Size homotopy groups for computation of natural size distances

For every manifold M endowed with a structure described by a function from M to the vector space R k , a parametric family of groups, called size homotopy groups, is introduced and studied. Some lower bounds for natural size distances are obtained in this way.

[1]  Mikhael Gromov.  Structures métriques pour les variétés riemanniennes , 1981 .

[2]  J. W. Bruce,et al.  Seeing—the mathematical viewpoint , 1984 .

[3]  D. Mumford,et al.  Optimal approximations by piecewise smooth functions and associated variational problems , 1989 .

[4]  P. Frosini,et al.  A distance for similarity classes of submanifolds of a Euclidean space , 1990, Bulletin of the Australian Mathematical Society.

[5]  Patrizio Frosini,et al.  Measuring shapes by size functions , 1992, Other Conferences.

[6]  Andrew Zisserman,et al.  Applications of Invariance in Computer Vision , 1993, Lecture Notes in Computer Science.

[7]  A. Bruckstein,et al.  Some mathematical problems in computer vision , 1993 .

[8]  Alessandro Verri,et al.  Studying Shape Through Size Functions , 1994 .

[9]  Massimo Ferri,et al.  Leukocyte classifications by size functions , 1994, Proceedings of 1994 IEEE Workshop on Applications of Computer Vision.

[10]  Alessandro Verri,et al.  On the recognition of the alphabet of the sign language through size functions , 1994, Proceedings of the 12th IAPR International Conference on Pattern Recognition, Vol. 3 - Conference C: Signal Processing (Cat. No.94CH3440-5).

[11]  P. Frosini,et al.  Connections between Size Functions and Critical Points , 1996 .

[12]  Alessandro Verri,et al.  Metric-topological approach to shape representation and recognition , 1996, Image Vis. Comput..