Reconstruction of surfaces with ordinary singularities from their silhouettes

We present algorithms for reconstructing, up to unavoidable projective automorphisms, surfaces with ordinary singularities in three dimensional space starting from their silhouette, or "apparent contour" - namely the branching locus of a projection on the plane - and the projection of their singular locus.

[1]  F. Zak.  Tangents and Secants of Algebraic Varieties , 1993 .

[2]  Federigo Enriques.  Sulla costruzione delle funzioni algebriche di due variabili possedenti una data curva di diramazione , 1924 .

[3]  Jean d’Almeida,et al.  Courbe de ramification de la projection sur $\mathbb{P}^2$ d’une surface de $\mathbb{P}^3$ , 1992 .

[4]  Martial Hebert,et al.  On Image Contours of Projective Shapes , 2014, ECCV.

[5]  Fredrik Kahl,et al.  Motion estimation in image sequences using the deformation of apparent contours , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[6]  David A. Forsyth,et al.  Recognizing algebraic surfaces from their outlines , 1993, Vision.

[7]  Jean Ponce,et al.  Invariant Properties of Straight Homogeneous Generalized Cylinders and Their Contours , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[8]  Marie-Odile Berger,et al.  3D Surface Reconstruction Using Occluding Contours , 2004, International Journal of Computer Vision.

[9]  Flaminio Flamini,et al.  On the branch curve of a general projection of a surface to a plane , 2008, 0811.0467.

[10]  O. Faugeras,et al.  The Geometry of Multiple Images , 1999 .

[11]  Стефан Юрьевич Немировский,et al.  К теореме Куликова о гипотезе Кизини@@@Kulikov's theorem on the Chisini conjecture , 2001 .

[12]  R. Nevatia,et al.  Quasi-invariant properties and 3-D shape recovery of non-straight, non-constant generalized cylinders , 1993, Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

[13]  C. Hoffmann.  Algebraic curves , 1988 .

[14]  Bernhard P. Wrobel,et al.  Multiple View Geometry in Computer Vision , 2001 .

[15]  Roberto Pignatelli,et al.  Chisini's conjecture for curves with singularities of type xn=ym , 2000 .

[16]  Robin Hartshorne,et al.  Algebraic geometry , 1977, Graduate texts in mathematics.

[17]  Oscar Zariski,et al.  On the Problem of Existence of Algebraic Functions of Two Variables Possessing a Given Branch Curve , 1929 .

[18]  Bernd Sturmfels,et al.  Changing Views on Curves and Surfaces , 2017, ArXiv.

[19]  Martial Hebert,et al.  Consistency of Silhouettes and Their Duals , 2016, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[20]  Oscar Chisini,et al.  Sulla caratterizzazione delle curve di diramazione dei piani tripli , 1946 .

[21]  Jean Ponce,et al.  Congruences and Concurrent Lines in Multi-View Geometry , 2016, Adv. Appl. Math..

[22]  Sergey Finashin,et al.  Apparent contours of nonsingular real cubic surfaces , 2013, 1306.2002.

[23]  Joe Kileel,et al.  Minimal Problems for the Calibrated Trifocal Variety , 2016, SIAM J. Appl. Algebra Geom..

[24]  Vik S Kulikov,et al.  On Chisini's conjecture , 1999 .

[25]  Fabrizio Catanese.  On a problem of Chisini , 1986 .

[26]  Bernd Sturmfels,et al.  Rigid multiview varieties , 2015, Int. J. Algebra Comput..

[27]  Nicolas Bourbaki,et al.  Elements of mathematics , 2004 .