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Dr.
Marcos Craizer
Associate Professor |
Biographical Information
Dr. Craizer received a B. degree in mathematics in 1983 from Federal
University of Rio de Janeiro (UFRJ), a M.Sc degree in 1985 and a Ph.D. degree
in 1989, both in mathematics at the Institute for Pure and Applied
Mathematics (IMPA).
Dr. Craizer is a professor at the Department of Mathematics of Pontifical Catholic University of Rio de Janeiro (PUC-Rio) since 1988.
Dr.
Craizer was the vice-dean for undergraduate studies of the Center of
Technology and Sciences of Pontifical Catholic University of Rio de
Janeiro (PUC-Rio) from march/2006 to february/2010.
Research Interests
- Affine Differential Geometry
- Discrete Geometry
Former Students
- Bruno Coelho Maciel - M.Sc. Dissertation:
Multi-resolution edge detection and image reconstruction from the edges,
- Marcilene Fátima Dianin-
M.Sc. Dissertation: Mathematical morphology, segmentation and curve
evolution,
- Décio Ângelo Fonini Jr.-
Ph.D. Thesis (co-advised with E.A.B.da Silva): Successive approximation
quantization,
- João Domingos Gomes da
Silva Jr. - M.Sc. Dissertation (co-advised with H.Lopes): Curvature
estimators based on parametric curve fitting,
- Cinthia de Oliveira
Lage Ferreira- M.Sc. Dissertation: Evolution of a union of balls from its
medial axis,
- Lhaylla dos Santos Cryssaff- Ph.D. Thesis: Geometric energies on triangulated surfaces, 17/02/2009.
- Paulo César Alves Araujo- M.Sc.Dissertation: Algumas Desigualdades Isoperimétricas para Curvas Planas, 28/04/2011.
Publications
- Papers
- M.Craizer, Entropy of inner functions, Israel Journal of Mathematics, vol.74, 2-3, pp.129-168, 1991.
- M.Craizer, The Bernoulli property of inner functions. Ergodic Theory and Dynamical Systems, 12, p.209-215, 1992.
- J.L.Arraut,
M. Craizer, Stability of blocks of compact orbits of an action of R^2
on M^3. Advanced series in non-linear dynamics, 4,p.15-21,1993.
- M.Craizer, Homogenization of
codimension 1 actions of R^n near a compact orbit, Annales de L'Institut Fourier, vol.44,
n.5, pp.1435-1448, 1994.
- J.L.Arraut, M.Craizer, Foliations of
M^3 defined by R^2-actions, Annales de L'Institut Fourier, vol.45, n.4, pp.1091-1118,
1995.
- M.Craizer, E.A.B.da Silva and E.G.Ramos, New results on
successive approximation vector quantization, Electronics Letters IEE, vol.34, n.1.,
pp.59-60, 1998.
- M.Craizer, E.A.B.da Silva and E.G.Ramos, Convergent
algorithms for successive approximation vector quantization with
applications to wavelet image compression, IEE Proceedings - Vision, Image
and Signal Processing, vol. 146, n.3, pp 159-164, 1999.
- M.Craizer, A.O.Lopes, The
capacity-cost function of hard-constrained channels, International Journal of
Applied Mathematics, vol.2, n.10, pp. 1165-1180, 2000.
- M.Craizer, D.A.Fonini Jr. and E.A.B.da
Silva, Alpha-expansions: A class of frame decompositions, Applied and Computational
Harmonic Analysis, vol.13, pp.103-115, 2002.
- M.Craizer, D.A.Fonini Jr. and E.A.B.da
Silva, Successive approximation for image compression, IEEE Circuits and Systems
Magazine, vol.2,n.3, 3rd quarter, 2002.
- M.Craizer, Evolution of critical
points in curvature and affine morphological scale spaces, IV International
Conference on Scale-Space theories in Computer Vision,
- M.Craizer and R.Teixeira, Evolution of an
extremum by curvature motion, Journal of Mathematical Analysis and Applications, 293,
p.721-737, 2004.
- M.Craizer, S.Pesco and R.Teixeira, A numerical
scheme for the curvature equation near the singularities, Journal of Mathematical
Imaging and Vision, 22, p.89-95, 2005.
- M.Craizer, T.Lewiner, J.D.G.Silva Jr, H.C.V.Lopes. Curvature and Torsion Estimators based on Parametric Curve Fitting, Computer & Graphics, 29, n.5, 2005.
- T.Lewiner,
M.Craizer, H.Lopes, S.Pesco,L.Velho, E.Medeiros, GEncode:
Geometry-driven compression for general meshes. Computer Graphics
Forum, 25, p.685-695, 2006.
- T.Lewiner, C.Ferreira, M.Craizer,
R.Teixeira, Curvature Motion for
- M.Craizer,
T.Lewiner, J.M.Morvan, Combining points and tangents into parabolic
polygons, Journal of Mathematical Imaging and Vision, 29, p.131-140,
2007.
- M.A.H.B. da Silva, R.C.Teixeira, S.Pesco, M.Craizer, A Fast Marching Method for the Area based Affine Distance, Journal of Mathematical Imaging and Vision, 22(1), p.89-95, 2008.
- M.Craizer, M.A.H.B. da Silva, R.C.Teixeira, Area Distances of Convex Plane Curves and Improper Affine Spheres, SIAM Journal on Mathematical Imaging, 1(3), p.209-227, 2008.
- T.Lewiner, M.Craizer, Projective splines and estimators for planar curves, Journal of Mathematical Imaging and Vision, 36(1), p.81-89, 2010.
- M.Craizer, H.Anciaux, T.Lewiner, Discrete affine minimal surfaces with indefinite metric, Differential Geometry and its Applications, 28, 158-169, 2010.
- M.Craizer,
T.Lewiner, R. Teixeira, Cauchy problems for discrete affine minimal
surfaces, to appear in Archivum Mathematicum, 2011.
- M.Craizer,
R.Teixeira, M.da Silva, A geometric representation of improper
indefinite affine spheres with singularities, 2011.
- M.Craizer, R.Teixeira, M.da Silva, Affine properties of convex equal-area polygons, 2011.
- M.Craizer, R.C.Teixeira, Some properties of the volume distance to hypersurfaces, 2012.
- M.Craizer, Singularities of Convex Improper Affine Maps, 2012.
- Books and Course Notes
- M.Craizer and G.Tavares, Cálculo Integral de Várias Variáveis EDPUC, 2002 (in portuguese).
- M.Craizer and G.Tavares, Equações de Evolução em Processamento de Imagens, CNMAC2001 (in portuguese).
- M.Craizer, Equações de Evolução em Processamento de Imagens, Sibgrapi2001 (in portuguese). Revista de Informática Teórica e Aplicada, volume 8, número 2, 2001.
e-mail: craizer@puc-rio.br