From Frenet to Cartan: The Method of Moving Frames

2017 ◽  
Author(s):  
Jeanne Clelland
Keyword(s):  
Moving Frames ◽  
Method Of Moving Frames

scholarly journals Invariants of Surfaces in Three-Dimensional Affine Geometry

2021 ◽  
Author(s):  
Örn Arnaldsson ◽  
◽  
Francis Valiquette ◽  
Keyword(s):  
Three Dimensional ◽  
Affine Geometry ◽  
Differential Invariants ◽  
Moving Frames ◽  
Method Of Moving Frames

Using the method of moving frames we analyze the algebra of differential invariants for surfaces in three-dimensional affine geometry. For elliptic, hyperbolic, and parabolic points, we show that if the algebra of differential invariants is non-trivial, then it is generically generated by a single invariant.

scholarly journals Holomorphic curves in the complex quadric

1987 ◽  
Vol 35 (1) ◽  
pp. 125-148 ◽  
Author(s):  
Gary R. Jensen ◽  
Marco Rigoli ◽  
Kichoon Yang
Keyword(s):  
Holomorphic Curves ◽  
Local Theory ◽  
Moving Frames ◽  
Complex Quadric ◽  
Complex Hyperquadric ◽  
Method Of Moving Frames

A local theory of holomorphic curves in the complex hyperquadric is worked out using the method of moving frames. As a consequence a complete global characterization of totally isotropic curves is obtained.

Equi-affine differential invariants for invariant feature point detection

2019 ◽  
Vol 31 (2) ◽  
pp. 277-296
Author(s):  
STANLEY L. TUZNIK ◽  
PETER J. OLVER ◽  
ALLEN TANNENBAUM
Keyword(s):  
Feature Point ◽  
Image Feature ◽  
Differential Invariants ◽  
Feature Points ◽  
Affine Invariant ◽  
Moving Frames ◽  
Feature Detectors ◽  
Point Detection ◽  
Point Detector ◽  
Method Of Moving Frames

Image feature points are detected as pixels which locally maximise a detector function, two commonly used examples of which are the (Euclidean) image gradient and the Harris–Stephens corner detector. A major limitation of these feature detectors is that they are only Euclidean-invariant. In this work, we demonstrate the application of a 2D equi-affine-invariant image feature point detector based on differential invariants as derived through the equivariant method of moving frames. The fundamental equi-affine differential invariants for 3D image volumes are also computed.

Benenti's theorem and the method of moving frames

2001 ◽  
Vol 48 (1-2) ◽  
pp. 227-234
Author(s):  
Aaron T. Bruce ◽  
Raymond G. McLenaghan ◽  
Roman G. Smirnov
Keyword(s):  
Moving Frames ◽  
Method Of Moving Frames
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