Displaying similar documents to “Robust affine invariant descriptors.”

Curvature functionals for curves in the equi-affine plane

Steven Verpoort (2011)

Czechoslovak Mathematical Journal

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After having given the general variational formula for the functionals indicated in the title, the critical points of the integral of the equi-affine curvature under area constraint and the critical points of the full-affine arc-length are studied in greater detail. Notice. An extended version of this article is available on arXiv:0912.4075.

Affine bijections of C(X,I)

Janko Marovt (2006)

Studia Mathematica

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Let 𝒳 be a compact Hausdorff space which satisfies the first axiom of countability, I = [0,1] and 𝓒(𝒳,I) the set of all continuous functions from 𝒳 to I. If φ: 𝓒(𝒳,I) → 𝓒(𝒳,I) is a bijective affine map then there exists a homeomorphism μ: 𝒳 → 𝒳 such that for every component C in 𝒳 we have either φ(f)(x) = f(μ(x)), f ∈ 𝓒(𝒳,I), x ∈ C, or φ(f)(x) = 1-f(μ(x)), f ∈ 𝓒(𝒳,I), x ∈ C.

An affine framework for analytical mechanics

Paweł Urbański (2003)

Banach Center Publications

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An affine Cartan calculus is developed. The concepts of special affine bundles and special affine duality are introduced. The canonical isomorphisms, fundamental for Lagrangian and Hamiltonian formulations of the dynamics in the affine setting are proved.

Self-affine fractals of finite type

Christoph Bandt, Mathias Mesing (2009)

Banach Center Publications

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In the class of self-affine sets on ℝⁿ we study a subclass for which the geometry is rather tractable. A type is a standardized position of two intersecting pieces. For a self-affine tiling, this can be identified with an edge or vertex type. We assume that the number of types is finite. We study the topology of such fractals and their boundary sets, and we show how new finite type fractals can be constructed. For finite type self-affine tiles in the plane we give an algorithm which...

Affinely invariant symmetry sets

Peter Giblin (2008)

Banach Center Publications

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The classical medial axis and symmetry set of a smooth simple plane curve M, depending as they do on circles bitangent to M, are invariant under euclidean transformations. This article surveys the various ways in which the construction has been adapted to be invariant under affine transformations. They include affine distance and area constructions, and also the 'centre symmetry set' which generalizes central symmetry. A connexion is also made with the tricentre set of a convex plane...