613-9583-6_2},
}

@article {fo-2,
    AUTHOR = {Fels, Mark and Olver, Peter J.},
     TITLE = {Moving coframes. {II}.~{R}egularization and theoretical
              foundations},
   JOURNAL = {Acta Appl. Math.},
  FJOURNAL = {Acta Applicandae Mathematicae},
    VOLUME = {55},
      YEAR = {1999},
    NUMBER = {2},
     PAGES = {127--208},
       URL = {https://doi.org/10.1023/A:1006195823000},
}

@article {gh,
    AUTHOR = {Gage, M. and Hamilton, R. S.},
     TITLE = {The heat equation shrinking convex plane curves},
   JOURNAL = {J.~Differential Geom.},
  FJOURNAL = {Journal of Differential Geometry},
    VOLUME = {23},
      YEAR = {1986},
    NUMBER = {1},
     PAGES = {69--96},
       URL = {https://doi.org/10.4310/jdg/1214439902},
}

@article {gw,
    AUTHOR = {Gardner, Robert B. and Wilkens, George R.},
     TITLE = {The fundamental theorems of curves and hypersurfaces in
              centro-affine geometry},
   JOURNAL = {Bull. Belg. Math. Soc. Simon Stevin},
  FJOURNAL = {Bulletin of the Belgian Mathematical Society. Simon Stevin},
    VOLUME = {4},
      YEAR = {1997},
    NUMBER = {3},
     PAGES = {379--401},
       URL = {https://doi.org/10.36045/bbms/1105733254},
}

@article {gra-1,
    AUTHOR = {Grayson, Matthew A.},
     TITLE = {The heat equation shrinks embedded plane curves to round
              points},
   JOURNAL = {J.~Differential Geom.},
  FJOURNAL = {Journal of Differential Geometry},
    VOLUME = {26},
      YEAR = {1987},
    NUMBER = {2},
     PAGES = {285--314},
       URL = {https://doi.org/10.4310/jdg/1214441371},
}

@article {gra-2,
    AUTHOR = {Grayson, Matthew A.},
     TITLE = {Shortening embedded curves},
   JOURNAL = {Ann. of Math.},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {129},
      YEAR = {1989},
    NUMBER = {1},
     PAGES = {71--111},
       URL = {https://doi.org/10.2307/1971486},
}

@article {hh,
    AUTHOR = {Hann, C. E. and Hickman, M. S.},
     TITLE = {Projective curvature and integral invariants},
   JOURNAL = {Acta Appl. Math.},
  FJOURNAL = {Acta Applicandae Mathematicae},
    VOLUME = {74},
      YEAR = {2002},
    NUMBER = {2},
     PAGES = {177--193},
       URL = {https://doi.org/10.1023/A:1020617228313},
}


@article {hw,
    AUTHOR = {Hartigan, J. A. and Wong, M. A.},
     TITLE = {Algorithm AS 136: A k-means clustering algorithm},
   JOURNAL = {J.~Roy. Stat. Soc. Ser.~C. Appl. Stat.},
  FJOURNAL = {Journal of the Royal Statistical Society. Series C (Applied Statistics)},
    VOLUME = {28},
      YEAR = {1979},
    NUMBER = {1},
     PAGES = {100--108},
       URL = {https://doi.org/10.2307/2346830},
}

@article {Hasimoto,
    AUTHOR = {Hasimoto, Hidenori},
     TITLE = {A soliton on a vortex filament},
   JOURNAL = {J.~Fluid Mech.},
  FJOURNAL = {Journal of Fluid Mechanics},
    VOLUME = {51},
      YEAR = {1972},
    NUMBER = {3},
     PAGES = {477--485},
       URL = {https://doi.org/10.1017/S0022112072002307},
}

@article {hc,
    AUTHOR = {Huang, Z. and Cohen, F. S.},
     TITLE = {Affine-invariant B-spline moments for curve matching},
   JOURNAL = {IEEE Trans. Image Process.},
  FJOURNAL = {IEEE Transactions on Image Processing},
    VOLUME = {5},
      YEAR = {1996},
     PAGES = {1473--1480},
       URL = {https://doi.org/10.1109/83.536895},
}

@article {KuSc,
    AUTHOR = {Kuwert, Ernst and Sch\"atzle, Reiner},
     TITLE = {Gradient flow for the {W}illmore functional},
   JOURNAL = {Comm. Anal. Geom.},
  FJOURNAL = {Communications in Analysis and Geometry},
    VOLUME = {10},
      YEAR = {2002},
    NUMBER = {2},
     PAGES = {307--339},
       URL = {https://doi.org/10.4310/CAG.2002.v10.n2.a4},
}

@article {LangPer,
    AUTHOR = {Langer, Joel and Perline, Ron},
     TITLE = {Poisson geometry of the filament equation},
   JOURNAL = {J.~Nonlinear Sci.},
  FJOURNAL = {Journal of Nonlinear Science},
    VOLUME = {1},
      YEAR = {1991},
    NUMBER = {1},
     PAGES = {71--93},
       URL = {https://doi.org/10.1007/BF01209148},
}

@article {lhd,
    AUTHOR = {Li, Chunming and Huang, Rui and Ding, Zhaohua and Gatenby, J.
              Chris and Metaxas, Dimitris N. and Gore, John C.},
     TITLE = {A level set method for image segmentation in the presence of
              intensity inhomogeneities with application to {MRI}},
   JOURNAL = {IEEE Trans. Image Process.},
  FJOURNAL = {IEEE Transactions on Image Processing},
    VOLUME = {20},
      YEAR = {2011},
    NUMBER = {7},
     PAGES = {2007--2016},
       URL = {https://doi.org/10.1109/TIP.2011.2146190},
}

@inproceedings {low,
    AUTHOR = {Lowe, D. G.},
     TITLE = {Object recognition from local scale-invariant features},
 BOOKTITLE = {Proceedings of the Seventh IEEE International Conference on Computer Vision, Vol.~2 (Kerkyra, Greece)},
     PAGES = {1150--1157},
 PUBLISHER = {IEEE},
      YEAR = {1999},
       URL = {https://doi.org/10.1109/ICCV.1999.790410},
}

@article {ms,
    AUTHOR = {Mikolajczyk, K. and Schmid, C.},
     TITLE = {A performance evaluation of local descriptors},
   JOURNAL = {IEEE Trans. Pattern Anal. Mach. Intell.},
  FJOURNAL = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
    VOLUME = {27},
      YEAR = {2005},
    NUMBER = {10},
     PAGES = {1615--1630},
       URL = {https://doi.org/10.1109/TPAMI.2005.188},
}

@article {mts,
    AUTHOR = {Mikolajczyk, K. and Tuytelaars, T. and Schmid, C. and Matas, A. Z. J. and Schaffalitzky, F. and Kadir, T. and Van Gool, L.},
     TITLE = {A comparison of affine region detectors},
   JOURNAL = {Int.~J. Comput. Vis.},
  FJOURNAL = {International Journal of Computer Vision},
    VOLUME = {65},
      YEAR = {2005},
     PAGES = {43--72},
       URL = {https://doi.org/10.1007/s11263-005-3848-x},
}

@article {mos,
    AUTHOR = {Mokhtarian, F. and Suomela, R.},
     TITLE = {Robust image corner detection through curvature scale space},
   JOURNAL = {IEEE Trans. Pattern Anal. Mach. Intell.},
  FJOURNAL = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
    VOLUME = {20},
      YEAR = {1998},
    NUMBER = {12},
     PAGES = {1376--1381},
       URL = {https://doi.org/10.1109/34.735812},
}

@article {mul,
    AUTHOR = {Mullins, W. W.},
     TITLE = {Two-dimensional motion of idealized grain boundaries},
   JOURNAL = {J.~Appl. Phys.},
  FJOURNAL = {Journal of Applied Physics},
    VOLUME = {27},
      YEAR = {1956},
     PAGES = {900--904},
       URL = {https://doi.org/10.1063/1.1722511},
}

@book {ns,
    AUTHOR = {Nomizu, Katsumi and Sasaki, Takeshi},
     TITLE = {Affine differential geometry: geometry of affine immersions},
    SERIES = {Cambridge Tracts in Mathematics},
    VOLUME = {111},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {1994},
     PAGES = {xiv+263},
}

@book {olv-eis,
    AUTHOR = {Olver, Peter J.},
     TITLE = {Equivalence, invariants, and symmetry},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {1995},
     PAGES = {xvi+525},
       URL = {https://doi.org/10.1017/CBO9780511609565},
}

@article {olv-sinmf,
    AUTHOR = {Olver, Peter J.},
     TITLE = {Moving frames and singularities of prolonged group actions},
   JOURNAL = {Selecta Math. (N.S.)},
  FJOURNAL = {Selecta Mathematica. New Series},
    VOLUME = {6},
      YEAR = {2000},
    NUMBER = {1},
     PAGES = {41--77},
       URL = {https://doi.org/10.1007/s000290050002},
}

@article {olv-41,
    AUTHOR = {Olver, Peter J.},
     TITLE = {Invariant submanifold flows},
   JOURNAL = {J.~Phys.~A: Math. Theor.},
  FJOURNAL = {Journal of Physics. A. Mathematical and Theoretical},
    VOLUME = {41},
      YEAR = {2008},
    NUMBER = {34},
     PAGES = {344017, 22~pages},
       URL = {https://doi.org/10.1088/1751-8113/41/34/344017},
}

@article {olv-max,
    AUTHOR = {Olver, Peter J.},
     TITLE = {Differential invariants of maximally symmetric submanifolds},
   JOURNAL = {J.~Lie Theory},
  FJOURNAL = {Journal of Lie Theory},
    VOLUME = {19},
      YEAR = {2009},
    NUMBER = {1},
     PAGES = {79--99},
}

@article {olv-5,
    AUTHOR = {Olver, Peter J.},
     TITLE = {Moving frames and differential invariants in centro-affine
              geometry},
   JOURNAL = {Lobachevskii~J. Math.},
  FJOURNAL = {Lobachevskii Journal of Mathematics},
    VOLUME = {31},
      YEAR = {2010},
    NUMBER = {2},
     PAGES = {77--89},
       URL = {https://doi.org/10.1134/S1995080210020010},
}

@incollection {olv-6,
    AUTHOR = {Olver, Peter J.},
     TITLE = {Modern developments in the theory and applications of moving frames},
 BOOKTITLE = {Impact150: Stories of the Impact of Mathematics},
     PAGES = {14--50},
 PUBLISHER = {London Mathematical Society, London},
      YEAR = {2015},
}

@article {olv-sg,
    AUTHOR = {Olver, Peter J.},
     TITLE = {The symmetry groupoid and weighted signature of a geometric
              object},
   JOURNAL = {J.~Lie Theory},
  FJOURNAL = {Journal of Lie Theory},
    VOLUME = {26},
      YEAR = {2016},
    NUMBER = {1},
     PAGES = {235--267},
}

@incollection {ost-1,
    AUTHOR = {Olver, Peter J. and Sapiro, Guillermo and Tannenbaum, Allen},
     TITLE = {Differential invariant signatures and flows in computer vision: a symmetry group approach},
 BOOKTITLE = {Geometry-Driven Diffusion in Computer Vision},
     PAGES = {255--306},
 PUBLISHER = {Springer, Dordrecht},
      YEAR = {1994},
       URL = {https://doi.org/10.1007/978-94-017-1699-4_11},
}

@article {ost-2,
    AUTHOR = {Olver, Peter J. and Sapiro, Guillermo and Tannenbaum, Allen},
     TITLE = {Affine invariant detection: edge maps, anisotropic diffusion,
              and active contours},
   JOURNAL = {Acta Appl. Math.},
  FJOURNAL = {Acta Applicandae Mathematicae},
    VOLUME = {59},
      YEAR = {1999},
    NUMBER = {1},
     PAGES = {45--77},
       URL = {https://doi.org/10.1023/A:1006295328209},
}

@article {pk,
    AUTHOR = {Pek\c{s}en, \"Omer and Khadjiev, Djavvat},
     TITLE = {On invariants of curves in centro-affine geometry},
   JOURNAL = {J.~Math. Kyoto Univ.},
  FJOURNAL = {Journal of Mathematics of Kyoto University},
    VOLUME = {44},
      YEAR = {2004},
    NUMBER = {3},
     PAGES = {603--613},
       URL = {https://doi.org/10.1215/kjm/1250283086},
}

@article {rdm,
    AUTHOR = {Rodr\'{\i}guez, Mariano and Delon, Julie and Morel, Jean-Michel},
     TITLE = {Fast affine invariant image matching},
   JOURNAL = {IPOL~J. Image Process. Online},
  FJOURNAL = {IPOL Journal. Image Processing Online},
    VOLUME = {8},
      YEAR = {2018},
     PAGES = {251--281},
       URL = {https://doi.org/10.5201/ipol.2018.225},
}

@article {sc,
    AUTHOR = {Salvador, S. and Chan, P.},
     TITLE = {FastDTW: toward accurate dynamic time warping in linear time and space},
   JOURNAL = {Intellig. Data Anal.},
  FJOURNAL = {Intelligence Data Analysis},
    VOLUME = {11},
      YEAR = {2007},
    NUMBER = {5},
     PAGES = {561--580},
       URL = {https://doi.org/10.3233/IDA-2007-11508},
}

@article {st-2,
    AUTHOR = {Sapiro, Guillermo and Tannenbaum, Allen},
     TITLE = {On affine plane curve evolution},
   JOURNAL = {J.~Funct. Anal.},
  FJOURNAL = {Journal of Functional Analysis},
    VOLUME = {119},
      YEAR = {1994},
    NUMBER = {1},
     PAGES = {79--120},
       URL = {https://doi.org/10.1006/jfan.1994.1004},
}

@incollection {sim,
    AUTHOR = {Simon, Udo},
     TITLE = {Affine differential geometry},
 BOOKTITLE = {Handbook of Differential Geometry, {V}ol.~{I}},
     PAGES = {905--961},
 PUBLISHER = {North-Holland, Amsterdam},
      YEAR = {2000},
       URL = {https://doi.org/10.1016/S1874-5741(00)80012-6},
}

@article {tot,
    AUTHOR = {Tuznik, Stanley L. and Olver, Peter J. and Tannenbaum, Allen},
     TITLE = {Equi-affine differential invariants for invariant feature
              point detection},
   JOURNAL = {European~J. Appl. Math.},
  FJOURNAL = {European Journal of Applied Mathematics},
    VOLUME = {31},
      YEAR = {2020},
    NUMBER = {2},
     PAGES = {277--296},
       URL = {https://doi.org/10.1017/s0956792519000020},
    EPRINT = {1803.01669},
}

@incollection {wil,
    AUTHOR = {Wilkens, George R.},
     TITLE = {Centro-affine geometry in the plane and feedback invariants of
              two-state scalar control systems},
 BOOKTITLE = {Differential Geometry and Control ({B}oulder, {CO}, 1997)},
    EDITOR = {Ferreyra, G. and Gardner, R. and Sussmann, H.},
    SERIES = {Proc. Sympos. Pure Math.},
    VOLUME = {64},
     PAGES = {319--333},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {1999},
       URL = {https://doi.org/10.1090/pspum/064/1654544},
}

@article {wwq,
    AUTHOR = {Wo, Weifeng and Wang, Xiaoliu and Qu, Changzheng},
     TITLE = {The centro-affine invariant geometric heat flow},
   JOURNAL = {Math.~Z.},
  FJOURNAL = {Mathematische Zeitschrift},
    VOLUME = {288},
      YEAR = {2018},
    NUMBER = {1-2},
     PAGES = {311--331},
       URL = {https://doi.org/10.1007/s00209-017-1890-3},
}

@article {ym,
    AUTHOR = {Yu, Guoshen and Morel, Jean-Michel},
     TITLE = {A{SIFT}: an algorithm for fully affine invariant comparison},
   JOURNAL = {Image Process. Line},
  FJOURNAL = {Image Processing On Line},
    VOLUME = {1},
      YEAR = {2011},
     PAGES = {11--38},
       URL = {https://doi.org/10.5201/ipol.2011.my-asift},
}
