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These invariants include the minimal number of generators, deficiency, Betti numbers over arbitrary fields, various spectral and representation theoretic invariants, graph polynomials and entropy.
In addition, finding loop invariants in software programs has historically been a challenging task requiring extensive training and insight.
Literature [7] adopted wavelet transform to extract rotation invariant texture features, but with this algorism, only approximate rotation invariant features could be obtained.
Invariant submanifolds of a contact manifold have been a major area of research for a long time since the concept was borrowed from complex geometry.
An interesing invariant of a concircular transformation is the concircular curvature tensor C.
Vilcu: On Chen invariants and inequalities in quaternionic geometry, J.
In [Borie and Thiery(2011)], the authors calculate the secondary invariants of the 61st transitive group over 14 variables whose cardinality is 50803200.
We would like to obtain a geometric invariant, which is both unique for isometric surfaces and allows using simple rigid surface matching to compare the invariants.
The method is implemented in the Aligator software tool and was further extended in (Henzinger et al, 2010) to also generate quantified loop invariants for programs over unbounded data structures, such as arrays.
Put differently: The underlying manifold of an algebraic variety does not determine these invariants," he added.
Chapters cover Cartesian products, more classical products such as Hamiltonian graphs, invariants, Algebra and other topics.
Moment invariants are well-known in literature and characterize properties of connected regions in binary images.