scholarly journals Matching Deformable Regions Using Local Histograms of Differential Invariants

2005 ◽  
pp. 251-258 ◽  
Author(s):  
Nicolás Pérez de la Blanca ◽  
José M. Fuertes ◽  
Manuel J. Lucena
Keyword(s):  
Differential Invariants

Differential invariants of immersions of manifolds with metric fields

2003 ◽  
Vol 51 (2-3) ◽  
pp. 307-313 ◽  
Author(s):  
Pavla Musilová ◽  
Demeter Krupka
Keyword(s):  
Differential Invariants

scholarly journals Computing differential invariants of hybrid systems as fixedpoints

2009 ◽  
Vol 35 (1) ◽  
pp. 98-120 ◽  
Author(s):  
André Platzer ◽  
Edmund M. Clarke
Keyword(s):  
Hybrid Systems ◽  
Differential Invariants

scholarly journals Detection of the homotopy type of an object using differential invariants of an approximating map

2019 ◽  
Vol 43 (4) ◽  
pp. 611-617
Author(s):  
S.V. Kurochkin
Keyword(s):  
Neural Network ◽  
Data Analysis ◽  
Homotopy Type ◽  
Morse Theory ◽  
Object Representation ◽  
Differential Invariants ◽  
Topological Data Analysis ◽  
Higher Dimension ◽  
Differential Topology ◽  
Open Questions

A method of topological data analysis is proposed that allows one to find out the homotopy type of the object under study. Unlike mature and widely used methods based on persistent homologies, our method is based on computing differential invariants of some map associated with an approximating map. Differential topology tools and the analogy with the main result in Morse theory are used. The approximating map can be constructed in the usual way using a neural network or otherwise. The method allows one to identify the homotopy type of an object in the plane because the number of circles in the homotopy equivalent object representation as a wedge is expressed through the degree of some map associated with the approximating map. The performance of the algorithm is illustrated by examples from the MNIST database and transforms thereof. Generalizations and open questions relating to a higher-dimension case are discussed.

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