Modeling Planar Shape Variation via Hamiltonian Flows of Curves
نویسندگان
چکیده
The application of the theory of deformable templates to the study of the action of a group of diffeomorphisms on deformable objects provides a powerful framework to compute dense one-to-one matchings on d-dimensional domains. In this paper, we derive the geodesic equations that govern the time evolution of an optimal matching in the case of the action on 2D curves with various driving matching terms, and provide a Hamiltonian formulation in which the initial momentum is represented by an L vector field on the boundary of the template.
منابع مشابه
Remarks on Kdv-type Flows on Star-shaped Curves
We study the relation between the centro-affine geometry of starshaped planar curves and the projective geometry of parametrized maps into RP. We show that projectivization induces a map between differential invariants and a bi-Poisson map between Hamiltonian structures. We also show that a Hamiltonian evolution equation for closed star-shaped planar curves, discovered by Pinkall, has the Schwa...
متن کاملMetamorphosis of Planar Parametric Curves Via Curvature Interpolation
This work considers the problem of metamorphosis interpolation between two freeform planar curves. Given two planar parametric curves, the curvature signature of the two curves is linearly blended, yielding a gradual change that is not only smooth but also employs intrinsic curvature shape properties, and hence is highly appealing. In order to be able to employ this curvature blending, we prese...
متن کاملModeling the Tensile Behavior of Fibers with Geometrical and Structural Irregularities
Virtually all fibers exhibit some dimensional and structural irregularities. These include the conventional textile fibers, the high-performance brittle fibers and even the newly developed nano-fibers. In recent years, we have systematically examined the effect of fiber dimensional irregularities on the mechanical behavior of the irregular fibers. This paper extends our research to include the ...
متن کاملBifurcation of limit cycles from a quadratic reversible center with the unbounded elliptic separatrix
The paper is concerned with the bifurcation of limit cycles in general quadratic perturbations of a quadratic reversible and non-Hamiltonian system, whose period annulus is bounded by an elliptic separatrix related to a singularity at infinity in the poincar'{e} disk. Attention goes to the number of limit cycles produced by the period annulus under perturbations. By using the appropriate Picard...
متن کاملModeling Flexibility Effects in Robotic Arms Via the Modified 4x4 D-H Homogeneous Transformation
This paper presents a method for the kinematical modeling of robot manipulator arms with flexible members. Development of such techniques are important for the improvement of robotic arms precision performance and their mechanical design. The approach employs the (4X4) Denavit-Hartenberg homogeneous transformations to describe the kinematics of light weight flexible manipulator arms. The method...
متن کامل