Elastica and computer vision
D Mumford - Algebraic Geometry and its Applications: Collections of …, 1994 - Springer
Algebraic Geometry and its Applications: Collections of Papers from Shreeram S …, 1994•Springer
I want to discuss the problem from differential geometry of describing those plane curves C
which minimize the integral ∫ (α k^ 2+ β) ds. Here α and β are constants, k is the curvature
of C, ds the arc length and, to make the fewest boundary conditions, we mean minimizing for
infinitesimal variations of C on a compact set not containing the endpoints of C. Alternately,
one may minimize ∫ k^ 2 ds over variations of C which preserve the total length.
which minimize the integral ∫ (α k^ 2+ β) ds. Here α and β are constants, k is the curvature
of C, ds the arc length and, to make the fewest boundary conditions, we mean minimizing for
infinitesimal variations of C on a compact set not containing the endpoints of C. Alternately,
one may minimize ∫ k^ 2 ds over variations of C which preserve the total length.
Abstract
I want to discuss the problem from differential geometry of describing those plane curves C which minimize the integral Here α and β are constants, kis the curvature of C, ds the arc length and, to make the fewest boundary conditions, we mean minimizing for infinitesimal variations of C on a compact set not containing the endpoints of C. Alternately, one may minimize over variations of C which preserve the total length.
Springer